In this paper, the completeness and minimality properties of some random exponential system in a weighted Banach space of complex functions continuous on the real line for convex nonnegative weight are studied. The re...In this paper, the completeness and minimality properties of some random exponential system in a weighted Banach space of complex functions continuous on the real line for convex nonnegative weight are studied. The results may be viewed as a probabilistic version of Malliavin＇s classical results.展开更多
Let F=C（x1,x2,…,xe,xe＋1,…,xm）, where x1, x2,… , xe are differential variables, and xe＋1,…,xm are shift variables. We show that a hyperexponential function, which is algebraic over F,is of form g（x1, x2, …,xm...Let F=C（x1,x2,…,xe,xe＋1,…,xm）, where x1, x2,… , xe are differential variables, and xe＋1,…,xm are shift variables. We show that a hyperexponential function, which is algebraic over F,is of form g（x1, x2, …,xm）q（x1,x2,…,xe）^1/lwe＋1^xe＋1…wm^xm, where g∈ F, q ∈ C（x1,x2,…,xe）,t∈Z^＋ and we＋1,…,wm are roots of unity. Furthermore,we present an algorithm for determining whether a hyperexponential function is algebraic over F.展开更多
The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-E...The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-EPC) method. The space of the state variables of the large-scale nonlinear stochastic dynamic system excited by Gaussian white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system are then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in the other subspace is formulated. Therefore, the FPK equations in low dimensions are obtained from the original FPK equation in high dimensions and the FPK equations in low dimensions are solvable with the exponential polynomial closure method. Examples about multi-degree-offreedom NSD systems with various polynomial types of nonlinearities in displacements are given to show the effectiveness of the subspace-EPC method in these cases.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10371005)the Scientific Research Foundation of the Ministry of Education of China for Returned Overseas Chinese Scholars
文摘In this paper, the completeness and minimality properties of some random exponential system in a weighted Banach space of complex functions continuous on the real line for convex nonnegative weight are studied. The results may be viewed as a probabilistic version of Malliavin＇s classical results.
基金The research is supported in part by the 973 project of China(2004CB31830).
文摘Let F=C（x1,x2,…,xe,xe＋1,…,xm）, where x1, x2,… , xe are differential variables, and xe＋1,…,xm are shift variables. We show that a hyperexponential function, which is algebraic over F,is of form g（x1, x2, …,xm）q（x1,x2,…,xe）^1/lwe＋1^xe＋1…wm^xm, where g∈ F, q ∈ C（x1,x2,…,xe）,t∈Z^＋ and we＋1,…,wm are roots of unity. Furthermore,we present an algorithm for determining whether a hyperexponential function is algebraic over F.
文摘The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-EPC) method. The space of the state variables of the large-scale nonlinear stochastic dynamic system excited by Gaussian white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system are then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in the other subspace is formulated. Therefore, the FPK equations in low dimensions are obtained from the original FPK equation in high dimensions and the FPK equations in low dimensions are solvable with the exponential polynomial closure method. Examples about multi-degree-offreedom NSD systems with various polynomial types of nonlinearities in displacements are given to show the effectiveness of the subspace-EPC method in these cases.
