1 IntroductionLet R<sup>n×n</sup> be the set of all n×n real matrices.R<sup>n</sup>=R<sup>n×1</sup>.C<sup>n×n</sup>denotes the set of all n×n co...1 IntroductionLet R<sup>n×n</sup> be the set of all n×n real matrices.R<sup>n</sup>=R<sup>n×1</sup>.C<sup>n×n</sup>denotes the set of all n×n complex matrices.We are interested in solving the following inverse eigenvalue prob-lems:Problem A （Additive inverse eigenvalue problem） Given an n×n real matrix A=(a<sub>ij</sub>),and n distinct real numbers λ<sub>1</sub>,λ<sub>2</sub>,…,λ<sub>n</sub>,find a real n×n diagonal matrix展开更多
In this paper we consider two problems. The first is connected with the optimal recovery of functions satisfyiog boundary conditions. The second is the characterization of the unique func- tion whose r-th derivative h...In this paper we consider two problems. The first is connected with the optimal recovery of functions satisfyiog boundary conditions. The second is the characterization of the unique func- tion whose r-th derivative has minimum L_∞-norm, taking given values of alternating signs and satis fying boundary conditions.展开更多
In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of ne...In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.展开更多
We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We ...We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.展开更多
This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann con...This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.展开更多
In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and pro...In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and prove their spectral accuracy by using the recent results on the Jacobi quasi-orthogonal approximation. Numerical results demonstrate the high accuracy of suggested algorithm, which also works well even for oscillating solutions.展开更多
A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as mea...A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers' robust optimal path in a sampled STD network with computation complexity of O(n2+n·m). The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.展开更多
文摘1 IntroductionLet R<sup>n×n</sup> be the set of all n×n real matrices.R<sup>n</sup>=R<sup>n×1</sup>.C<sup>n×n</sup>denotes the set of all n×n complex matrices.We are interested in solving the following inverse eigenvalue prob-lems:Problem A （Additive inverse eigenvalue problem） Given an n×n real matrix A=(a<sub>ij</sub>),and n distinct real numbers λ<sub>1</sub>,λ<sub>2</sub>,…,λ<sub>n</sub>,find a real n×n diagonal matrix
基金Partially supported by Ministry of Science under Project MM--414.
文摘In this paper we consider two problems. The first is connected with the optimal recovery of functions satisfyiog boundary conditions. The second is the characterization of the unique func- tion whose r-th derivative has minimum L_∞-norm, taking given values of alternating signs and satis fying boundary conditions.
基金Projects Supported by the Science Fund of the Chinese Academy of Sciences
文摘In this paper, some misunderstam igs concerning the necessary conditions for resonance for ordinary differential equations with turning point have been corrected, and a recursive process for finding the sequence of necessary conditions for resonance has beenoffered.
基金This work is supported by the Youth Foundation, NSFC.
文摘In this paper, we get the existence result of the nontrivial weak solution (λ, u) of the following eigenvalue problem with natural growth conditions.
文摘We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.
文摘This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.
文摘In this paper, we investigate numerical methods for high order differential equations. We propose new spectral and spectral element methods for high order problems with mixed inhomogeneous boundary conditions, and prove their spectral accuracy by using the recent results on the Jacobi quasi-orthogonal approximation. Numerical results demonstrate the high accuracy of suggested algorithm, which also works well even for oscillating solutions.
基金Project(71001079)supported by the National Natural Science Foundation of China
文摘A theoretical study was conducted on finding optimal paths in transportation networks where link travel times were stochastic and time-dependent(STD). The methodology of relative robust optimization was applied as measures for comparing time-varying, random path travel times for a priori optimization. In accordance with the situation in real world, a stochastic consistent condition was provided for the STD networks and under this condition, a mathematical proof was given that the STD robust optimal path problem can be simplified into a minimum problem in specific time-dependent networks. A label setting algorithm was designed and tested to find travelers' robust optimal path in a sampled STD network with computation complexity of O(n2+n·m). The validity of the robust approach and the designed algorithm were confirmed in the computational tests. Compared with conventional probability approach, the proposed approach is simple and efficient, and also has a good application prospect in navigation system.
