To eliminate oscillation and overbounding of finite element solutions of classical heat conduction equation, the author and Xiao have put forward two new concepts of monotonies and have derived and proved several crit...To eliminate oscillation and overbounding of finite element solutions of classical heat conduction equation, the author and Xiao have put forward two new concepts of monotonies and have derived and proved several criteria. This idea is borrowed here to deal with generalized conduction equation and finite element criteria for eliminating oscillation and overbounding are also presented. Some new and useful conclusions are drawn.展开更多
Due to the fact that the fourth-order partial differential equation （PDE） for noise removal can provide a good trade-off between noise removal and edge preservation and avoid blocky effects often caused by the secon...Due to the fact that the fourth-order partial differential equation （PDE） for noise removal can provide a good trade-off between noise removal and edge preservation and avoid blocky effects often caused by the second-order PDE, a domain-based fourth-order PDE method for noise removal is proposed. First, the proposed method segments the image domain into two domains, a speckle domain and a non-speckle domain, based on the statistical properties of isolated speckles in the Laplacian domain. Then, depending on the domain type, different conductance coefficients in the proposed fourth-order PDE are adopted. Moreover, the frequency approach is used to determine the optimum iteration stopping time. Compared with the existing fourth-order PDEs, the proposed fourth-order PDE can remove isolated speckles and keeps the edges from being blurred. Experimental results show the effectiveness of the proposed method.展开更多
This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covarianc...This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.展开更多
The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat con...The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat conduction model has been reconstructed. Numerical results show that the solution of the initial boundary value problem of the new model is similar to that of the classical heat conduction equation, but its propagation speed is slower than that of the latter. In addition, the propagation speed of the former is also affected by time delay and kernel function.展开更多
This work describes the deterministic interaction of a diffusing particle of efavirenz through concentration gradient. Simulated pharmacokinetic data from patients on efavirenz are used. The Fourier’s Equation is use...This work describes the deterministic interaction of a diffusing particle of efavirenz through concentration gradient. Simulated pharmacokinetic data from patients on efavirenz are used. The Fourier’s Equation is used to infer on transfer of movement between solution particles. The work investigates diffusion using Fick’s analogy, but in a different variable space. Two important movement fluxes of a solution particle are derived an absorbing one identified as conductivity and a dispersing one identified as diffusivity. The Fourier’s Equation can be used to describe the process of gain/loss of movement in formation of a solution particle in an individual.展开更多
文摘To eliminate oscillation and overbounding of finite element solutions of classical heat conduction equation, the author and Xiao have put forward two new concepts of monotonies and have derived and proved several criteria. This idea is borrowed here to deal with generalized conduction equation and finite element criteria for eliminating oscillation and overbounding are also presented. Some new and useful conclusions are drawn.
基金The National Natural Science Foundation of China(No.60972001)the National Key Technology R&D Program of China during the 11th Five-Year Period(No.2009BAG13A06)
文摘Due to the fact that the fourth-order partial differential equation （PDE） for noise removal can provide a good trade-off between noise removal and edge preservation and avoid blocky effects often caused by the second-order PDE, a domain-based fourth-order PDE method for noise removal is proposed. First, the proposed method segments the image domain into two domains, a speckle domain and a non-speckle domain, based on the statistical properties of isolated speckles in the Laplacian domain. Then, depending on the domain type, different conductance coefficients in the proposed fourth-order PDE are adopted. Moreover, the frequency approach is used to determine the optimum iteration stopping time. Compared with the existing fourth-order PDEs, the proposed fourth-order PDE can remove isolated speckles and keeps the edges from being blurred. Experimental results show the effectiveness of the proposed method.
基金supported by an NSERC granta startup fund of University of Alberta
文摘This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.
文摘The classical heat conduction equation is derived from the assumption that the temperature increases immediately after heat transfer, but the increase of temperature is a slow process, so the memory-dependent heat conduction model has been reconstructed. Numerical results show that the solution of the initial boundary value problem of the new model is similar to that of the classical heat conduction equation, but its propagation speed is slower than that of the latter. In addition, the propagation speed of the former is also affected by time delay and kernel function.
文摘This work describes the deterministic interaction of a diffusing particle of efavirenz through concentration gradient. Simulated pharmacokinetic data from patients on efavirenz are used. The Fourier’s Equation is used to infer on transfer of movement between solution particles. The work investigates diffusion using Fick’s analogy, but in a different variable space. Two important movement fluxes of a solution particle are derived an absorbing one identified as conductivity and a dispersing one identified as diffusivity. The Fourier’s Equation can be used to describe the process of gain/loss of movement in formation of a solution particle in an individual.
