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Articles 1 - 18 of 18
Full-Text Articles in Mathematics
Commuting Self-Adjoint Extensions Of Symmetric Operators Defined From The Partial Derivatives, Palle Jorgensen, Steen Pedersen
Commuting Self-Adjoint Extensions Of Symmetric Operators Defined From The Partial Derivatives, Palle Jorgensen, Steen Pedersen
Mathematics and Statistics Faculty Publications
We consider the problem of finding commuting self-adjoint extensions of the partial derivatives {(1/i)(∂/∂xj):j=1,...,d} with domain C∞c(Ω) where the self-adjointness is defined relative to L2(Ω), and Ω is a given open subset of Rd.
The Expected Wet Period Of Finite Dam With Exponential Inputs, Eui Yong Lee, Kimberly Kinateder
The Expected Wet Period Of Finite Dam With Exponential Inputs, Eui Yong Lee, Kimberly Kinateder
Mathematics and Statistics Faculty Publications
We use martingale methods to obtain an explicit formula for the expected wet period of the finite dam of capacity V, where the amounts of inputs are i.i.d exponential random variables and the output rate is one, when the reservoir is not empty. As a consequence, we obtain an explicit formula for the expected hitting time of either 0 or V and a new expression for the distribution of the number of overflows during the wet period, both without the use of complex analysis.
A Nonlinear Parabolic Equation Modelling Surfactant Diffusion, Xinfu Chen, Chaocheng Huang, Jennifer Zhao
A Nonlinear Parabolic Equation Modelling Surfactant Diffusion, Xinfu Chen, Chaocheng Huang, Jennifer Zhao
Mathematics and Statistics Faculty Publications
An initial-boundary value problem for nonlinear parabolic equations modelling surfactant diffusions is investigated. The boundary conditions are of nonlinear adsorptive types, and the initial value has a single point jump. We study the well-posedness of the problem, the convergence of a numerical scheme, and the regularity as well as quantitative behaviour of solutions.
Openness Of Induced Projections, J. J. Charatonik, W. J. Charatonik, Alejandro Illanes
Openness Of Induced Projections, J. J. Charatonik, W. J. Charatonik, Alejandro Illanes
Mathematics and Statistics Faculty Research & Creative Works
For continua X and Y it is shown that if the projection f : X x Y ->X has its induced mapping C(f) open, then X is C*-smooth. As a corollary, a characterization of dendrites in these terms is obtained.
Some Applications Of The Ultrapower Theorem To The Theory Of Compacta, Paul Bankston
Some Applications Of The Ultrapower Theorem To The Theory Of Compacta, Paul Bankston
Mathematics, Statistics and Computer Science Faculty Research and Publications
The ultrapower theorem of Keisler and Shelah allows such model-theoretic notions as elementary equivalence, elementary embedding and existential embedding to be couched in the language of categories (limits, morphism diagrams). This in turn allows analogs of these (and related) notions to be transported into unusual settings, chiefly those of Banach spaces and of compacta. Our interest here is the enrichment of the theory of compacta, especially the theory of continua, brought about by the importation of model-theoretic ideas and techniques.
Cramer-Rao Bound And Optimal Amplitude Estimator Of Superimposed Sinusoidal Signals With Unknown Frequencies, Shaohui Jia
Cramer-Rao Bound And Optimal Amplitude Estimator Of Superimposed Sinusoidal Signals With Unknown Frequencies, Shaohui Jia
Doctoral Dissertations
This dissertation addresses optimally estimating the amplitudes of superimposed sinusoidal signals with unknown frequencies. The Cramer-Rao Bound of estimating the amplitudes in white Gaussian noise is given, and the maximum likelihood estimator of the amplitudes in this case is shown to be asymptotically efficient at high signal to noise ratio but finite sample size. Applying the theoretical results to signal resolutions, it is shown that the optimal resolution of multiple signals using a finite sample is given by the maximum likelihood estimator of the amplitudes of signals.
A Rational Solution To Cootie, Arthur T. Benjamin, Matthew T. Fluet '99
A Rational Solution To Cootie, Arthur T. Benjamin, Matthew T. Fluet '99
All HMC Faculty Publications and Research
No abstract provided in this article.
Dendrites And Light Open Mappings, J. J. Charatonik, W. J. Charatonik, Pawel Krupski
Dendrites And Light Open Mappings, J. J. Charatonik, W. J. Charatonik, Pawel Krupski
Mathematics and Statistics Faculty Research & Creative Works
It is shown that a metric continuum X is a dendrite if and only if for every compact space Y and for every light open mapping f : Y ->f(Y ) such that X c f(Y ) there is a copy X1 of X in Y for which the restriction fjX1 : X1 ->X is a homeomorphism. Another characterization of dendrites in terms of continuous selections of multivalued functions is also obtained.
Inverse Limits On [0,1] Using Piecewise Linear Unimodal Bonding Maps, William Thomas Ingram
Inverse Limits On [0,1] Using Piecewise Linear Unimodal Bonding Maps, William Thomas Ingram
Mathematics and Statistics Faculty Research & Creative Works
In this paper we investigate inverse limits on [0,1] using a single bonding map chosen from a two-parameter family of piecewise linear unimodal bonding maps. This investigation focuses on the parameter values at the boundary between a hereditarily decomposable inverse limit and an inverse limit containing an indecomposable continuum. © 1999 American Mathematical Society.
Remarks On The Prandtl Equation For A Permeable Wall, R. Temam, X. Wang
Remarks On The Prandtl Equation For A Permeable Wall, R. Temam, X. Wang
Mathematics and Statistics Faculty Research & Creative Works
The goal of this article is to study the boundary layer for a flow in a channel with permeable walls. Observing that the Prandtl equation can be solved almost exactly in this case, we are able to derive rigorously a number of results concerning the boundary layer and the convergence of the Navier-Stokes equations to the Euler equations. We indicate also how to derive higher order terms in the inner and outer expansions with respect to the kinematic viscosity v.
Wonderful Blowups Associated To Group Actions, Lev A. Borisov, Paul Gunnells
Wonderful Blowups Associated To Group Actions, Lev A. Borisov, Paul Gunnells
Paul Gunnells
A group action on a smooth variety provides it with the natural stratification by irreducible components of the fixed point sets of arbitrary sub-groups. We show that the corresponding maximal wonderful blowup in the sense of MacPherson-Procesi has only abelian stabilizers. The result is inspired by the abelianization algorithm of Batyrev.
Triunduloids: Embedded Constant Mean Curvature Surfaces With Three Ends And Genus Zero, Karsten Grosse-Brauckmann, Robert Kusner, John M. Sullivan
Triunduloids: Embedded Constant Mean Curvature Surfaces With Three Ends And Genus Zero, Karsten Grosse-Brauckmann, Robert Kusner, John M. Sullivan
Robert Kusner
We announce the classification of complete almost embedded surfaces of constant mean curvature, with three ends and genus zero. They are classified by triples of points on the sphere whose distances are the asymptotic necksizes of the three ends.
Separation Property Of Solutions For A Semilinear Elliptic Equation, Yi Liu, Yi Li, Yinbin Deng
Separation Property Of Solutions For A Semilinear Elliptic Equation, Yi Liu, Yi Li, Yinbin Deng
Yi Li
In this paper, we study the following elliptic problem[formula]where K(x) is a given function in Cα(n\0) for some fixed α∈(0, 1), p>1 is a constant. Some existence, monotonicity and asymptotic expansion at infinity of solutions of (*) are discussed.
Nonparametric Bayes Estimation Of Contamination Levels Using Observations From The Residual Distribution, Paul H. Kvam, Ram C. Tiwari, Jyoti N. Zalkikar
Nonparametric Bayes Estimation Of Contamination Levels Using Observations From The Residual Distribution, Paul H. Kvam, Ram C. Tiwari, Jyoti N. Zalkikar
Department of Math & Statistics Faculty Publications
A nonparametric Bayes estimator of the survival function is derived for right censored data where additional observations from the residual distribution are available. The estimation is motivated by data on contamination concentrations for chromium from one of the EPA's toxic waste sites. The residual sample can be produced by hot spot sampling, where only samples above a given threshold value are collected. The Dirichlet process is used to formulate prior information about the chromium contamination, and we compare the Bayes estimator of the mean concentration level to other estimators currently considered by the EPA and other sources. The Bayes estimator …
Separation Property Of Solutions For A Semilinear Elliptic Equation, Yi Liu, Yi Li, Yinbin Deng
Separation Property Of Solutions For A Semilinear Elliptic Equation, Yi Liu, Yi Li, Yinbin Deng
Mathematics and Statistics Faculty Publications
In this paper, we study the following elliptic problem[formula]where K(x) is a given function in Cα(n\0) for some fixed α∈(0, 1), p>1 is a constant. Some existence, monotonicity and asymptotic expansion at infinity of solutions of (*) are discussed.
A Leveque-Type Lower Bound For Discrepancy, Francis E. Su
A Leveque-Type Lower Bound For Discrepancy, Francis E. Su
All HMC Faculty Publications and Research
A sharp lower bound for discrepancy on R / Z is derived that resembles the upper bound due to LeVeque. An analogous bound is proved for discrepancy on Rk / Zk. These are discussed in the more general context of the discrepancy of probablity measures. As applications, the bounds are applied to Kronecker sequences and to a random walk on the torus.
Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn
Oif Spaces, Zoltan Balogh, Harold Bennett, Dennis Burke, Gary Gruenhage, David Lutzer, Joe D. Mashburn
Mathematics Faculty Publications
A base β of a space X is called an OIF base when every element of B is a subset of only a finite number of other elements of β. We will explore the fundamental properties of spaces having such bases. In particular, we will show that in T2 spaces, strong OIF bases are the same as uniform bases, and that in T3 spaces where all subspaces have OIF bases, compactness, countable compactness, or local compactness will give metrizability.
Incentives To Settle Under Joint And Several Liability: An Empirical Analysis Of Superfund Litigation, Howard F. Chang, Hilary Sigman
Incentives To Settle Under Joint And Several Liability: An Empirical Analysis Of Superfund Litigation, Howard F. Chang, Hilary Sigman
All Faculty Scholarship
Congress may soon restrict joint and several liability for cleanup of contaminated sites under Superfund. We explore whether this change would discourage settlements and is therefore likely to increase the program 's already high litigation costs per site. Recent theoretical research by Kornhauser and Revesz finds that joint and several liability may either encourage or discourage settlement, depending on the correlation of outcomes at trial across defendants. We extend their two-defendant model to a richer framework with N defendants. This extension allows us to test the theoretical model empirically using data on Superfund litigation. We find that joint and several …