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Articles 1 - 30 of 284
Full-Text Articles in Entire DC Network
Noncommutative Computer Algebra In The Control Of Singularly Perturbed Dynamical Systems, J. W. Helton, F. Dell Kronewitter, Mark Stankus
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 …
Grundlagenreflexionen Zur Thematik Anthropomorpher Schnittstellen, Rudolf Kaehr
Grundlagenreflexionen Zur Thematik Anthropomorpher Schnittstellen, Rudolf Kaehr
Rudolf Kaehr
Report for the EMBASSI Project
Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing
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 …
Anneli Lax: In Memoriam, Elena Anne Corie Marchisotto
Anneli Lax: In Memoriam, Elena Anne Corie Marchisotto
Humanistic Mathematics Network Journal
No abstract provided.
Teaching A Humanities Course: A Mathematician’S View, Bill Marion
Teaching A Humanities Course: A Mathematician’S View, Bill Marion
Humanistic Mathematics Network Journal
No abstract provided.
Word Problems, Don Pfaff
A Response To Dancis, Margaret Schaffer
A Response To Dancis, Margaret Schaffer
Humanistic Mathematics Network Journal
No abstract provided.
Another Response To Dancis, Ted Eisenberg
Another Response To Dancis, Ted Eisenberg
Humanistic Mathematics Network Journal
No abstract provided.
Evaluation In The Mathematics Classroom, Emam Hoosain, B. Naraine
Evaluation In The Mathematics Classroom, Emam Hoosain, B. Naraine
Humanistic Mathematics Network Journal
No abstract provided.
What Is The Thing Called “Humanistic Mathematics?”, Tamar Apel
What Is The Thing Called “Humanistic Mathematics?”, Tamar Apel
Humanistic Mathematics Network Journal
No abstract provided.
Mathematics Is An Art: The Story Of A One-Time Course, Paul Fjelstad
Mathematics Is An Art: The Story Of A One-Time Course, Paul Fjelstad
Humanistic Mathematics Network Journal
No abstract provided.
A Reflection On The Word: Remembering The Word “Word” Is Reflexive, Paul Fjelstad, Ivan Ginchev
A Reflection On The Word: Remembering The Word “Word” Is Reflexive, Paul Fjelstad, Ivan Ginchev
Humanistic Mathematics Network Journal
No abstract provided.
Calculus For The Liberal Arts: A Humanistic Approach, Kathleen Shannon
Calculus For The Liberal Arts: A Humanistic Approach, Kathleen Shannon
Humanistic Mathematics Network Journal
No abstract provided.
Ode To Mathematics, Sandra Z. Keith
Ode To Mathematics, Sandra Z. Keith
Humanistic Mathematics Network Journal
No abstract provided.
Excerpts From Ivan’S Commandments To Himself, Ivan Niven
Excerpts From Ivan’S Commandments To Himself, Ivan Niven
Humanistic Mathematics Network Journal
No abstract provided.
Divisibility: A Problem Solving Approach Through Generalizing And Specializing, Rina Zazkis
Divisibility: A Problem Solving Approach Through Generalizing And Specializing, Rina Zazkis
Humanistic Mathematics Network Journal
No abstract provided.
The Role Of Values In Mathematics Education, Murad Jurdak
The Role Of Values In Mathematics Education, Murad Jurdak
Humanistic Mathematics Network Journal
No abstract provided.
Book Review: A Tour Of The Calculus By David Berlinski, Bernard Fleishman
Book Review: A Tour Of The Calculus By David Berlinski, Bernard Fleishman
Humanistic Mathematics Network Journal
No abstract provided.
Book Review: Mathematical Reflections By Peter Hilton, Derek Holton And Jean Pedersen, Ladnor Geissinger
Book Review: Mathematical Reflections By Peter Hilton, Derek Holton And Jean Pedersen, Ladnor Geissinger
Humanistic Mathematics Network Journal
No abstract provided.
Roots, Don Pfaff
Hopf Bifurcation In Models For Pertussis Epidemiology, Herbert W. Hethcote, Yi Li, Zhujun Jing
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 …
Self-Consistency Algorithms, Thaddeus Tarpey
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.
The Weyr Characteristic, Helene Shapiro
The Weyr Characteristic, Helene Shapiro
Mathematics & Statistics Faculty Works
No abstract provided.
Rental Harmony: Sperner's Lemma In Fair Division, Francis E. Su
Rental Harmony: Sperner's Lemma In Fair Division, Francis E. Su
All HMC Faculty Publications and Research
No abstract provided in this article.
Computational Geometry Column 36, Joseph O'Rourke
Computational Geometry Column 36, Joseph O'Rourke
Computer Science: Faculty Publications
Two results in "computational origami" are illustrated.
A Hierarchy Of Maps Between Compacta, Paul Bankston
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 …
What Else Do We Forget To Tell Our Teachers?: A Response To Dancis, Stephen Sproule
What Else Do We Forget To Tell Our Teachers?: A Response To Dancis, Stephen Sproule
Humanistic Mathematics Network Journal
No abstract provided.
Interior-Point Methods And Modern Optimization Codes, Goran Lesaja
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 …
Pushpush Is Np-Hard In 3d, Joseph O'Rourke, The Smith Problem Solving Group
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.
A Construction Of Orthogonal Compactly-Supported Multiwavelets On $\R^{2}$, Bruce Kessler
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.