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Full-Text Articles in Mathematics

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 …


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 …


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.


Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li Nov 1999

Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

For very general two-point boundary value problems we show that any positive solution satisfies a certain integral relation. As a consequence we obtain some new uniqueness and multiplicity results.


Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li Nov 1999

Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li

Yi Li

For very general two-point boundary value problems we show that any positive solution satisfies a certain integral relation. As a consequence we obtain some new uniqueness and multiplicity results.


Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li Oct 1999

Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li

Yi Li

Image resolution is the primary parameter for performance characterization of any imaging system. In this work, we present an axiomatic approach for quantification of image resolution, and demonstrate that a good image resolution measure should be proportional to the standard deviation of the point spread function of an imaging system.


Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li Oct 1999

Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li

Mathematics and Statistics Faculty Publications

Image resolution is the primary parameter for performance characterization of any imaging system. In this work, we present an axiomatic approach for quantification of image resolution, and demonstrate that a good image resolution measure should be proportional to the standard deviation of the point spread function of an imaging system.


Random Fluctuations Of Convex Domains And Lattice Points, Alex Iosevich, Kimberly Kinateder Oct 1999

Random Fluctuations Of Convex Domains And Lattice Points, Alex Iosevich, Kimberly Kinateder

Mathematics and Statistics Faculty Publications

In this paper, we examine a random version of the lattice point problem.


Variational Principles For Average Exit Time Moments For Diffusions In Euclidean Space, Kimberly Kinateder, Patrick Mcdonald Sep 1999

Variational Principles For Average Exit Time Moments For Diffusions In Euclidean Space, Kimberly Kinateder, Patrick Mcdonald

Mathematics and Statistics Faculty Publications

Let D be a smoothly bounded domain in Euclidean space and let Xt be a diffusion in Euclidean space. For a class of diffusions, we develop variational principles which characterize the average of the moments of the exit time from D of a particle driven by Xt, where the average is taken overall starting points in D.


Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li Aug 1999

Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li

Yi Li

No abstract provided.


Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li Aug 1999

Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li

Mathematics and Statistics Faculty Publications

No abstract provided.


Why The Player Never Wins In The Long Run At La Blackjack, Arthur T. Benjamin, Michael Lauzon '00, Christopher Moore '00 Jul 1999

Why The Player Never Wins In The Long Run At La Blackjack, Arthur T. Benjamin, Michael Lauzon '00, Christopher Moore '00

All HMC Faculty Publications and Research

No abstract provided in this article.


Anticommuting Derivations, Steen Pedersen Apr 1999

Anticommuting Derivations, Steen Pedersen

Mathematics and Statistics Faculty Publications

We show that the re are no non-trivial closable derivations of a C*-algebra anticommuting with an ergodic action of a compact group, supposing that the set of squares is dense in the group. We also show that the re are no non-trivial closable densely defined rank one derivations on any C*-algebra.


Bayes Estimation Of A Distribution Function Using Ranked Set Samples, Paul H. Kvam, Ram C. Tiwari Jan 1999

Bayes Estimation Of A Distribution Function Using Ranked Set Samples, Paul H. Kvam, Ram C. Tiwari

Department of Math & Statistics Faculty Publications

Aranked set sample (RSS), if not balanced, is simply a sample of independent order statistics generated from the same underlying distribution F. Kvam and Samaniego (1994) derived maximum likelihood estimates of F for a general RSS. In many applications, including some in the environmental sciences, prior information about F is available to supplement the data-based inference. In such cases, Bayes estimators should be considered for improved estimation. Bayes estimation (using the squared error loss function) of the unknown distribution function F is investigated with such samples. Additionally, the Bayes generalized maximum likelihood estimator (GMLE) is derived. An iterative scheme based …


Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh Jan 1999

Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh

Department of Math & Statistics Faculty Publications

Standard inference procedures assume a random sample from a population with density fμ(x) for estimating the parameter μ. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) ¸ 0, and constructed a weighted distribution with a density fμw(x) that is proportional to w(x)fμ(x). In this paper, we assume that fμ(x) belongs to an exponential family, and study the Fisher information about μ in observations obtained from some commonly arising weighted distributions: (i) the kth order …


A Quantile‐Based Approach For Relative Efficiency Measurement, Paul M. Griffin, Paul H. Kvam Jan 1999

A Quantile‐Based Approach For Relative Efficiency Measurement, Paul M. Griffin, Paul H. Kvam

Department of Math & Statistics Faculty Publications

Two popular approaches for efficiency measurement are a non‐stochastic approach called data envelopment analysis (DEA) and a parametric approach called stochastic frontier analysis (SFA). Both approaches have modeling difficulty, particularly for ranking firm efficiencies. In this paper, a new parametric approach using quantile statistics is developed. The quantile statistic relies less on the stochastic model than SFA methods, and accounts for a firm's relationship to the other firms in the study by acknowledging the firm's influence on the empirical model, and its relationship, in terms of similarity of input levels, to the other firms.


Stability Of A Semilinear Cauchy Problem, Yi Liu, Yi Li, Yinbin Deng Jan 1999

Stability Of A Semilinear Cauchy Problem, Yi Liu, Yi Li, Yinbin Deng

Mathematics and Statistics Faculty Publications

A report of progress in linear and nonlinear partial differential equations, microlocal analysis, singular partial differential operators, spectral analysis and hyperfunction theory. The papers aretaken from a conference on partial differential equations and their applications, held in Wuhan.


On The Exactness Of An S-Shaped Bifurcation Curve, Philip Korman, Yi Li Jan 1999

On The Exactness Of An S-Shaped Bifurcation Curve, Philip Korman, Yi Li

Mathematics and Statistics Faculty Publications

For a class of two-point boundary value problems we prove exactness of an S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like for .