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Articles 1 - 7 of 7
Full-Text Articles in Entire DC Network
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 …
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.
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 …
Inertial Manifolds And Stabilization Of Nonlinear Beam Equations With Balakrishnan-Taylor Damping, Yuncheng You
Inertial Manifolds And Stabilization Of Nonlinear Beam Equations With Balakrishnan-Taylor Damping, Yuncheng You
Mathematics and Statistics Faculty Publications
In this paper we study a hinged, extensible, and elastic nonlinear beam equation with structural damping and Balakrishnan-Taylor damping with the full exponent 2(n+β)+1. This strongly nonlinear equation, initially proposed by Balakrishnan and Taylor in 1989, is a very general and useful model for large aerospace structures. In this work, the existence of global solutions and the existence of absorbing sets in the energy space are proved. For this equation, the feature is that the exponential rate of the absorbing property is not a global constant, but which is uniform for the family of trajectories starting from any given bounded …
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.
Iterative Solution Of Unstable Variational Inequalities On Approximately Given Sets, Y. I. Alber, A. G. Kartsatos, E. Litsyn
Iterative Solution Of Unstable Variational Inequalities On Approximately Given Sets, Y. I. Alber, A. G. Kartsatos, E. Litsyn
Mathematics and Statistics Faculty Publications
The convergence and the stability of the iterative regularization method for solving variational inequalities with bounded nonsmooth properly monotone (i.e., degenerate) operators in Banach spaces are studied. All the items of the inequality (i.e., the operator A, the “right hand side” f and the set of constraints Ω) are to be perturbed. The connection between the parameters of regularization and perturbations which guarantee strong convergence of approximate solutions is established. In contrast to previous publications by Bruck, Reich and the first author, we do not suppose here that the approximating sequence is a priori bounded. Therefore the present results are …