While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge t...While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny＇s transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semielassical Landauer Buttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.展开更多
Let T：X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f：X → R^d is a Hlder continuous function with ∫_X^（fdm） = 0.If the components of f are cohomologously i...Let T：X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f：X → R^d is a Hlder continuous function with ∫_X^（fdm） = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ~2：=σ~2 （f ） such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ~2 . Moreover, there exists a real number A 〉 0 such that, for any integer n ≥ 1,Π（ m＊（ 1√ nS f n ）,N （0,σ~2 ） ≤A√n, where m＊（1√ n S^fn）denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.展开更多
We prove a generalized Gauss-Kuzmin-L′evy theorem for the generalized Gauss transformation Tp（x） = {p/x}.In addition, we give an estimate for the constant that appears in the theorem.
In this paper, a V-cycle multigrid method is presented for a Hermite rectangular element. By defining proper mesh-dependent inner product and transfer operator, we obtain its convergence property and the uniform conve...In this paper, a V-cycle multigrid method is presented for a Hermite rectangular element. By defining proper mesh-dependent inner product and transfer operator, we obtain its convergence property and the uniform convergence rate independent of mesh size and level are established.展开更多
One of the key elements in real estate management is streamlining the construction process. Thus, the facilities can be built on a faster, cheaper, and higher quality base. Consequently, it will enhance the owner’s c...One of the key elements in real estate management is streamlining the construction process. Thus, the facilities can be built on a faster, cheaper, and higher quality base. Consequently, it will enhance the owner’s competitiveness. Due to the high cost and lengthy duration of mega-construction projects in recent years, Build-Operate-Transfer (BOT) contracts are getting popular in delivering constructed projects in the public sector. With BOT, the public owners are able to focus on the effectiveness of fair resource allocation as well as bring the efficiency of private enterprise into governmental operations. This paper uses Taiwan High Speed Rail project to exemplify the BOT method in executing the constructed projects in the chain of real estate management processes. The paper explains the reasons for building HSR and adopting BOT approach. The detail of the HSR project and the feasibility analysis of the project will be presented in this paper. The feasibility analysis comprises the comparisons of different transportation means, the financial analysis, and other benefits from HSR. Finally, conclusions will be drawn.展开更多
We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated co...We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated computationally.The numerical studies in 3D provide the first estimates of the quantitative differences between a range of transfer operators between non-nested finite element spaces.We consider the standard finite element interpolation,Cl´ement’s quasi-interpolation with different local polynomial degrees,the global L^(2)-orthogonal projection,a local L^(2)-quasi-projection via a discrete inner product,and a pseudo-L^(2)-projection defined by a Petrov-Galerkin variational equation with a discontinuous test space.Understanding their qualitative and quantitative behaviors in this computational way is interesting per se;it could also be relevant in the context of discretization and solution techniques which make use of different non-nested meshes.It turns out that the pseudo-L^(2)-projection approximates the actual L^(2)-orthogonal projection best.The obtained results seem to be largely independent of the underlying computational domain;this is demonstrated by four examples(ball,cylinder,half torus and Stanford Bunny).展开更多
We consider Young＇s nonuniformly hyperbolic system （X, T, u） where u is the SRB measure corresponding to the system （X, T）, and show that if the components of a Holder observable f ： X → R^d are cohomologously ...We consider Young＇s nonuniformly hyperbolic system （X, T, u） where u is the SRB measure corresponding to the system （X, T）, and show that if the components of a Holder observable f ： X → R^d are cohomologously independent, then f satisfies the multidimensional central limit theorem. Moreover if f is aperiodic, then f satisfies the local multidimensional central limit theorem.展开更多
基金Supported by the National Science Council at Taiwan through Grants No. NSC 97-2112-M-009-008-MY3
文摘While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny＇s transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semielassical Landauer Buttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.
基金supported by the National Natural Science Foundation of China(10571174)the Scientific Research Foundation of Ministry of Education for Returned Overseas Chinese ScholarsScientific Research Foundation of Ministry of Human Resources and Social Security for Returned Overseas Chinese Scholars
文摘Let T：X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f：X → R^d is a Hlder continuous function with ∫_X^（fdm） = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ~2：=σ~2 （f ） such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ~2 . Moreover, there exists a real number A 〉 0 such that, for any integer n ≥ 1,Π（ m＊（ 1√ nS f n ）,N （0,σ~2 ） ≤A√n, where m＊（1√ n S^fn）denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.
文摘We prove a generalized Gauss-Kuzmin-L′evy theorem for the generalized Gauss transformation Tp（x） = {p/x}.In addition, we give an estimate for the constant that appears in the theorem.
基金Supported by NSF of China(10971203)Supported by the NSF of the education Department of Henan Province (2009A110017)
文摘In this paper, a V-cycle multigrid method is presented for a Hermite rectangular element. By defining proper mesh-dependent inner product and transfer operator, we obtain its convergence property and the uniform convergence rate independent of mesh size and level are established.
文摘One of the key elements in real estate management is streamlining the construction process. Thus, the facilities can be built on a faster, cheaper, and higher quality base. Consequently, it will enhance the owner’s competitiveness. Due to the high cost and lengthy duration of mega-construction projects in recent years, Build-Operate-Transfer (BOT) contracts are getting popular in delivering constructed projects in the public sector. With BOT, the public owners are able to focus on the effectiveness of fair resource allocation as well as bring the efficiency of private enterprise into governmental operations. This paper uses Taiwan High Speed Rail project to exemplify the BOT method in executing the constructed projects in the chain of real estate management processes. The paper explains the reasons for building HSR and adopting BOT approach. The detail of the HSR project and the feasibility analysis of the project will be presented in this paper. The feasibility analysis comprises the comparisons of different transportation means, the financial analysis, and other benefits from HSR. Finally, conclusions will be drawn.
基金supported by the Bonn International Graduate School in Mathematics and by the Iniziativa Ticino in Rete.
文摘We present quantitative studies of transfer operators between finite element spaces associated with unrelated meshes.Several local approximations of the global L^(2)-orthogonal projection are reviewed and evaluated computationally.The numerical studies in 3D provide the first estimates of the quantitative differences between a range of transfer operators between non-nested finite element spaces.We consider the standard finite element interpolation,Cl´ement’s quasi-interpolation with different local polynomial degrees,the global L^(2)-orthogonal projection,a local L^(2)-quasi-projection via a discrete inner product,and a pseudo-L^(2)-projection defined by a Petrov-Galerkin variational equation with a discontinuous test space.Understanding their qualitative and quantitative behaviors in this computational way is interesting per se;it could also be relevant in the context of discretization and solution techniques which make use of different non-nested meshes.It turns out that the pseudo-L^(2)-projection approximates the actual L^(2)-orthogonal projection best.The obtained results seem to be largely independent of the underlying computational domain;this is demonstrated by four examples(ball,cylinder,half torus and Stanford Bunny).
文摘We consider Young＇s nonuniformly hyperbolic system （X, T, u） where u is the SRB measure corresponding to the system （X, T）, and show that if the components of a Holder observable f ： X → R^d are cohomologously independent, then f satisfies the multidimensional central limit theorem. Moreover if f is aperiodic, then f satisfies the local multidimensional central limit theorem.
