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Full-Text Articles in Physical Sciences and 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.
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.
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.