The concept of double conditional expectation is introduced.A series of properties for the double conditional expectation are obtained several convergence theorems and Jensen inequality are proved.Finally we discuss t...The concept of double conditional expectation is introduced.A series of properties for the double conditional expectation are obtained several convergence theorems and Jensen inequality are proved.Finally we discuss the special cases and application for double conditional expectation.展开更多
In this paper, we first provide a generalized difference method for the 2-dimensional Navier-Stokes equations by combing the ideas of staggered scheme m and generalized upwind scheme in space, and by backward Euler ti...In this paper, we first provide a generalized difference method for the 2-dimensional Navier-Stokes equations by combing the ideas of staggered scheme m and generalized upwind scheme in space, and by backward Euler time-stepping. Then we apply the abstract framework of to prove its long-time convergence. Finally, a numerical example for solving driven cavity flows is given.展开更多
In this paper, the authers introduce certain entire exponential type interpolation operatots and study the convergence problem of these operatots in c(R) or Lp(R) (1≤p<∞)
Subdivision schemes provide important techniques for the fast generation of curves and surfaces.A recusive refinement of a given control polygon will lead in the limit to a desired visually smooth object.These methods...Subdivision schemes provide important techniques for the fast generation of curves and surfaces.A recusive refinement of a given control polygon will lead in the limit to a desired visually smooth object.These methods play also an important role in wavelet analysis.In this paper,we use a rather simple way to characterize the convergence of subdivision schemes for multivariate cases.The results will be used to investigate the regularity of the solutions for dilation equations.展开更多
The concise and divergent total syntheses of rearranged fusicoccanes,namely brassicicenes C,F,H,J,and K,are described here.The syntheses feature a substrate-controlled aldol reaction and an optimized Barbier reaction ...The concise and divergent total syntheses of rearranged fusicoccanes,namely brassicicenes C,F,H,J,and K,are described here.The syntheses feature a substrate-controlled aldol reaction and an optimized Barbier reaction to forge the rigid 5/9/5-bridged ring system followed by concise oxidation state adjustments including Martin dehydration,Upjohn dihydroxylation,and final selenoxide elimination to form the exomethylene within brassicicene K.展开更多
The object of this paper is to establish the relation between stability and convergence of the numerical methods for the evolution equation u(t) - Au - f(u) = g(t) on Banach space V, and to prove the long-time error e...The object of this paper is to establish the relation between stability and convergence of the numerical methods for the evolution equation u(t) - Au - f(u) = g(t) on Banach space V, and to prove the long-time error estimates for the approximation solutions. At first, we give the definition of long-time stability, and then prove the fact that stability and compatibility imply the uniform convergence on the infinite time region. Thus, we establish a general frame in order to prove the long-time convergence. This frame includes finite element methods and finite difference methods of the evolution equations, especially the semilinear parabolic and hyperbolic partial differential equations. As applications of these results we prove the estimates obtained by Larsson [5] and Sanz-serna and Stuart [6].展开更多
基金Supported by the National Natural Science Foundation of China(10371092)the Foundation of Wuhan University
文摘The concept of double conditional expectation is introduced.A series of properties for the double conditional expectation are obtained several convergence theorems and Jensen inequality are proved.Finally we discuss the special cases and application for double conditional expectation.
基金The project supported by Laboratory of Computational Physics,Institute of Applied Physics & Computational Mathematics,T.O.Box 80 0 9,Beijing 1 0 0 0 88
文摘In this paper, we first provide a generalized difference method for the 2-dimensional Navier-Stokes equations by combing the ideas of staggered scheme m and generalized upwind scheme in space, and by backward Euler time-stepping. Then we apply the abstract framework of to prove its long-time convergence. Finally, a numerical example for solving driven cavity flows is given.
文摘In this paper, the authers introduce certain entire exponential type interpolation operatots and study the convergence problem of these operatots in c(R) or Lp(R) (1≤p<∞)
文摘Subdivision schemes provide important techniques for the fast generation of curves and surfaces.A recusive refinement of a given control polygon will lead in the limit to a desired visually smooth object.These methods play also an important role in wavelet analysis.In this paper,we use a rather simple way to characterize the convergence of subdivision schemes for multivariate cases.The results will be used to investigate the regularity of the solutions for dilation equations.
基金the Fundamental Research Funds for the Central Universities(grant nos.63243109 and 63241203)National Natural Science Foundation of China(grant nos.82273794 and 82073695)+2 种基金Hundred Young Academic Leaders Program of Nankai University to L.W.(Nankai University)the Frontiers Science Center for New Organic Matter(grant no.63181206)the China Postdoctoral Science Foundation(grant no.2023M731790).
文摘The concise and divergent total syntheses of rearranged fusicoccanes,namely brassicicenes C,F,H,J,and K,are described here.The syntheses feature a substrate-controlled aldol reaction and an optimized Barbier reaction to forge the rigid 5/9/5-bridged ring system followed by concise oxidation state adjustments including Martin dehydration,Upjohn dihydroxylation,and final selenoxide elimination to form the exomethylene within brassicicene K.
文摘The object of this paper is to establish the relation between stability and convergence of the numerical methods for the evolution equation u(t) - Au - f(u) = g(t) on Banach space V, and to prove the long-time error estimates for the approximation solutions. At first, we give the definition of long-time stability, and then prove the fact that stability and compatibility imply the uniform convergence on the infinite time region. Thus, we establish a general frame in order to prove the long-time convergence. This frame includes finite element methods and finite difference methods of the evolution equations, especially the semilinear parabolic and hyperbolic partial differential equations. As applications of these results we prove the estimates obtained by Larsson [5] and Sanz-serna and Stuart [6].
