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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
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 …