The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regulari...The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regularities in Orlicz for the second order derivatives of the solutions of the Dirichlet problems are also given.展开更多
In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularit...In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularity results for the solution of MNSE,which seem to be not available in the literature.Next,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete solution.Furthermore,certain regularity results for the time discrete solution are establishes rigorously.Based on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of MNSE.Finally,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.展开更多
Source term identification is very important for the contaminant gas emission event. Thus, it is necessary to study the source parameter estimation method with high computation efficiency, high estimation accuracy and...Source term identification is very important for the contaminant gas emission event. Thus, it is necessary to study the source parameter estimation method with high computation efficiency, high estimation accuracy and reasonable confidence interval. Tikhonov regularization method is a potential good tool to identify the source parameters. However, it is invalid for nonlinear inverse problem like gas emission process. 2-step nonlinear and linear PSO （partial swarm optimization）-Tikhonov regularization method proposed previously have estimated the emission source parameters successfully. But there are still some problems in computation efficiency and confidence interval. Hence, a new 1-step nonlinear method combined Tikhonov regularizafion and PSO algorithm with nonlinear forward dispersion model was proposed. First, the method was tested with simulation and experiment cases. The test results showed that 1-step nonlinear hybrid method is able to estimate multiple source parameters with reasonable confidence interval. Then, the estimation performances of different methods were compared with different cases. The estimation values with 1-step nonlinear method were close to that with 2-step nonlinear and linear PSO-Tikhonov regularization method, 1-step nonlinear method even performs better than other two methods in some cases, especially for source strength and downwind distance estimation. Compared with 2-step nonlinear method, 1-step method has higher computation efficiency. On the other hand, the confidence intervals with the method proposed in this paper seem more reasonable than that with other two methods. Finally, single PSO algorithm was compared with 1-step nonlinear PSO-Tikhonov hybrid regularization method. The results showed that the skill scores of 1-step nonlinear hybrid method to estimate source parameters were close to that of single PSO method and even better in some cases. One more important property of 1-step nonlinear PSO-Tikhonov regularization method is its reasonable confidence interval, which is not obtained by single PSO algorithm. Therefore, 1-step nonlinear hybrid regularization method proposed in this paper is a potential good method to estimate contaminant gas emission source term.展开更多
The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets ...The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets of semi-flow,the properties of the global attractor for strongly damped wave equation are discussed. The existence of multiple equilibrium points in global attractor for strongly damped wave equations with critical growth of nonlinearity is obtained. And under some additional condition, the infinite dimension of the attractor is proven.展开更多
The initial value problem of the multi-dimensional drift-flux model for two-phase flow is investigated in this paper,and the global existence of weak solutions with finite energy is established for general pressure-de...The initial value problem of the multi-dimensional drift-flux model for two-phase flow is investigated in this paper,and the global existence of weak solutions with finite energy is established for general pressure-density functions without the monotonicity assumption.展开更多
In this paper, we derive a priori bounds for global solutions of 2m-th order semilinear parabolic equations with superlinear and subcritical growth conditions. The proof is obtained by a bootstrap argument and maximal...In this paper, we derive a priori bounds for global solutions of 2m-th order semilinear parabolic equations with superlinear and subcritical growth conditions. The proof is obtained by a bootstrap argument and maximal regularity estimates. If n≥ 10/3m, we also give another proof which does not use maximal regularity estimates.展开更多
In many settings,multiple data collections and analyses on the same topic are summarised separately through statistical estimators of parameters and variances,and yet there are scientificreasons for sharing some stati...In many settings,multiple data collections and analyses on the same topic are summarised separately through statistical estimators of parameters and variances,and yet there are scientificreasons for sharing some statistical parameters across these different studies.This paper summarises what is known from large-sample theory about when estimators of a common structuralparameter from several independent samples can be combined functionally,or more specificallylinearly,to obtain an asymptotically efficient estimator from the combined sample.The main ideais that such combination can be done when the separate-sample nuisance parameters,if anyexist,vary freely and independently of one another.The issues are illustrated using data from amulti-centre lung cancer clinical trial.Examples are presented to show that separate estimatorscannot always be combined in this way,and that the functionally combined separate estimators may have low or 0 efficiency compared to the unified analysis that could be performed bypooling the datasets.展开更多
基金Supported by the NNSF of China(10771110,11171306)Supported by the the New Century 151 Talent Project of Zhejiang Province
文摘The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regularities in Orlicz for the second order derivatives of the solutions of the Dirichlet problems are also given.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871467,11471329).
文摘In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularity results for the solution of MNSE,which seem to be not available in the literature.Next,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete solution.Furthermore,certain regularity results for the time discrete solution are establishes rigorously.Based on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of MNSE.Finally,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.
基金Supported by the National Natural Science Foundation of China(21676216)China Postdoctoral Science Foundation(2015M582667)+2 种基金Natural Science Basic Research Plan in Shaanxi Province of China(2016JQ5079)Key Research Project of Shaanxi Province(2015ZDXM-GY-115)the Fundamental Research Funds for the Central Universities(xjj2017124)
文摘Source term identification is very important for the contaminant gas emission event. Thus, it is necessary to study the source parameter estimation method with high computation efficiency, high estimation accuracy and reasonable confidence interval. Tikhonov regularization method is a potential good tool to identify the source parameters. However, it is invalid for nonlinear inverse problem like gas emission process. 2-step nonlinear and linear PSO （partial swarm optimization）-Tikhonov regularization method proposed previously have estimated the emission source parameters successfully. But there are still some problems in computation efficiency and confidence interval. Hence, a new 1-step nonlinear method combined Tikhonov regularizafion and PSO algorithm with nonlinear forward dispersion model was proposed. First, the method was tested with simulation and experiment cases. The test results showed that 1-step nonlinear hybrid method is able to estimate multiple source parameters with reasonable confidence interval. Then, the estimation performances of different methods were compared with different cases. The estimation values with 1-step nonlinear method were close to that with 2-step nonlinear and linear PSO-Tikhonov regularization method, 1-step nonlinear method even performs better than other two methods in some cases, especially for source strength and downwind distance estimation. Compared with 2-step nonlinear method, 1-step method has higher computation efficiency. On the other hand, the confidence intervals with the method proposed in this paper seem more reasonable than that with other two methods. Finally, single PSO algorithm was compared with 1-step nonlinear PSO-Tikhonov hybrid regularization method. The results showed that the skill scores of 1-step nonlinear hybrid method to estimate source parameters were close to that of single PSO method and even better in some cases. One more important property of 1-step nonlinear PSO-Tikhonov regularization method is its reasonable confidence interval, which is not obtained by single PSO algorithm. Therefore, 1-step nonlinear hybrid regularization method proposed in this paper is a potential good method to estimate contaminant gas emission source term.
基金National Natural Science Foundations of China(Nos.11501096,11526100)Fundamental Research Funds for the Central Universities,China(No.2232015D3-36)+1 种基金Natural Science Fund for Colleges and Universities in Jiangsu Province,China(No.15KJB110005)Qinglan Project,China
文摘The aim of this paper is to study the long-term behavior of strongly damped wave equations with a Lyapunov function. Using the theory established by estimating the Z2 index of some sets and the idea of invariant sets of semi-flow,the properties of the global attractor for strongly damped wave equation are discussed. The existence of multiple equilibrium points in global attractor for strongly damped wave equations with critical growth of nonlinearity is obtained. And under some additional condition, the infinite dimension of the attractor is proven.
基金supported by National Natural Science Foundation of China(Grant Nos.11931010,11671384 and 11871047)the key research project of Academy for Multidisciplinary Studies,Capital Normal Universitythe Capacity Building for Sci-Tech Innovation-Fundamental Scientific Research Funds(Grant No.007/20530290068)。
文摘The initial value problem of the multi-dimensional drift-flux model for two-phase flow is investigated in this paper,and the global existence of weak solutions with finite energy is established for general pressure-density functions without the monotonicity assumption.
文摘In this paper, we derive a priori bounds for global solutions of 2m-th order semilinear parabolic equations with superlinear and subcritical growth conditions. The proof is obtained by a bootstrap argument and maximal regularity estimates. If n≥ 10/3m, we also give another proof which does not use maximal regularity estimates.
基金The authors gratefully acknowledge the Eastern Cooperative Oncology Group as the source for the ECOG EST 1582dataset,and the suggestion of a referee to expand our treatment of(V)to estimating equations.
文摘In many settings,multiple data collections and analyses on the same topic are summarised separately through statistical estimators of parameters and variances,and yet there are scientificreasons for sharing some statistical parameters across these different studies.This paper summarises what is known from large-sample theory about when estimators of a common structuralparameter from several independent samples can be combined functionally,or more specificallylinearly,to obtain an asymptotically efficient estimator from the combined sample.The main ideais that such combination can be done when the separate-sample nuisance parameters,if anyexist,vary freely and independently of one another.The issues are illustrated using data from amulti-centre lung cancer clinical trial.Examples are presented to show that separate estimatorscannot always be combined in this way,and that the functionally combined separate estimators may have low or 0 efficiency compared to the unified analysis that could be performed bypooling the datasets.
