Node interpolation cell method（NICM）is a micromechanics method employing the virtual displacement principle and the representative volume element（RVE）scheme to obtain the relationship between the global and the lo...Node interpolation cell method（NICM）is a micromechanics method employing the virtual displacement principle and the representative volume element（RVE）scheme to obtain the relationship between the global and the local strain.Mechanical properties of 2-D textile fabric reinforced ceramic matrix composites are predicted by NICM.Microstructures of 2-D woven and braided fabric reinforced composite are modeled by two kinds of RVE scheme.NICM is used to predict the macroscopic mechanical properties.The fill and warp yarns are simulated with cubic B-spline and their undulating forms are approximated by sinusoid.The effect of porosity on the fiber and matrix are considered as a reduction of elastic module.The connection of microstructure parameters and fiber volume fraction is modeled to investigate the reflection on the mechanical properties.The results predicted by NICM are compared with that by the finite element method（FEM）.The comparison shows that NICM is a valid and feasible method for predicting the mechanics properties of 2-D woven and braided fabric reinforced ceramic matrix composites.展开更多
Weighted Lp mean convergence of Extended Hermite-Fejer operators based on the zeros of orthogonal polynomials with respct to the general weight and Jacobi weight is investigated. Suf ficient conditions for such conve...Weighted Lp mean convergence of Extended Hermite-Fejer operators based on the zeros of orthogonal polynomials with respct to the general weight and Jacobi weight is investigated. Suf ficient conditions for such convergence for all continuous functions are given.展开更多
In this paper, the authers introduce certain entire exponential type interpolation operatots and study the convergence problem of these operatots in c(R) or Lp(R) (1≤p<∞)
The choice of the particle's distribution model and the consistency of the result are very important for FastSLAM.The improved auxiliary variable model with FastSLAM,and Stirling Interpolation which is used to app...The choice of the particle's distribution model and the consistency of the result are very important for FastSLAM.The improved auxiliary variable model with FastSLAM,and Stirling Interpolation which is used to approximate the nonlinear functions are provided.This approach improves the precision of the approximation for the nonlinear functions,conquers the drawback of the FastSLAM1.0 by using a model ignoring the measurement data,enhances the estimation consistency of the robot pose,and reduces the degradation speed of the particle in FastSLAM algorithm.Simulation results demonstrate the excellence of the proposed algorithm and give the noise parameter influence on the proposed algorithm.展开更多
In the smoothed particle hydrodynamics (SPH) method, a meshless interpolation scheme is needed for the unknown function in order to discretize the governing equation.A particle approximation method has so far been use...In the smoothed particle hydrodynamics (SPH) method, a meshless interpolation scheme is needed for the unknown function in order to discretize the governing equation.A particle approximation method has so far been used for this purpose.Traditional particle interpolation (TPI) is simple and easy to do, but its low accuracy has become an obstacle to its wider application.This can be seen in the cases of particle disorder arrangements and derivative calculations.There are many different methods to improve accuracy, with the moving least square (MLS) method one of the most important meshless interpolation methods.Unfortunately, it requires complex matrix computing and so is quite time-consuming.The authors developed a simpler scheme, called higher-order particle interpolation (HPI).This scheme can get more accurate derivatives than the MLS method, and its function value and derivatives can be obtained simultaneously.Although this scheme was developed for the SPH method, it has been found useful for other meshless methods.展开更多
In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theo...In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.展开更多
Instanton configurations of （1＋1）-dimensions in an antiferromagnetic biaxial-anisotropy-spin-chain are obtained explicitly in the strong anisotropy limit, which interpolate between degenerate equilibrium orientatio...Instanton configurations of （1＋1）-dimensions in an antiferromagnetic biaxial-anisotropy-spin-chain are obtained explicitly in the strong anisotropy limit, which interpolate between degenerate equilibrium orientations of the Neel vector along easy axis and are seen to be responsible for quantum tunneling. Macroscopic quantum coherence of the domain walls is demonstrated in terms of the instantons.展开更多
In the present paper,we provide an error bound for the learning rates of the regularized Shannon sampling learning scheme when the hypothesis space is a reproducing kernel Hilbert space(RKHS) derived by a Mercer kerne...In the present paper,we provide an error bound for the learning rates of the regularized Shannon sampling learning scheme when the hypothesis space is a reproducing kernel Hilbert space(RKHS) derived by a Mercer kernel and a determined net.We show that if the sample is taken according to the determined set,then,the sample error can be bounded by the Mercer matrix with respect to the samples and the determined net.The regularization error may be bounded by the approximation order of the reproducing kernel Hilbert space interpolation operator.The paper is an investigation on a remark provided by Smale and Zhou.展开更多
This paper presents an improved early termination algorithm for sparse black box multivariate polynomials, which reduces the interpolation problem into several sub-interpolation problems with less variables and fewer ...This paper presents an improved early termination algorithm for sparse black box multivariate polynomials, which reduces the interpolation problem into several sub-interpolation problems with less variables and fewer terms. Actually, all interpolations are eventually reduced to the interpolation of a list of polynomials with less terms than that of the original polynomial. Extensive experiments show that the new algorithm is much faster than the original algorithm.展开更多
In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimen...In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.展开更多
In this article, we test the nature of X（3872）, which is assumed to be a P-wave [cq]-scalar-diquark [cq]- axial-vector-antidiquark tetraquark state with JP = 2^-. The interpolating current representing the JP = 2^- ...In this article, we test the nature of X（3872）, which is assumed to be a P-wave [cq]-scalar-diquark [cq]- axial-vector-antidiquark tetraquark state with JP = 2^-. The interpolating current representing the JP = 2^- state is proposed. Technically, contributions of the operators up to dimension six are included in the operator product expansion. The mass obtained for such state is m2- = （4.38±0.15） GeV. We conclude that it is impossible to describe the X（3872） structure as JV = 2^- tetraauark state.展开更多
The authors prove the Hardy-Littlewood-Sobolev theorems for generalized fractional integrals L?α/2 for 0 < α < n/m, where L is a complex elliptic operator of arbitrary order 2m on Rn.
We compare the direct free energy interpolation(DFEI) method and the quasi-harmonic approximation(QHA) in calculating of the equation of states and thermodynamic properties of prototype Al. The Gibbs free energy of Al...We compare the direct free energy interpolation(DFEI) method and the quasi-harmonic approximation(QHA) in calculating of the equation of states and thermodynamic properties of prototype Al. The Gibbs free energy of Al is calculated using the DFEI method based on the high-temperature phonon density of states reduced from classical molecular dynamics simulations. Then, we reproduce the thermal expansion coefficients, the specific heat, the isothermal bulk modulus of Al accurately. By comparing the results from the DFEI method and the QHA, we find that the DFEI method is indeed more accurate in calculating anharmonic properties than the QHA.展开更多
基金Supported by the Aviation Science Foundationof China(2009ZB5052)the Specialized Research Foundation for the Doctor Program of Higher Education(20070287039)~~
文摘Node interpolation cell method（NICM）is a micromechanics method employing the virtual displacement principle and the representative volume element（RVE）scheme to obtain the relationship between the global and the local strain.Mechanical properties of 2-D textile fabric reinforced ceramic matrix composites are predicted by NICM.Microstructures of 2-D woven and braided fabric reinforced composite are modeled by two kinds of RVE scheme.NICM is used to predict the macroscopic mechanical properties.The fill and warp yarns are simulated with cubic B-spline and their undulating forms are approximated by sinusoid.The effect of porosity on the fiber and matrix are considered as a reduction of elastic module.The connection of microstructure parameters and fiber volume fraction is modeled to investigate the reflection on the mechanical properties.The results predicted by NICM are compared with that by the finite element method（FEM）.The comparison shows that NICM is a valid and feasible method for predicting the mechanics properties of 2-D woven and braided fabric reinforced ceramic matrix composites.
文摘Weighted Lp mean convergence of Extended Hermite-Fejer operators based on the zeros of orthogonal polynomials with respct to the general weight and Jacobi weight is investigated. Suf ficient conditions for such convergence for all continuous functions are given.
文摘In this paper, the authers introduce certain entire exponential type interpolation operatots and study the convergence problem of these operatots in c(R) or Lp(R) (1≤p<∞)
基金National High-Tech Research and Development Program of China(No.2003AA1Z2130)Science and Technology Project of Zhejiang Province,China(No.2005C11001-02)
文摘The choice of the particle's distribution model and the consistency of the result are very important for FastSLAM.The improved auxiliary variable model with FastSLAM,and Stirling Interpolation which is used to approximate the nonlinear functions are provided.This approach improves the precision of the approximation for the nonlinear functions,conquers the drawback of the FastSLAM1.0 by using a model ignoring the measurement data,enhances the estimation consistency of the robot pose,and reduces the degradation speed of the particle in FastSLAM algorithm.Simulation results demonstrate the excellence of the proposed algorithm and give the noise parameter influence on the proposed algorithm.
基金Supported by the National Natural Science Foundation of China under Grant No.10572041,50779008Doctoral Fund of Ministry of Education of China under Grant No.20060217009
文摘In the smoothed particle hydrodynamics (SPH) method, a meshless interpolation scheme is needed for the unknown function in order to discretize the governing equation.A particle approximation method has so far been used for this purpose.Traditional particle interpolation (TPI) is simple and easy to do, but its low accuracy has become an obstacle to its wider application.This can be seen in the cases of particle disorder arrangements and derivative calculations.There are many different methods to improve accuracy, with the moving least square (MLS) method one of the most important meshless interpolation methods.Unfortunately, it requires complex matrix computing and so is quite time-consuming.The authors developed a simpler scheme, called higher-order particle interpolation (HPI).This scheme can get more accurate derivatives than the MLS method, and its function value and derivatives can be obtained simultaneously.Although this scheme was developed for the SPH method, it has been found useful for other meshless methods.
文摘In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.
基金Supported by the Natural Science Basic Research Plan in Henan Province of China under Grant No.2007140009
文摘Instanton configurations of （1＋1）-dimensions in an antiferromagnetic biaxial-anisotropy-spin-chain are obtained explicitly in the strong anisotropy limit, which interpolate between degenerate equilibrium orientations of the Neel vector along easy axis and are seen to be responsible for quantum tunneling. Macroscopic quantum coherence of the domain walls is demonstrated in terms of the instantons.
基金supported by National Natural Science Foundation of China (Grant No.10871226)Natural Science Foundation of Zhejiang Province (Grant No. Y6100096)
文摘In the present paper,we provide an error bound for the learning rates of the regularized Shannon sampling learning scheme when the hypothesis space is a reproducing kernel Hilbert space(RKHS) derived by a Mercer kernel and a determined net.We show that if the sample is taken according to the determined set,then,the sample error can be bounded by the Mercer matrix with respect to the samples and the determined net.The regularization error may be bounded by the approximation order of the reproducing kernel Hilbert space interpolation operator.The paper is an investigation on a remark provided by Smale and Zhou.
基金supported by the National Natural Science Foundation of China under Grant No.11688101
文摘This paper presents an improved early termination algorithm for sparse black box multivariate polynomials, which reduces the interpolation problem into several sub-interpolation problems with less variables and fewer terms. Actually, all interpolations are eventually reduced to the interpolation of a list of polynomials with less terms than that of the original polynomial. Extensive experiments show that the new algorithm is much faster than the original algorithm.
基金Supported by the National Natural Science Foundation of China under Grant No. 61173050
文摘In this paper,we study two different nonlinear interpolating paths in adiabatic evolution algorithms for solving a particular class of quantum search problems where both the initial and final Hamiltonian are one-dimensional projector Hamiltonians on the corresponding ground state.If the overlap between the initial state and final state of the quantum system is not equal to zero,both of these models can provide a constant time speedup over the usual adiabatic algorithms by increasing some another corresponding "complexity".But when the initial state has a zero overlap with the solution state in the problem,the second model leads to an infinite time complexity of the algorithm for whatever interpolating functions being applied while the first one can still provide a constant running time.However,inspired by a related reference,a variant of the first model can be constructed which also fails for the problem when the overlap is exactly equal to zero if we want to make up the "intrinsic" fault of the second model - an increase in energy.Two concrete theorems are given to serve as explanations why neither of these two models can improve the usual adiabatic evolution algorithms for the phenomenon above.These just tell us what should be noted when using certain nonlinear evolution paths in adiabatic quantum algorithms for some special kind of problems.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10975184,11047117,11105222,and 11105223
文摘In this article, we test the nature of X（3872）, which is assumed to be a P-wave [cq]-scalar-diquark [cq]- axial-vector-antidiquark tetraquark state with JP = 2^-. The interpolating current representing the JP = 2^- state is proposed. Technically, contributions of the operators up to dimension six are included in the operator product expansion. The mass obtained for such state is m2- = （4.38±0.15） GeV. We conclude that it is impossible to describe the X（3872） structure as JV = 2^- tetraauark state.
基金Project supported by the National Natural Science Foundation of China (No.10171111, No.10371734)and the Foundation of Advanced Research Center, Zhongshan University.
文摘The authors prove the Hardy-Littlewood-Sobolev theorems for generalized fractional integrals L?α/2 for 0 < α < n/m, where L is a complex elliptic operator of arbitrary order 2m on Rn.
基金Supported by the National Natural Science Foundation of China under Grant No.41574076the Young Core Teacher Scheme of Henan Province under Grant No.2014GGJS-108the Fundamental and Cutting-edge Technology Research Program of Henan Province under Grant No.152300410218
文摘We compare the direct free energy interpolation(DFEI) method and the quasi-harmonic approximation(QHA) in calculating of the equation of states and thermodynamic properties of prototype Al. The Gibbs free energy of Al is calculated using the DFEI method based on the high-temperature phonon density of states reduced from classical molecular dynamics simulations. Then, we reproduce the thermal expansion coefficients, the specific heat, the isothermal bulk modulus of Al accurately. By comparing the results from the DFEI method and the QHA, we find that the DFEI method is indeed more accurate in calculating anharmonic properties than the QHA.
