In this paper, the existence of global attractors for the 2D autonomous g- Navier-Stokes equations on multi-connected bounded domains is investigated under the general assumptions of boundaries. The estimation of the ...In this paper, the existence of global attractors for the 2D autonomous g- Navier-Stokes equations on multi-connected bounded domains is investigated under the general assumptions of boundaries. The estimation of the Hausdorff dimensions for global attractors is given.展开更多
The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence...The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback ：D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.展开更多
Let X = {X(t), t ∈ ? N } be a Gaussian random field with values in ? d defined by (1) $$ X(t) = (X_1 (t),...,X_d (t)),\forall t \in \mathbb{R}^N . $$ . The properties of space and time anisotropy of X and their conne...Let X = {X(t), t ∈ ? N } be a Gaussian random field with values in ? d defined by (1) $$ X(t) = (X_1 (t),...,X_d (t)),\forall t \in \mathbb{R}^N . $$ . The properties of space and time anisotropy of X and their connections to uniform Hausdorff dimension results are discussed. It is shown that in general the uniform Hausdorff dimension result does not hold for the image sets of a space-anisotropic Gaussian random field X.When X is an (N, d)-Gaussian random field as in (1), where X 1,...,X d are independent copies of a real valued, centered Gaussian random field X 0 which is anisotropic in the time variable. We establish uniform Hausdorff dimension results for the image sets of X. These results extend the corresponding results on one-dimensional Brownian motion, fractional Brownian motion and the Brownian sheet.展开更多
Let (R, m) be a local GCD domain. R is called a U 2 ring if there is an element u ∈ m ? m2 such that R/(u) is a valuation domain and R u is a Bézout domain. In this case u is called a normal element of R. In thi...Let (R, m) be a local GCD domain. R is called a U 2 ring if there is an element u ∈ m ? m2 such that R/(u) is a valuation domain and R u is a Bézout domain. In this case u is called a normal element of R. In this paper we prove that if R is a U 2 ring, then R and R[x] are coherent; moreover, if R has a normal element u and dim(R/(u)) = 1, then every finitely generated projective module over R[X] is free.展开更多
In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to sele...In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to select the best estimate from the WVE and to estimate the structure dimension. And this selected best estimate usually performs better than the existing methods such as Sliced Inverse Regression (SIR), SAVE, etc. Many methods such as SIR, SAVE, etc. usually put the same weight on each observation to estimate central subspace (CS). By introducing a weight function, WVE puts different weights on different observations according to distance of observations from CS. The weight function makes WVE have very good performance in general and complicated situations, for example, the distribution of regressor deviating severely from elliptical distribution which is the base of many methods, such as SIR, etc. And compared with many existing methods, WVE is insensitive to the distribution of the regressor. The consistency of the WVE is established. Simulations to compare the performances of WVE with other existing methods confirm the advantage of WVE.展开更多
基金Supported by the Special Foundation of Doctoral Unit of the Ministry of Education of China(No.20070128001)Scientific Research innovation Project of Shanghai Education Committee(No.09YZ239)~~
基金Project supported by the National Natural Science Fundation of China (No. 11171269)the Natural Science Basic Research Plan in Shaanxi Province of China (No. 2012JM1012)the Scientific Research Program Funded by Shaanxi Provincial Education Department (No. 12JK0849)
文摘In this paper, the existence of global attractors for the 2D autonomous g- Navier-Stokes equations on multi-connected bounded domains is investigated under the general assumptions of boundaries. The estimation of the Hausdorff dimensions for global attractors is given.
基金supported by the National Natural Science Foundation of China (No.10871156)the Fund of Xi'an Jiaotong University (No.2009xjtujc30)
文摘The pullback attractors for the 2D nonautonomous g-Navier-Stokes equations with linear dampness axe investigated on some unbounded domains. The existence of the pullback attractors is proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback ：D-asymptotic compactness. Furthermore, the estimation of the fractal dimensions for the 2D g-Navier-Stokes equations is given.
基金supported by National Science Foundation of the United States (Grant No.DMS-0706728)
文摘Let X = {X(t), t ∈ ? N } be a Gaussian random field with values in ? d defined by (1) $$ X(t) = (X_1 (t),...,X_d (t)),\forall t \in \mathbb{R}^N . $$ . The properties of space and time anisotropy of X and their connections to uniform Hausdorff dimension results are discussed. It is shown that in general the uniform Hausdorff dimension result does not hold for the image sets of a space-anisotropic Gaussian random field X.When X is an (N, d)-Gaussian random field as in (1), where X 1,...,X d are independent copies of a real valued, centered Gaussian random field X 0 which is anisotropic in the time variable. We establish uniform Hausdorff dimension results for the image sets of X. These results extend the corresponding results on one-dimensional Brownian motion, fractional Brownian motion and the Brownian sheet.
基金supported by the National Natural Science Foundation of China (Grant No. 10671137)the Ph. D. Programs Foundation of Ministry of Education of China (Grant No. 20060636001)
文摘Let (R, m) be a local GCD domain. R is called a U 2 ring if there is an element u ∈ m ? m2 such that R/(u) is a valuation domain and R u is a Bézout domain. In this case u is called a normal element of R. In this paper we prove that if R is a U 2 ring, then R and R[x] are coherent; moreover, if R has a normal element u and dim(R/(u)) = 1, then every finitely generated projective module over R[X] is free.
基金supported by National Natural Science Foundation of China (Grant No. 10771015)
文摘In this paper, we propose a new estimate for dimension reduction, called the weighted variance estimate (WVE), which includes Sliced Average Variance Estimate (SAVE) as a special case. Bootstrap method is used to select the best estimate from the WVE and to estimate the structure dimension. And this selected best estimate usually performs better than the existing methods such as Sliced Inverse Regression (SIR), SAVE, etc. Many methods such as SIR, SAVE, etc. usually put the same weight on each observation to estimate central subspace (CS). By introducing a weight function, WVE puts different weights on different observations according to distance of observations from CS. The weight function makes WVE have very good performance in general and complicated situations, for example, the distribution of regressor deviating severely from elliptical distribution which is the base of many methods, such as SIR, etc. And compared with many existing methods, WVE is insensitive to the distribution of the regressor. The consistency of the WVE is established. Simulations to compare the performances of WVE with other existing methods confirm the advantage of WVE.
