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1999

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Articles 1 - 30 of 278

Full-Text Articles in Mathematics

Noncommutative Computer Algebra In The Control Of Singularly Perturbed Dynamical Systems, J. W. Helton, F. Dell Kronewitter, Mark Stankus Dec 1999

Noncommutative Computer Algebra In The Control Of Singularly Perturbed Dynamical Systems, J. W. Helton, F. Dell Kronewitter, Mark Stankus

Mathematics

Most algebraic calculations which one sees in linear systems theory, for example in IEEE TAC, involve block matrices and so are highly noncommutative. Thus conventional commutative computer algebra packages, as in Mathematica and Maple, do not address them. Here we investigate the usefulness of noncommutative computer algebra in a particular area of control theory-singularly perturbed dynamic systems-where working with the noncommutative polynomials involved is especially tedious. Our conclusion is that they have considerable potential for helping practitioners with such computations. For example, the methods introduced here take the most standard textbook singular perturbation calculation, [KK086], one step further than had …

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Grundlagenreflexionen Zur Thematik Anthropomorpher Schnittstellen, Rudolf Kaehr Dec 1999

Grundlagenreflexionen Zur Thematik Anthropomorpher Schnittstellen, Rudolf Kaehr

Rudolf Kaehr

Report for the EMBASSI Project

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Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing Dec 1999

Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing

Yi Li

Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …

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Anneli Lax: In Memoriam, Elena Anne Corie Marchisotto Dec 1999

Anneli Lax: In Memoriam, Elena Anne Corie Marchisotto

Humanistic Mathematics Network Journal

No abstract provided.

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Teaching A Humanities Course: A Mathematician’S View, Bill Marion Dec 1999

Teaching A Humanities Course: A Mathematician’S View, Bill Marion

Humanistic Mathematics Network Journal

No abstract provided.

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Word Problems, Don Pfaff Dec 1999

Word Problems, Don Pfaff

Humanistic Mathematics Network Journal

No abstract provided.

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A Response To Dancis, Margaret Schaffer Dec 1999

A Response To Dancis, Margaret Schaffer

Humanistic Mathematics Network Journal

No abstract provided.

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Another Response To Dancis, Ted Eisenberg Dec 1999

Another Response To Dancis, Ted Eisenberg

Humanistic Mathematics Network Journal

No abstract provided.

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Evaluation In The Mathematics Classroom, Emam Hoosain, B. Naraine Dec 1999

Evaluation In The Mathematics Classroom, Emam Hoosain, B. Naraine

Humanistic Mathematics Network Journal

No abstract provided.

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What Is The Thing Called “Humanistic Mathematics?”, Tamar Apel Dec 1999

What Is The Thing Called “Humanistic Mathematics?”, Tamar Apel

Humanistic Mathematics Network Journal

No abstract provided.

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Mathematics Is An Art: The Story Of A One-Time Course, Paul Fjelstad Dec 1999

Mathematics Is An Art: The Story Of A One-Time Course, Paul Fjelstad

Humanistic Mathematics Network Journal

No abstract provided.

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A Reflection On The Word: Remembering The Word “Word” Is Reflexive, Paul Fjelstad, Ivan Ginchev Dec 1999

A Reflection On The Word: Remembering The Word “Word” Is Reflexive, Paul Fjelstad, Ivan Ginchev

Humanistic Mathematics Network Journal

No abstract provided.

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Calculus For The Liberal Arts: A Humanistic Approach, Kathleen Shannon Dec 1999

Calculus For The Liberal Arts: A Humanistic Approach, Kathleen Shannon

Humanistic Mathematics Network Journal

No abstract provided.

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Ode To Mathematics, Sandra Z. Keith Dec 1999

Ode To Mathematics, Sandra Z. Keith

Humanistic Mathematics Network Journal

No abstract provided.

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Excerpts From Ivan’S Commandments To Himself, Ivan Niven Dec 1999

Excerpts From Ivan’S Commandments To Himself, Ivan Niven

Humanistic Mathematics Network Journal

No abstract provided.

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Divisibility: A Problem Solving Approach Through Generalizing And Specializing, Rina Zazkis Dec 1999

Divisibility: A Problem Solving Approach Through Generalizing And Specializing, Rina Zazkis

Humanistic Mathematics Network Journal

No abstract provided.

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The Role Of Values In Mathematics Education, Murad Jurdak Dec 1999

The Role Of Values In Mathematics Education, Murad Jurdak

Humanistic Mathematics Network Journal

No abstract provided.

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Book Review: A Tour Of The Calculus By David Berlinski, Bernard Fleishman Dec 1999

Book Review: A Tour Of The Calculus By David Berlinski, Bernard Fleishman

Humanistic Mathematics Network Journal

No abstract provided.

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Book Review: Mathematical Reflections By Peter Hilton, Derek Holton And Jean Pedersen, Ladnor Geissinger Dec 1999

Book Review: Mathematical Reflections By Peter Hilton, Derek Holton And Jean Pedersen, Ladnor Geissinger

Humanistic Mathematics Network Journal

No abstract provided.

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Roots, Don Pfaff Dec 1999

Roots, Don Pfaff

Humanistic Mathematics Network Journal

No abstract provided.

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Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing Dec 1999

Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing

Mathematics and Statistics Faculty Publications

Pertussis (whooping cough) incidence in the United States has oscillated with a period of about four years since data was first collected in 1922. An infection with pertussis confers immunity for several years, but then the immunity wanes, so that reinfection is possible. A pertussis reinfection is mild after partial loss of immunity, but the reinfection can be severe after complete loss of immunity. Three pertussis transmission models with waning of immunity are examined for periodic solutions. Equilibria and their stability are determined. Hopf bifurcation of periodic solutions around the endemic equilibrium can occur for some parameter values in two …

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Self-Consistency Algorithms, Thaddeus Tarpey Dec 1999

Self-Consistency Algorithms, Thaddeus Tarpey

Mathematics and Statistics Faculty Publications

The k-means algorithm and the principal curve algorithm are special cases of a self-consistency algorithm. A general self-consistency algorithm is described and results are provided describing the behavior of the algorithm for theoretical distributions, in particular elliptical distributions. The results are used to contrast the behavior of the algorithms when applied to a theoretical model and when applied to finite datasets from the model. The algorithm is also used to determine principal loops for the bivariate normal distribution.

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A Hierarchy Of Maps Between Compacta, Paul Bankston Dec 1999

A Hierarchy Of Maps Between Compacta, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

Let CH be the class of compacta (i.e., compact Hausdorff spaces), with BS the subclass of Boolean spaces. For each ordinal α and pair $\langle K,L\rangle$ of subclasses of CH, we define Lev≥α K,L), the class of maps of level at least α from spaces in K to spaces in L, in such a way that, for finite α, Lev≥α (BS,BS) consists of the Stone duals of Boolean lattice embeddings that preserve all prenex first-order formulas of quantifier rank α. Maps of level ≥ 0 are just the continuous surjections, and the maps of level ≥ 1 are …

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The Weyr Characteristic, Helene Shapiro Dec 1999

The Weyr Characteristic, Helene Shapiro

Mathematics & Statistics Faculty Works

No abstract provided.

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Rental Harmony: Sperner's Lemma In Fair Division, Francis E. Su Dec 1999

Rental Harmony: Sperner's Lemma In Fair Division, Francis E. Su

All HMC Faculty Publications and Research

No abstract provided in this article.

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Computational Geometry Column 36, Joseph O'Rourke Dec 1999

Computational Geometry Column 36, Joseph O'Rourke

Computer Science: Faculty Publications

Two results in "computational origami" are illustrated.

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What Else Do We Forget To Tell Our Teachers?: A Response To Dancis, Stephen Sproule Nov 1999

What Else Do We Forget To Tell Our Teachers?: A Response To Dancis, Stephen Sproule

Humanistic Mathematics Network Journal

No abstract provided.

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Interior-Point Methods And Modern Optimization Codes, Goran Lesaja Nov 1999

Interior-Point Methods And Modern Optimization Codes, Goran Lesaja

Department of Mathematical Sciences Faculty Publications

During the last fifteen years we have witnessed an explosive development in the area of optimization theory due to the introduction and development of interior-point methods. This development has quickly led to the development of new and more efficient optimization codes. In this paper, the basic elements of interior-point methods for linear programming will be discussed as well as extensions to convex programming, complementary problems, and semidefinite programming. Interior-point methods are polynomial and effective algorithms based on Newton 's method. Since they have been introduced, the classical distinction between linear programming methods, based on the simplex algorithm, and those methods …

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Pushpush Is Np-Hard In 3d, Joseph O'Rourke, The Smith Problem Solving Group Nov 1999

Pushpush Is Np-Hard In 3d, Joseph O'Rourke, The Smith Problem Solving Group

Computer Science: Faculty Publications

We prove that a particular pushing-blocks puzzle is intractable in 3D. The puzzle, inspired by the game PushPush, consists of unit square blocks on an integer lattice. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover, each block, when pushed, slides the maximal extent of its free range. We prove this version is NP-hard in 3D by reduction from SAT. The corresponding problem in 2D remains open.

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A Construction Of Orthogonal Compactly-Supported Multiwavelets On $\R^{2}$, Bruce Kessler Nov 1999

A Construction Of Orthogonal Compactly-Supported Multiwavelets On $\R^{2}$, Bruce Kessler

Mathematics Faculty Publications

This paper will provide the general construction of the continuous, orthogonal, compactly-supported multiwavelets associated with a class of continuous, orthogonal, compactly-supported scaling functions that contain piecewise linears on a uniform triangulation of $\R^2$. This class of scaling functions is a generalization of a set of scaling functions first constructed by Donovan, Geronimo, and Hardin. A specific set of scaling functions and associated multiwavelets with symmetry properties will be constructed.

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