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Articles 61 - 90 of 144
Full-Text Articles in Applied Mathematics
On Adaptive Estimation In Orthogonal Saturated Designs, Weizhen Wang, Daniel T. Voss
On Adaptive Estimation In Orthogonal Saturated Designs, Weizhen Wang, Daniel T. Voss
Mathematics and Statistics Faculty Publications
A simple method is provided to construct a general class of individual and simultaneous confidence intervals for the effects in orthogonal saturated designs. These intervals use the data adaptively, maintain the confidence levels sharply at 1 - α at the least favorable parameter configuration, work effectively under effect sparsity, and include the intervals by Wang and Voss (2001) as a special case.
On The Stability Of The Positive Radial Steady States For A Semilinear Cauchy Problem, Yinbin Deng, Yi Li, Yi Liu
On The Stability Of The Positive Radial Steady States For A Semilinear Cauchy Problem, Yinbin Deng, Yi Li, Yi Liu
Mathematics and Statistics Faculty Publications
No abstract provided.
The Global Dynamics Of Isothermal Chemical Systems With Critical Nonlinearity, Yi Li, Yuanwei Qi
The Global Dynamics Of Isothermal Chemical Systems With Critical Nonlinearity, Yi Li, Yuanwei Qi
Mathematics and Statistics Faculty Publications
In this paper, we study the Cauchy problem of a cubic autocatalytic chemical reaction system u1,t = u1,xx − uα1 uβ2, u2,t = du2,xx+ uα1 uβ2 with non-negative initial data, where the exponents α,β satisfy 1<α,βd>0 is the Lewis number. Our purpose is to study the global dynamics of solutions under mild decay of initial data as |x|→∞. We show the exact large time behaviour of solutions which is universal.
Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang
Perturbation Of Global Solution Curves For Semilinear Problems, Philip Korman, Yi Li, Tiancheng Ouyang
Mathematics and Statistics Faculty Publications
We revisit the question of exact multiplicity of positive solutions for a class of Dirichlet problems for cubic-like nonlinearities, which we studied in 161. Instead of computing the direction of bifurcation as we did in [6], we use an indirect approach, and study the evolution of turning points. We give conditions under which the critical (turning) points continue on smooth curves, which allows us to reduce the problem to the easier case of f (0) = 0. We show that the smallest root of f (u) does not have to be restricted.
An Algebraic Characterization Of Projective-Planar Graphs, Lowell Abrams, Dan Slilaty
An Algebraic Characterization Of Projective-Planar Graphs, Lowell Abrams, Dan Slilaty
Mathematics and Statistics Faculty Publications
We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G∗ on the same edge set as G which satisfies algebraic conditions inspired by homology groups and intersection products in homology groups.
Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao
Multiple Solutions For An Inhomogeneous Semilinear Elliptic Equation In Rn, Yinbin Deng, Yi Li, Xuejin Zhao
Mathematics and Statistics Faculty Publications
No abstract provided.
Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic, Dan Slilaty
Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic, Dan Slilaty
Mathematics and Statistics Faculty Publications
Let G be a connected graph that is 2-cell embedded in a surface S, and let G* be its topological dual graph. We will define and discuss several matroids whose element set is E(G), for S homeomorphic to the plane, projective plane, or torus. We will also state and prove old and new results of the type that the dual matroid of G is the matroid of the topological dual G*.
Parameter Identification For Semiconductor Diodes By Lbic Imaging, Weifu Fang, Kazufumi Ito, David A. Redfern
Parameter Identification For Semiconductor Diodes By Lbic Imaging, Weifu Fang, Kazufumi Ito, David A. Redfern
Mathematics and Statistics Faculty Publications
Laser-beam-induced-current (LBIC) imaging is a nondestructive technique used for the characterization of the electrical structure within a semiconductor. In this paper a model is formulated for this technique using the standard drift-diffusion model, and, subsequently, an approximate version and its dual are derived for the study of the inverse problem. The formulation is then applied to a cross-sectional model for n-on-p devices of finite depth to study in detail the relation between the LBIC images and the device parameters. Numerical methods are developed for the simulation of the LBIC image of a diode as well as for the identification of …
On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li
On The Existence Of Multiple Positive Solutions For A Semilinear Problem In Exterior Domains, Yinbin Deng, Yi Li
Mathematics and Statistics Faculty Publications
In this paper, we study the existence and nonexistence of multiple positive solutions for problem where Ω=N\ω is an exterior domain in N, ω⊂N is a bounded domain with smooth boundary, and N>2. μ⩾0, p>1 are some given constants. K(x) satisfies: K(x)∈Cαloc(Ω) and ∃C, ϵ, M>0 such that |K(x)|⩽C |x|l for any |x|⩾M, with l⩽ −2−ϵ. Some existence and …
On The Regularity Of Solutions To Fully Nonlinear Elliptic Equations Via The Liouville Property, Qingbo Huang
On The Regularity Of Solutions To Fully Nonlinear Elliptic Equations Via The Liouville Property, Qingbo Huang
Mathematics and Statistics Faculty Publications
We show that any C1,1 solution to the uniformly elliptic equation F(D2u) = 0 must belong to C2,α, if the equation has the Liouville property.
Absolutely Continuous Jacobi Operators, Steen Pedersen
Absolutely Continuous Jacobi Operators, Steen Pedersen
Mathematics and Statistics Faculty Publications
No abstract provided.
Domain Functionals And Exit Times For Brownian Motion, Chaocheng Huang, David Miller
Domain Functionals And Exit Times For Brownian Motion, Chaocheng Huang, David Miller
Mathematics and Statistics Faculty Publications
Two domain functionals describing the averaged expectation of exit times and averaged variance of exit times of Brownian motion from a domain, respectively, are studied.
Control Of Error Rates In Adaptive Analysis Of Orthogonal Saturated Designs, Weizhen Wang, Daniel T. Voss
Control Of Error Rates In Adaptive Analysis Of Orthogonal Saturated Designs, Weizhen Wang, Daniel T. Voss
Mathematics and Statistics Faculty Publications
Individual and simultaneous confidence intervals using the data adaptively are constructed for the effects in orthogonal saturated designs under the assumption of effect sparsity. The minimum coverage probabilities of the intervals are equal to the nominal level 1 - α.
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.
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.
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.
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 …
Generalized Averages For Solutions Of Two-Point Dirichlet Problems, Philip Korman, Yi Li
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.
Random Fluctuations Of Convex Domains And Lattice Points, Alex Iosevich, Kimberly Kinateder
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.
Axiomatic Approach For Quantification Of Image Resolution, Ge Wang, Yi Li
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.
Variational Principles For Average Exit Time Moments For Diffusions In Euclidean Space, Kimberly Kinateder, Patrick Mcdonald
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
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.
Solutions To A Nonlinear Drift-Diffusion Model Of Semiconductors, Weifu Fang, Kazufumi Ito
Solutions To A Nonlinear Drift-Diffusion Model Of Semiconductors, Weifu Fang, Kazufumi Ito
Mathematics and Statistics Faculty Publications
A nonlinear drift-diffusion model for semiconductors is analyzed to show the existence of non-vacuum global solutions and stationary solutions. The long time behavior of the solutions is studied by establishing the existence of an absorbing set and a compact attractor of the dynamical system. Parallel results on vacuum solutions are also obtained under weaker conditions on model parameters.
Anticommuting Derivations, Steen Pedersen
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.
Stability Of A Semilinear Cauchy Problem, Yi Liu, Yi Li, Yinbin Deng
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
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 .
A Structural Result Of Irreducible Inclusions Of Type Iii Lambda Factors, Lambda Is An Element Of (0,1), Phan Loi
Mathematics and Statistics Faculty Publications
Given an irreducible inclusion of factors with finite index N ⊂ M, where M is of type IIIλ1/m, N of type IIIλ1/n, 0 < λ < 1, and m,n are relatively prime positive integers, we will prove that if N ⊂ M satisfies a commuting square condition, then its structure can be characterized by using fixed point algebras and crossed products of automorphisms acting on the middle inclusion of factors associated with N ⊂ M. Relations between N ⊂ M and a certain G-kernel on subfactors are also discussed.
Evolution Of Mixed-State Regions In Type-Ii Superconductors, Chaocheng Huang, Tom Svobodny
Evolution Of Mixed-State Regions In Type-Ii Superconductors, Chaocheng Huang, Tom Svobodny
Mathematics and Statistics Faculty Publications
A mean-field model for dynamics of superconducting vortices is studied. The model, consisting of an elliptic equation coupled with a hyperbolic equation with discontinuous initial data, is formulated as a system of nonlocal integrodifferential equations. We show that there exists a unique classical solution in C1+α(Ω0) for all t > Ω, where Ω0 is the initial vortex region that is assumed to be in C1+α. Consequently, for any time t, the vortex region Ωt is of C1+α, and the vorticity is in Cα(Ωt).