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Articles 361 - 390 of 418
Full-Text Articles in Mathematics
Hypersurfaces In R-D And The Variance Of Exit Times For Brownian Motion, Kimberly Kinateder, Patrick Mcdonald
Hypersurfaces In R-D And The Variance Of Exit Times For Brownian Motion, Kimberly Kinateder, Patrick Mcdonald
Mathematics and Statistics Faculty Publications
Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.
Travelling Fronts In Cylinders And Their Stability, Jerrold W. Bebernes, Comgming Li, Yi Li
Travelling Fronts In Cylinders And Their Stability, Jerrold W. Bebernes, Comgming Li, Yi Li
Mathematics and Statistics Faculty Publications
No abstract provided.
Eigenfunction And Harmonic Function Estimates In Domains With Horns And Cusps, Michael Cranston, Yi Li
Eigenfunction And Harmonic Function Estimates In Domains With Horns And Cusps, Michael Cranston, Yi Li
Mathematics and Statistics Faculty Publications
No abstract provided.
Existence And Bifurcation Of The Positive Solutions For A Semilinear Equation With Critical Exponent, Yinbin Deng, Yi Li
Existence And Bifurcation Of The Positive Solutions For A Semilinear Equation With Critical Exponent, Yinbin Deng, Yi Li
Mathematics and Statistics Faculty Publications
In this paper, we consider the semilinear elliptic equation[formula]Forp=2N/(N−2), we show that there exists a positive constantμ*>0 such that (∗)μpossesses at least one solution ifμ∈(0, μ*) and no solutions ifμ>μ*. Furthermore, (∗)μpossesses a unique solution whenμ=μ*, and at least two solutions whenμ∈(0, μ*) and 2<NN⩾6, under some monotonicity conditions onf((1.6)) we show that there exist two constants 0<μ**⩽μ**<μ* such that problem (∗)μ …
Self-Consistency: A Fundamental Concept In Statistics, Thaddeus Tarpey, Bernard Flury
Self-Consistency: A Fundamental Concept In Statistics, Thaddeus Tarpey, Bernard Flury
Mathematics and Statistics Faculty Publications
The term ''self-consistency'' was introduced in 1989 by Hastie and Stuetzle to describe the property that each point on a smooth curve or surface is the mean of all points that project orthogonally onto it. We generalize this concept to self-consistent random vectors: a random vector Y is self-consistent for X if E[X|Y] = Y almost surely. This allows us to construct a unified theoretical basis for principal components, principal curves and surfaces, principal points, principal variables, principal modes of variation and other statistical methods. We provide some general results on self-consistent random variables, give …
Bounds On Squares Of Two-Sets, Daniel Slilaty, Jeffrey Vanderkam
Bounds On Squares Of Two-Sets, Daniel Slilaty, Jeffrey Vanderkam
Mathematics and Statistics Faculty Publications
Let G be a finite group and let pi(G) denote the proportion of (x, y) ∈ G2 for which the set {x2,xy,yx,y2} has cardinality i. We show that either 0 < pi(G) + p2(G) ≤ 1/2 or pi(G) + p2(G) = 1, and that either p4(G) = 0 or 5/32 ≤ p4(G) ≤ 1. Each of the preceding inequalities are the best possible.
Asymptotic Conservation Laws In Classical Field Theory, Ian M. Anderson, Charles G. Torre
Asymptotic Conservation Laws In Classical Field Theory, Ian M. Anderson, Charles G. Torre
Mathematics and Statistics Faculty Publications
A new, general, field theoretic approach to the derivation of asymptotic conservation laws is presented. In this approach asymptotic conservation laws are constructed directly from the field equations according to a universal prescription which does not rely upon the existence of Noether identities or any Lagrangian or Hamiltonian formalisms. The resulting general expressions of the conservation laws enjoy important invariance properties and synthesize all known asymptotic conservation laws, such as the Arnowitt-Deser-Misner energy in general relativity.
A Center-Unstable Manifold Theorem For Parametrically Excited Surface Waves, Larry Turyn
A Center-Unstable Manifold Theorem For Parametrically Excited Surface Waves, Larry Turyn
Mathematics and Statistics Faculty Publications
When fluid in a rectangular tank sits upon a platform which is oscillating with sufficient amplitude, surface waves appear in the ''Faraday resonance.'' Scientists and engineers have done bifurcation analyses which assume that there is a center manifold theory using a finite number of excited spatial modes. We establish such a center manifold theorem for Xiao-Biao Lin's model in which potential flow is assumed but an artificial dissipation term is included in the system of partial differential equations on the free surface. We use interpolation spaces developed by da Prate and Grisvard, establish maximal regularity for a family of evolution …
Exact Multiplicity Results For Boundary Value Problems With Nonlinearities Generalizing Cubic, Philip Korman, Yi Li, Tiancheng Ouyang
Exact Multiplicity Results For Boundary Value Problems With Nonlinearities Generalizing Cubic, Philip Korman, Yi Li, Tiancheng Ouyang
Mathematics and Statistics Faculty Publications
No abstract provided.
The Support Of Measure-Valued Branching Processes In A Random Environment, Donald A. Dawson, Yi Li, Carl Mueller
The Support Of Measure-Valued Branching Processes In A Random Environment, Donald A. Dawson, Yi Li, Carl Mueller
Mathematics and Statistics Faculty Publications
We consider the one-dimensional catalytic branching process introduced by Dawson and Fleischmann, which is a modification of the super Brownian motion. The catalysts are given by a nonnegative infinitely divisible random measure with independent increments. We give sufficient conditions for the global support of the process to be compact, and sufficient conditions for noncompact global support. Since the catalytic process is related to the heat equation, compact support may be surprising. On the other hand, the super-Brownian motion has compact global support. We find that all nonnegative stable random measures lead to compact global support, and we give an example …
Free-Boundary Problems For Potential And Stokes Flows Via Nonsmooth Analysis, Srdjan Stojanovic, Tom Svobodny
Free-Boundary Problems For Potential And Stokes Flows Via Nonsmooth Analysis, Srdjan Stojanovic, Tom Svobodny
Mathematics and Statistics Faculty Publications
A new approach to some free boundary problems of the type of jets and cavities for potential flows is introduced. Both potential and Stokes flows are considered. The variable domain problems are relaxed so that they become nonsmooth optimization problems on fixed domains for somewhat singular state equations. State equations are considered, and multivalued generalized gradients of the variational functionals are studied. The method is constructive.
Principal Points And Self-Consistent Points Of Elliptical Distributions, Thaddeus Tarpey, Luning Li, Bernard Flury
Principal Points And Self-Consistent Points Of Elliptical Distributions, Thaddeus Tarpey, Luning Li, Bernard Flury
Mathematics and Statistics Faculty Publications
In this paper we study principal points and self-consistent points of p-variate elliptical distributions. We also discuss implications of our results for the computation and estimation of principal points.
Singularity Of Super-Brownian Local Time At A Point Catalyst, Donald A. Dawson, Klaus Fleischmann, Yi Li, Carl Mueller
Singularity Of Super-Brownian Local Time At A Point Catalyst, Donald A. Dawson, Klaus Fleischmann, Yi Li, Carl Mueller
Mathematics and Statistics Faculty Publications
No abstract provided.
Reconstruction Of Semiconductor Doping Profile From Lbic Image, Weifu Fang, Kazufumi Ito
Reconstruction Of Semiconductor Doping Profile From Lbic Image, Weifu Fang, Kazufumi Ito
Mathematics and Statistics Faculty Publications
In this paper, the authors study the reconstruction of a semiconductor doping profile or, equivalently, the equilibrium potential, from its LBIC (laser-beam-induced current) image. For the one-dimensional case, the authors first characterize the attainable class of current measurements, and from this they show the nonuniqueness of the inverse problem. Then the reconstruction of the equilibrium potential is reduced to finding two constants subject to some constraints. A reconstruction algorithm is established based on a least squares formulation of the problem. The case of noise-collapsed data is also discussed. For a special case of two-dimensional domain, the authors apply the one-dimensional …
Evolving Plane Curves By Curvature In Relative Geometries Ii, Michael E. Gage, Yi Li
Evolving Plane Curves By Curvature In Relative Geometries Ii, Michael E. Gage, Yi Li
Mathematics and Statistics Faculty Publications
In this paper we prove the existence of self-similar solutions to the anisotropic curve shortening equation.
Remarks On Automorphisms Of Subfactors, Phan Loi
Remarks On Automorphisms Of Subfactors, Phan Loi
Mathematics and Statistics Faculty Publications
We establish certain properties of automorphisms on an inclusion of AFD type II1 factors with finite index and finite depth and discuss their applications to the classification problem of AFD type III subfactors, including a different proof of a result on subfactors with principal graph Dn.
Asymptotic Behavior Of Solutions Of Model Problems For A Coupled System, S. Shao
Asymptotic Behavior Of Solutions Of Model Problems For A Coupled System, S. Shao
Mathematics and Statistics Faculty Publications
We study the asymptotic behavior of solutions of model problems for a coupled system. By consistent use of a priori estimates and asymptotic analysis, we present here an more efficient approach which provides precise descriptions of the asymptotic behabior of solutions of this system. Our results amplify and extend earlier results of Dorr, Patter, and Shampine and their treatment of this system. Meanwhile, the stability of the steady-state solutions of the corresponding time-dependent system is discussed.
Boundary And Interior Layer Behavior In A Time-Dependent Singularly Perturbed System, S. Shao
Boundary And Interior Layer Behavior In A Time-Dependent Singularly Perturbed System, S. Shao
Mathematics and Statistics Faculty Publications
No abstract provided.
Controllability And Stabilizability Of Coupled Strings With Control Applied At The Coupled Points, Lop-Fat Ho
Controllability And Stabilizability Of Coupled Strings With Control Applied At The Coupled Points, Lop-Fat Ho
Mathematics and Statistics Faculty Publications
Controllability and stabilizability of a system of coupled strings with control applied at the coupled points is studied. By investigating the properties of certain exponential series, it is shown that the system is approximate controllable if and only if related systems of uncoupled strings do not share a common eigenvalue. A sufficient condition for exact controllability is also obtained in terms of the Riesz basis properties of those exponential series.
Harmonic-Analysis Of Fractal Measures Induced By Representations Of A Certain C*-Algebra, Palle Jorgensen, Steen Pedersen
Harmonic-Analysis Of Fractal Measures Induced By Representations Of A Certain C*-Algebra, Palle Jorgensen, Steen Pedersen
Mathematics and Statistics Faculty Publications
We describe a class of measurable subsets Ω in Rd such that L2(Ω) has an orthogonal basis of frequencies eλ(x) = ei2πλ.x(x ε Ω) indexed by λ ∈ Λ ⊂ Rd. We show that such spectral pairs (Ω, Λ) have a self-similarity which may be used to generate associated fractal measures μ with Cantor set support. The Hilbert space L2(μ) does not have a total set of orthogonal frequencies, but a harmonic analysis of mu may be built instead from a natural representation of the Cuntz …
Symmetries Of The Einstein Equations, Ian M. Anderson, C. Torre
Symmetries Of The Einstein Equations, Ian M. Anderson, C. Torre
Mathematics and Statistics Faculty Publications
We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions. They consist of constant scalings of the metric, and of the infinitesimal action of generalized spacetime diffeomorphisms. Our results rule out a large class of possible ‘‘observables’’ for the gravitational field, and suggest that the vacuum Einstein equations are not integrable.
Modeling And Analysis For Laser Beam Induced Current Images In Semiconductors, Weifu Fang, Stavros Busenberg, Kazufumi Ito
Modeling And Analysis For Laser Beam Induced Current Images In Semiconductors, Weifu Fang, Stavros Busenberg, Kazufumi Ito
Mathematics and Statistics Faculty Publications
A mathematical model is developed for the new nondestructive optical technique called laser-beam-induced currents (LBIC), which can be used to detect electrically active regions and defects in semiconductors. The wellposedness of the model equations is shown, and an approximate model that simplifies the numerical implementation of the identification problem is obtained. Some numerical results are presented to show that the approximate model preserves the significant features that the LBIC technique has been experimentally shown to possess.
The Full Group Of A Countable Measurable Equivalence Relation, Richard Mercer
The Full Group Of A Countable Measurable Equivalence Relation, Richard Mercer
Mathematics and Statistics Faculty Publications
We study the group of all ''R-automorphisms'' of a countable equivalence relation R on a standard Borel space, special Borel automorphisms whose graphs lie in R. We show that such a group always contains periodic maps of each order sufficient to generate R. A construction based on these periodic maps leads to totally nonperiodic R-automorphisms all of whose powers have disjoint graphs. The presence of a large number of periodic maps allows us to present a version of the Rohlin Lemma for R-automorphisms. Finally we show that this group always contains copies of free …
Radial Symmetry Of Positive Solutions Of Nonlinear Elliptic Equations In Rn, Yi Li, Wei-Ming Ni
Radial Symmetry Of Positive Solutions Of Nonlinear Elliptic Equations In Rn, Yi Li, Wei-Ming Ni
Mathematics and Statistics Faculty Publications
No abstract provided.
On The Positive Solutions Of The Matukuma Equation, Yi Li
On The Positive Solutions Of The Matukuma Equation, Yi Li
Mathematics and Statistics Faculty Publications
No abstract provided.
Identifiability Of Semiconductor Defects From Lbic Images, Weifu Fang, Kazufumi Ito
Identifiability Of Semiconductor Defects From Lbic Images, Weifu Fang, Kazufumi Ito
Mathematics and Statistics Faculty Publications
The identifiability of defects in a semiconductor from its laser-beam-induced current (LBIC) image is studied. It is shown that the LBIC technique is reliable for detecting any spatial defects in the semiconductor material. Continuous dependence of the current measurements on the spatial defects is proved, and sensitivity is also discussed in certain cases.
Inverse Problems For Metal Oxide Semiconductor Field-Effect Transistor Contact Resistivity, Weifu Fang, Ellis Cumberbatch
Inverse Problems For Metal Oxide Semiconductor Field-Effect Transistor Contact Resistivity, Weifu Fang, Ellis Cumberbatch
Mathematics and Statistics Faculty Publications
Inverse problems arising from the identification of transistor contact resistivity and contact window location are studied. A one-point boundary measurement of the potential is shown to be sufficient to identify each from a one-parameter monotone family, and such identification is both stable and continuously dependent on the parameter. For a nonmonotone family of locations with resistivity given, similar results are obtained for measurement made on almost all boundary points.
On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In Rn. I. Asymptotic Behavior, Yi Li, Wei-Ming Ni
On The Asymptotic Behavior And Radial Symmetry Of Positive Solutions Of Semilinear Elliptic Equations In Rn. I. Asymptotic Behavior, Yi Li, Wei-Ming Ni
Mathematics and Statistics Faculty Publications
No abstract provided.
Boundary Velocity Control Of Incompressible-Flow With An Application To Viscous Drag Reduction, Max D. Gunzberger, Lisheng Hou, Tom Svobodny
Boundary Velocity Control Of Incompressible-Flow With An Application To Viscous Drag Reduction, Max D. Gunzberger, Lisheng Hou, Tom Svobodny
Mathematics and Statistics Faculty Publications
An optimal boundary control problem for the Navier-Stokes equations is presented. The control is the velocity on the boundary, which is constrained to lie in a closed, convex subset of H1/2 of the boundary. A necessary condition for optimality is derived. Computations are done when the control set is actually finite-dimensional, resulting in all application to viscous drag reduction.
Uniqueness Of Radial Solutions Of Semilinear Elliptic Equations, Man Kam Kwong, Yi Li
Uniqueness Of Radial Solutions Of Semilinear Elliptic Equations, Man Kam Kwong, Yi Li
Mathematics and Statistics Faculty Publications
E. Yanagida recently proved that the classical Matukuma equation with a given exponent has only one finite mass solution. We show how similar ideas can be exploited to obtain uniqueness results for other classes of equations as well as Matukuma equations with more general coefficients.