In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, bas...In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.展开更多
As an emerging molecular imaging modality,cone-beam X-ray luminescence computed tomog-raphy(CB-XLCT)uses X-ray-excitable probes to produce near-infrared(NIR)luminescence and then reconst ructs three-dimensional(3D)dis...As an emerging molecular imaging modality,cone-beam X-ray luminescence computed tomog-raphy(CB-XLCT)uses X-ray-excitable probes to produce near-infrared(NIR)luminescence and then reconst ructs three-dimensional(3D)distribution of the probes from surface measurements.A proper photon-transportation model is critical to accuracy of XLCT.Here,we presented a systematic comparison between the common-used Monte Carlo model and simplified spherical harmonics(SPN).The performance of the two methods was evaluated over several main spec-trums using a known XLCT material.We designed both a global measurement based on the cosine similarity and a locally-averaged relative error,to quantitatively assess these methods.The results show that the SP_(3) could reach a good balance between the modeling accuracy and computational efficiency for all of the tested emission spectrums.Besides,the SP_(1)(which is equivalent to the difusion equation(DE))can be a reasonable alternative model for emission wavelength over 692nm.In vivo experiment further demonstrates the reconstruction perfor-mance of the SP:and DE.This study would provide a valuable guidance for modeling the photon-transportation in CB-XLCT.展开更多
This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of tho...This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of those on the circle.展开更多
As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the researc...As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.展开更多
The derivation of the harmonic approximation of the Hamiltonian of a model of coupled three-dimensional harmonic oscillator is presented. It is shown how the splitting of the total Hamiltonian into the intrinsic and c...The derivation of the harmonic approximation of the Hamiltonian of a model of coupled three-dimensional harmonic oscillator is presented. It is shown how the splitting of the total Hamiltonian into the intrinsic and collective Hamiltonians leads to the description of the mechanism for energy dissipation in physical systems.展开更多
We revisit the harmonic approximation (HA) for a large Josephson junction interacting with some charge qubits through the variational approach for the quantum dynamics of the junction-qubit coupling system. By making ...We revisit the harmonic approximation (HA) for a large Josephson junction interacting with some charge qubits through the variational approach for the quantum dynamics of the junction-qubit coupling system. By making use of numerical calculation and analytical treatment, the conditions under which HA works well can be precisely presented to control the parameters implementing the two-qubit quantum logical gate through the couplings to the large junction with harmonic oscillator Hamiltonian.展开更多
A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-...A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived.展开更多
The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation metho...The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.展开更多
高斯过程通过概率建模能够有效地捕捉数据中的复杂关系,并提供关于预测结果的不确定性评估,是一个强大而灵活的工具.但由于矩阵求逆的较高计算复杂度,限制了模型在其他领域内的应用.本文针对高斯过程模型的矩阵求逆问题,提出了一种基于...高斯过程通过概率建模能够有效地捕捉数据中的复杂关系,并提供关于预测结果的不确定性评估,是一个强大而灵活的工具.但由于矩阵求逆的较高计算复杂度,限制了模型在其他领域内的应用.本文针对高斯过程模型的矩阵求逆问题,提出了一种基于球谐函数的高斯过程近似模型(Variational Sparse Gaussian Processes based on Spherical Harmonic,SHVSGP),通过球谐函数将数据映射到超球面上,在一个不同于数据原始输入域的空间中寻找一个更紧凑的输入特征代表集,使得产生的稀疏高斯过程模型能够包含有更丰富的信息特征,同时获得诱导变量相关的对角协方差矩阵,这极大简化了矩阵运算的复杂度,节省了计算成本.本文将SHVSGP模型与当下流行的其他近似方法在大规模数据集上进行比较,结果表明SHVSGP模型可以获得高效且精确的预测.展开更多
This article is a improvement on author＇s early work （Acta Mathematica Scientia, Vol.30 No.2 Ser.A 2010）. In this article, there are two new contributions： 1） The restrictive conditions on approximation domain bo...This article is a improvement on author＇s early work （Acta Mathematica Scientia, Vol.30 No.2 Ser.A 2010）. In this article, there are two new contributions： 1） The restrictive conditions on approximation domain boundary is improved essentially. 2） The Fejer points is extended by perturbed Fejer points with stable order of approximation.展开更多
The narrow-gap semiconductor CsBi4Te6 is a promising material for low temperature thermoelectric applications. Its thermoelectric property is significantly better than the well-explored, high-performance thermoelectri...The narrow-gap semiconductor CsBi4Te6 is a promising material for low temperature thermoelectric applications. Its thermoelectric property is significantly better than the well-explored, high-performance thermoelectric material Bi2Te3 and related alloys. In this work, the thermal expansion and the heat capacity at constant pressure of CsBi4Te6 are determined within the quasiharmonic approximation within the density functional theory. Comparisons are made with available experimental data, as well as with calculated and measured data for Bi2Te3. The phonon band structures and the partial density of states are also investigated, and we find that both CsBi4Te6 and Bi2Te3 exhibit localized phonon states at low frequencies. At high temperatures, the decrease of the volume expansion with temperature indicates the potential of a good thermal conductivity in this temperature region.展开更多
A general spatial interpolation method for tidal properties has been developed by solving a partial differential equation with a combination of different orders of harmonic operators using a mixed finite element metho...A general spatial interpolation method for tidal properties has been developed by solving a partial differential equation with a combination of different orders of harmonic operators using a mixed finite element method. Numerically, the equation is solved implicitly without iteration on an unstructured triangular mesh grid. The paper demonstrates the performance of the method for tidal property fields with different characteristics, boundary complexity, number of input data points, and data point distribution. The method has been successfully applied under several different tidal environments, including an idealized distribution in a square basin, coamplitude and cophase lines in the Taylor semi-infiite rotating channel, and tide coamplitude and cophase lines in the Bohai Sea and Chesapeake Bay. Compared to Laplace’s equation that NOAA/NOS currently uses for interpolation in hydrographic and oceanographic applications, the multiple-order harmonic equation method eliminates the problem of singularities at data points, and produces interpolation results with better accuracy and precision.展开更多
We employed ab-initio calculations to investigate the structural and thermodynamic properties of Massicot or orthorhombic phase of PbO named β-PbO using the projector augmented-wave（PAW） method within the generaliz...We employed ab-initio calculations to investigate the structural and thermodynamic properties of Massicot or orthorhombic phase of PbO named β-PbO using the projector augmented-wave（PAW） method within the generalized gradient approximation（GGA）. The temperature and pressure dependence of bulk modulus, heat capacity at constant pressure and constant volume, entropy, thermal expansion coefficient and Grüneisen parameter were discussed. Accuracy of two different models, the Debye and Debye-Grüneisen which are based on the quasi-harmonic approximation（QHA） for producing thermodynamic properties of material were compared. According to calculation results, these two models can be used to designate thermodynamic properties for β-PbO with sensible accuracy over a wide range of temperatures and pressures, and our work on the properties of this structure will be useful for more deeply understanding various properties of this structure.展开更多
基金Supported by NSF of China(10531020)the Program of 985 Innovation Engieering on Information in Xiamen University(2004-2007).
文摘In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.
基金the School of Life Science and Technology of Xidian University for providing experimental data acquisition system.This work was supported by the National Natural Science Foundation of China under Grant(Nos.61372046,61401264,11571012,61601363,61640418,61572400)the Science and Technology Plan Program in Shaanxi Province of China under Grant(Nos.2013K12-20-12,2015KW-002)+2 种基金the Natural Science Research Plan Program in Shaanxi Province of China under Grant(No.2015JM6322)the Scienti¯c Research Founded by Shaanxi Provincial Education Department under Grant No.16JK1772the Scienti¯c Research Foundation of Northwest University under Grant Nos.338050018 and 338020012.
文摘As an emerging molecular imaging modality,cone-beam X-ray luminescence computed tomog-raphy(CB-XLCT)uses X-ray-excitable probes to produce near-infrared(NIR)luminescence and then reconst ructs three-dimensional(3D)distribution of the probes from surface measurements.A proper photon-transportation model is critical to accuracy of XLCT.Here,we presented a systematic comparison between the common-used Monte Carlo model and simplified spherical harmonics(SPN).The performance of the two methods was evaluated over several main spec-trums using a known XLCT material.We designed both a global measurement based on the cosine similarity and a locally-averaged relative error,to quantitatively assess these methods.The results show that the SP_(3) could reach a good balance between the modeling accuracy and computational efficiency for all of the tested emission spectrums.Besides,the SP_(1)(which is equivalent to the difusion equation(DE))can be a reasonable alternative model for emission wavelength over 692nm.In vivo experiment further demonstrates the reconstruction perfor-mance of the SP:and DE.This study would provide a valuable guidance for modeling the photon-transportation in CB-XLCT.
文摘This paper deals with the order of magnitude of the partial sums of the spherical harmonic series and its convergence rate in Bessel potential spaces. The partial results obtained in the paper are the analogue of those on the circle.
基金Supported by the NSF of China under the Grant 10471010partially by the NSERC Canada under Grant G121211001
文摘As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.
文摘The derivation of the harmonic approximation of the Hamiltonian of a model of coupled three-dimensional harmonic oscillator is presented. It is shown how the splitting of the total Hamiltonian into the intrinsic and collective Hamiltonians leads to the description of the mechanism for energy dissipation in physical systems.
基金the Cooperation Foundation of Nankai University，Tianjin University for research of nanoscience，国家自然科学基金
文摘We revisit the harmonic approximation (HA) for a large Josephson junction interacting with some charge qubits through the variational approach for the quantum dynamics of the junction-qubit coupling system. By making use of numerical calculation and analytical treatment, the conditions under which HA works well can be precisely presented to control the parameters implementing the two-qubit quantum logical gate through the couplings to the large junction with harmonic oscillator Hamiltonian.
文摘A manifestly gauge-invariant formulation of non-relativistic quantum mechanics is applied to the case of time-dependent harmonic oscillator in the magnetic dipole approximation. A general equation for obtaining gauge-invariant transition probability amplitudes is derived.
文摘The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.
文摘高斯过程通过概率建模能够有效地捕捉数据中的复杂关系,并提供关于预测结果的不确定性评估,是一个强大而灵活的工具.但由于矩阵求逆的较高计算复杂度,限制了模型在其他领域内的应用.本文针对高斯过程模型的矩阵求逆问题,提出了一种基于球谐函数的高斯过程近似模型(Variational Sparse Gaussian Processes based on Spherical Harmonic,SHVSGP),通过球谐函数将数据映射到超球面上,在一个不同于数据原始输入域的空间中寻找一个更紧凑的输入特征代表集,使得产生的稀疏高斯过程模型能够包含有更丰富的信息特征,同时获得诱导变量相关的对角协方差矩阵,这极大简化了矩阵运算的复杂度,节省了计算成本.本文将SHVSGP模型与当下流行的其他近似方法在大规模数据集上进行比较,结果表明SHVSGP模型可以获得高效且精确的预测.
基金supported by NSF of Henan Province P. R. China(974050900)
文摘This article is a improvement on author＇s early work （Acta Mathematica Scientia, Vol.30 No.2 Ser.A 2010）. In this article, there are two new contributions： 1） The restrictive conditions on approximation domain boundary is improved essentially. 2） The Fejer points is extended by perturbed Fejer points with stable order of approximation.
文摘The narrow-gap semiconductor CsBi4Te6 is a promising material for low temperature thermoelectric applications. Its thermoelectric property is significantly better than the well-explored, high-performance thermoelectric material Bi2Te3 and related alloys. In this work, the thermal expansion and the heat capacity at constant pressure of CsBi4Te6 are determined within the quasiharmonic approximation within the density functional theory. Comparisons are made with available experimental data, as well as with calculated and measured data for Bi2Te3. The phonon band structures and the partial density of states are also investigated, and we find that both CsBi4Te6 and Bi2Te3 exhibit localized phonon states at low frequencies. At high temperatures, the decrease of the volume expansion with temperature indicates the potential of a good thermal conductivity in this temperature region.
文摘A general spatial interpolation method for tidal properties has been developed by solving a partial differential equation with a combination of different orders of harmonic operators using a mixed finite element method. Numerically, the equation is solved implicitly without iteration on an unstructured triangular mesh grid. The paper demonstrates the performance of the method for tidal property fields with different characteristics, boundary complexity, number of input data points, and data point distribution. The method has been successfully applied under several different tidal environments, including an idealized distribution in a square basin, coamplitude and cophase lines in the Taylor semi-infiite rotating channel, and tide coamplitude and cophase lines in the Bohai Sea and Chesapeake Bay. Compared to Laplace’s equation that NOAA/NOS currently uses for interpolation in hydrographic and oceanographic applications, the multiple-order harmonic equation method eliminates the problem of singularities at data points, and produces interpolation results with better accuracy and precision.
基金Project supported by the Research Project of Islamic Azad University,Urmia Branch
文摘We employed ab-initio calculations to investigate the structural and thermodynamic properties of Massicot or orthorhombic phase of PbO named β-PbO using the projector augmented-wave（PAW） method within the generalized gradient approximation（GGA）. The temperature and pressure dependence of bulk modulus, heat capacity at constant pressure and constant volume, entropy, thermal expansion coefficient and Grüneisen parameter were discussed. Accuracy of two different models, the Debye and Debye-Grüneisen which are based on the quasi-harmonic approximation（QHA） for producing thermodynamic properties of material were compared. According to calculation results, these two models can be used to designate thermodynamic properties for β-PbO with sensible accuracy over a wide range of temperatures and pressures, and our work on the properties of this structure will be useful for more deeply understanding various properties of this structure.
