A new necessary conditions for separability of mixed states in bipartite and multipartite quantum systems of arbitrary dimensions are presented. This method requires only a few local measurements. If a quantum state i...A new necessary conditions for separability of mixed states in bipartite and multipartite quantum systems of arbitrary dimensions are presented. This method requires only a few local measurements. If a quantum state in a bipartite （or multipartite） system of arbitrary dimension is separable, we show that the trace norm of a constructive matrix is less than or equal to 1.展开更多
In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be est...In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.展开更多
We consider the sufficient and necessary conditions for the formal triangular matrix ring being right minsymmetric, right DS, semicommutative, respectively.
Cubic boron nitride （c-BN） thin films are deposited on p-type Si wafers using radio frequency （RF） sputtering and then doped by implanting S ions. Wile implantation energy of the ions is 19 keV, and the implantati...Cubic boron nitride （c-BN） thin films are deposited on p-type Si wafers using radio frequency （RF） sputtering and then doped by implanting S ions. Wile implantation energy of the ions is 19 keV, and the implantation dose is between 1015 ions/cm2 and 1016 ions/cm2. The doped c-BN thin films are then annealed at a temperature between 400℃ and 800℃. The results show that the surface resistivity of doped and annealed c-BN thin films is lowered by two to three orders, and the activation energy of c-BN thin films is 0.18 eV.展开更多
We restudy the master-equation approach to aggregation in freeway traffic based on the theory of birth-death process, in which the clustering behaviour in one-lane freeway traffic model is investigated. The transition...We restudy the master-equation approach to aggregation in freeway traffic based on the theory of birth-death process, in which the clustering behaviour in one-lane freeway traffic model is investigated. The transition probabilities for the jump processes are reconstructed by using Greenshields＇ model, and the equation of the mean size of the cluster at any time t is derived from the birth^death equation. Numerical experiments show the clustering behaviours varying with time very well.展开更多
The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boun...The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.展开更多
Digital holographic microscopy has been a powerful metrological technique for phase-contrast imaging.However inherent phase aberrations always exist and degrade the quality of the phase-contrast images.A surface fitti...Digital holographic microscopy has been a powerful metrological technique for phase-contrast imaging.However inherent phase aberrations always exist and degrade the quality of the phase-contrast images.A surface fitting method based on an improved mathematic model is proposed,which can be used to remove the phase aberrations without any pre-knowledge of the setup or manual operation.The improved mathematic model includes not only the usual terms but also the cross terms and the high order terms to describe the phase aberrations with high accuracy.Meanwhile,a non-iterative algorithm is used to solve the parametersand thus less computational load is imposed.The proposed method is applied to the live imaging of cells.The experimental results verify its validity.展开更多
Rubrene thin films are deposited on quartz substrates and silver nanoparticles （Ag NPs） films by the thermal evapo- ration technique. The optical properties of rubrene thin film are investigated in a spectral range ...Rubrene thin films are deposited on quartz substrates and silver nanoparticles （Ag NPs） films by the thermal evapo- ration technique. The optical properties of rubrene thin film are investigated in a spectral range of 190 nm-1600 nm. The analysis of the absorption coefficient （a） reveals direct allowed transition with a corresponding energy of 2.24 eV. The photoluminescence （PL） peak of the mbrene thin film is observed to be at 563 nm （2.21 eV）. With the use ofAg NPs which are fabricated by radio-frequency （RF） rnagnetron sputtering on the quartz, the PL intensity is 8.5 times that of as-deposited rubrene thin film. It is attributed to the fact that the surface plasmon enhances the photoluminescence.展开更多
In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance m...In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a penalized maximum likelihood method for variable selection in joint mean and covariance models based on this decomposition. Under certain regularity conditions, we establish the consistency and asymptotic normality of the penalized maximum likelihood estimators of parameters in the models. Simulation studies are undertaken to assess the finite sample performance of the proposed variable selection procedure.展开更多
We propose a simplified model to analyse the temporary behaviour of transmittance for holographic photopolyreefs, based on the existing first-harmonic diffusion theory, with assumptions of constant polymerization coef...We propose a simplified model to analyse the temporary behaviour of transmittance for holographic photopolyreefs, based on the existing first-harmonic diffusion theory, with assumptions of constant polymerization coefficient and negligible diffusion effect for noise gratings. By applying this model to measure real-fime transmittance of our novel blue-sensitized photopolymer, the bleaching time constant of dye and polymerization rate are extracted, and the effect of the material composite on the noise property is revealed. This provides a prompt method to assess the performances of holographic photopolymers.展开更多
CdGd2 （WO4）4 -δ single crystal was grown using the Czochralski＇s method. The crystal structure was tetragonal seheelite with lattice parameters a = b = 0.5203 nm and c = 1. 1359 nm. There were vacancies of （WO4）...CdGd2 （WO4）4 -δ single crystal was grown using the Czochralski＇s method. The crystal structure was tetragonal seheelite with lattice parameters a = b = 0.5203 nm and c = 1. 1359 nm. There were vacancies of （WO4）^2- , therefore, there were some Gd^2＋ ions. Langevin paramagnetism and anisotropy were observed from the δ-T curves at room temperature. The susceptibility X//was 3.5018×10^-3, and X⊥ was 3.4403× 10^-2. The anisotropy was also observed in the electron spin resonance （ESR） experiments. The anisotropic Land6 factors were g//= 2. 1333 and g~ = 2. 8411. The direction of easy magnetization was in the α-b plane. Anisotropic paramagnetic Curie constants C//and C⊥ were not only related to macroscopic a that was observed through the experiment, but were also related to J⊥ and J//, which were the microscopic quantum numbers of the Gd^2＋ and Gd^3｜ ions. Based on the detailed analyses, the proportion of 36.8% of Gd^3＋ ions to 63.2% of Gd^2＋ ions in the Gd ions of the CdGd2（WO4）4-δ crystal was calculated, and δ was 0.638 in the single crystal.展开更多
This paper addresses the aliasing error in multiresolution analysis associated with a 2× 2 dilation expression of the Fourier transform of the aliasing error optimal L^2（R^2）-norm estimation of the aliasing err...This paper addresses the aliasing error in multiresolution analysis associated with a 2× 2 dilation expression of the Fourier transform of the aliasing error optimal L^2（R^2）-norm estimation of the aliasing error. the setting of a class of bidimensional matrix of determinant ±2. The explicit is established, from which we obtain an展开更多
In this paper, we mainly study the global L2 stability for large solutions to the MHD equations in three-dimensional bounded or unbounded domains. Under suitable conditions of the large solutions, it is shown that the...In this paper, we mainly study the global L2 stability for large solutions to the MHD equations in three-dimensional bounded or unbounded domains. Under suitable conditions of the large solutions, it is shown that the large solutions are stable. And we obtain the equivalent condition of this stability condition. Moreover, the global existence and the stability of two-dimensional MHD equations under three-dimensional perturbations are also established.展开更多
Terahertz time-domaln spectroscopy （THz-TDS） is used to study the spectral response of lithium niobate crystals （LiNbO3） in the far infrared region. The optical constants are derived from the measured complex refr...Terahertz time-domaln spectroscopy （THz-TDS） is used to study the spectral response of lithium niobate crystals （LiNbO3） in the far infrared region. The optical constants are derived from the measured complex refractive index. A giant birefringence is observed in this material, and the average refractive-index difference between the ordinary wave and the extraordinary wave, no - ne, can reach up to about 1.6. Such a large birefrlngence is attributed to the different p honon modes orAl（z） and E （ x , y ）. This unusual property makes LiNbO3 a promising material to be used as a functional material in the terahertz region, e.g. employed as wave-plates and polarization separators.展开更多
In this paper, we study the effects of Pr substitution on the hydrogenating process and magnetocaloric properties of La（1-x）PrxFe11.4Si1.6Hy hydrides. The powder x-ray diffraction patterns of the La1-xPrxFe11.4Si1.6...In this paper, we study the effects of Pr substitution on the hydrogenating process and magnetocaloric properties of La（1-x）PrxFe11.4Si1.6Hy hydrides. The powder x-ray diffraction patterns of the La1-xPrxFe11.4Si1.6 and its hydrides show that each of the alloys is crystallized into the single phase of cubic Na Zn13-type structure. There are hydrogen-absorbing plateaus under 0.4938 MPa and 0.4882 MPa in the absorbing curves for the La0.8Pr0.2Fe11.4Si1.6 and La0.6Pr0.4Fe11.4Si1.6 compounds. The releasing processes lag behind the absorbing process, which is obviously different from the coincidence between absorbing and releasing curves of the La Fe11.4Si1.6 compound. The remnant hydrogen content for La0.6Pr0.4Fe11.4Si1.6 is significantly more than that for La0.8Pr0.2Fe11.4Si1.6 after hydrogen desorption, indicating that more substitutions of Pr for La are beneficial to retaining more hydrogen atoms in the alloys. The values of maximum magnetic entropy change are 14.91 J/kg·K and 17.995 J/kg·K for La0.8Pr0.2Fe11.4Si1.6H0.13 and La0.6Pr0.4Fe11.4Si1.6H0.87,respectively.展开更多
In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model.Different from others studies,we consider the physical case that the mobilities of the charges are different..The...In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model.Different from others studies,we consider the physical case that the mobilities of the charges are different..The quasi-neutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multi-scaling asymptotic expansions.展开更多
We investigate the entanglement of formation for a class of high-dimensional quantum mixed states. We present a kind of generalized concurrence for a class of high-dimensional quantum pure states such that the entangl...We investigate the entanglement of formation for a class of high-dimensional quantum mixed states. We present a kind of generalized concurrence for a class of high-dimensional quantum pure states such that the entanglement of formation is a monotonically increasing convex function of the generallzed concurrence, from the monotonicity and convexity the entanglement of formafion for a class of high-dimensional mixed states has been calculated analytically,展开更多
Dynamics of ions in biological ion channels has been classically analyzed using several types of Poisson-Nernst Planck (PNP) equations. However, due to complex interaction between individual ions and ions with the cha...Dynamics of ions in biological ion channels has been classically analyzed using several types of Poisson-Nernst Planck (PNP) equations. However, due to complex interaction between individual ions and ions with the channel walls, minimal incorporation of these interaction factors in the models to describe the flow phenomena accurately has been done. In this paper, we aim at formulating a modified PNP equation which constitutes finite size effects to capture ions interactions in the channel using Lennard Jonnes (LJ) potential theory. Particularly, the study examines existence and uniqueness of the approximate analytical solutions of the mPNP equations, First, by obtaining the priori energy estimate and providing solution bounds, and finally constructing the approximate solutions and establishing its convergence in a finite dimensional subspace in <em>L</em><sup>2</sup>, the approximate solution of the linearized mPNP equations was found to converge to the analytical solution, hence proof of existence.展开更多
The structures,grain sizes and magnetism were analyzed and computed for three typical samples:the stock of polycrystalline metal Gd(sample 1),the bulk nanocrystalline Gd prepared by spark plasma sintering(SPS) techniq...The structures,grain sizes and magnetism were analyzed and computed for three typical samples:the stock of polycrystalline metal Gd(sample 1),the bulk nanocrystalline Gd prepared by spark plasma sintering(SPS) technique and subjected to the annealing process of 623 K for 0.5 h(sample 2) and the bulk nanocrystalline Gd prepared by the SPS technique at 573 K(sample 3).The computation results indicated that the sample 3 had the efficiency of space filling up to 99.38%.The computation results of magnetization i...展开更多
基金Supported by the National Natural Science Foundation of China under Grant No10375038, the Natural Science Foundation of Beijing under Grant No1042004, the Doctor Research Star-up Foundation of Beijing University of Technology under grant No 5200601200151, and the Science Research Foundation of Beijing University of Technology under Grant No 9700601200151.
文摘A new necessary conditions for separability of mixed states in bipartite and multipartite quantum systems of arbitrary dimensions are presented. This method requires only a few local measurements. If a quantum state in a bipartite （or multipartite） system of arbitrary dimension is separable, we show that the trace norm of a constructive matrix is less than or equal to 1.
基金Supported by the National Natural Science Foundation of China (10571008)the Natural Science Foundation of Henan (092300410149)the Core Teacher Foundationof Henan (2006141)
文摘In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.
基金Foundation item： Supported by the Fund of Beijing Education Committee（KM200610005024） Supported by the National Natural Science Foundation of China（10671061）
文摘We consider the sufficient and necessary conditions for the formal triangular matrix ring being right minsymmetric, right DS, semicommutative, respectively.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60876006 and 60376007)the Natural Science Foundation of Beijing, China (Grant No. 4072007)+2 种基金the Scientific Research Program of Beijing Municipal Commission of Education, China (Grant No.KM200910005018)the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, Chinathe Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality
文摘Cubic boron nitride （c-BN） thin films are deposited on p-type Si wafers using radio frequency （RF） sputtering and then doped by implanting S ions. Wile implantation energy of the ions is 19 keV, and the implantation dose is between 1015 ions/cm2 and 1016 ions/cm2. The doped c-BN thin films are then annealed at a temperature between 400℃ and 800℃. The results show that the surface resistivity of doped and annealed c-BN thin films is lowered by two to three orders, and the activation energy of c-BN thin films is 0.18 eV.
基金Project supported by the National Natural Science Foundation of China （Grant No 10435080）, the State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, China.
文摘We restudy the master-equation approach to aggregation in freeway traffic based on the theory of birth-death process, in which the clustering behaviour in one-lane freeway traffic model is investigated. The transition probabilities for the jump processes are reconstructed by using Greenshields＇ model, and the equation of the mean size of the cluster at any time t is derived from the birth^death equation. Numerical experiments show the clustering behaviours varying with time very well.
基金supported by NSFC(11371042)China 973 program(2011 CB808002)+2 种基金BSFC(1132006)CIT&TCD(20130312)the fund of the Beijing Education Committee(KZ 201210005005)
文摘The incompressible limit of the non-isentropic magnetohydrodynamic equations with zero thermal coefficient, in a two dimensional bounded domain with the Dirichlet condi- tion for velocity and perfectly conducting boundary condition for magnetic field, is rigorously justified.
基金by the National Natural Science Foundation of China under Grant No 61077004the Science Foundation of Education Commission of Beijing under Grant No KZ200910005001Innovative Talent and Team Development for Serving Beijing.
文摘Digital holographic microscopy has been a powerful metrological technique for phase-contrast imaging.However inherent phase aberrations always exist and degrade the quality of the phase-contrast images.A surface fitting method based on an improved mathematic model is proposed,which can be used to remove the phase aberrations without any pre-knowledge of the setup or manual operation.The improved mathematic model includes not only the usual terms but also the cross terms and the high order terms to describe the phase aberrations with high accuracy.Meanwhile,a non-iterative algorithm is used to solve the parametersand thus less computational load is imposed.The proposed method is applied to the live imaging of cells.The experimental results verify its validity.
基金Project supported by the Funding for the Development Project of Beijing Municipal Education Commission of Science and Technology,China(Grant No.KZ201410005008)the Natural Science Foundation of Beijing City,China(Grant No.4102014)the Graduate Science Fund of the Beijing University of Technology,China(Grant No.ykj-2013-9835)
文摘Rubrene thin films are deposited on quartz substrates and silver nanoparticles （Ag NPs） films by the thermal evapo- ration technique. The optical properties of rubrene thin film are investigated in a spectral range of 190 nm-1600 nm. The analysis of the absorption coefficient （a） reveals direct allowed transition with a corresponding energy of 2.24 eV. The photoluminescence （PL） peak of the mbrene thin film is observed to be at 563 nm （2.21 eV）. With the use ofAg NPs which are fabricated by radio-frequency （RF） rnagnetron sputtering on the quartz, the PL intensity is 8.5 times that of as-deposited rubrene thin film. It is attributed to the fact that the surface plasmon enhances the photoluminescence.
文摘In this paper we reparameterize covariance structures in longitudinal data analysis through the modified Cholesky decomposition of itself. Based on this modified Cholesky decomposition, the within-subject covariance matrix is decomposed into a unit lower triangular matrix involving moving average coefficients and a diagonal matrix involving innovation variances, which are modeled as linear functions of covariates. Then, we propose a penalized maximum likelihood method for variable selection in joint mean and covariance models based on this decomposition. Under certain regularity conditions, we establish the consistency and asymptotic normality of the penalized maximum likelihood estimators of parameters in the models. Simulation studies are undertaken to assess the finite sample performance of the proposed variable selection procedure.
基金Supported by the National Natural Science Foundation of China under Grant No 60477004, and the Natural Science Foundation of Beijing under Grant No 4071001.
文摘We propose a simplified model to analyse the temporary behaviour of transmittance for holographic photopolyreefs, based on the existing first-harmonic diffusion theory, with assumptions of constant polymerization coefficient and negligible diffusion effect for noise gratings. By applying this model to measure real-fime transmittance of our novel blue-sensitized photopolymer, the bleaching time constant of dye and polymerization rate are extracted, and the effect of the material composite on the noise property is revealed. This provides a prompt method to assess the performances of holographic photopolymers.
基金Project supported by the National Natural Science Foundation of China (69977005)
文摘CdGd2 （WO4）4 -δ single crystal was grown using the Czochralski＇s method. The crystal structure was tetragonal seheelite with lattice parameters a = b = 0.5203 nm and c = 1. 1359 nm. There were vacancies of （WO4）^2- , therefore, there were some Gd^2＋ ions. Langevin paramagnetism and anisotropy were observed from the δ-T curves at room temperature. The susceptibility X//was 3.5018×10^-3, and X⊥ was 3.4403× 10^-2. The anisotropy was also observed in the electron spin resonance （ESR） experiments. The anisotropic Land6 factors were g//= 2. 1333 and g~ = 2. 8411. The direction of easy magnetization was in the α-b plane. Anisotropic paramagnetic Curie constants C//and C⊥ were not only related to macroscopic a that was observed through the experiment, but were also related to J⊥ and J//, which were the microscopic quantum numbers of the Gd^2＋ and Gd^3｜ ions. Based on the detailed analyses, the proportion of 36.8% of Gd^3＋ ions to 63.2% of Gd^2＋ ions in the Gd ions of the CdGd2（WO4）4-δ crystal was calculated, and δ was 0.638 in the single crystal.
基金Supported by the National Natural Science Foundation of China (10671008)Beijing Natural Science Foundation (1092001)+2 种基金the Scientific Research Common Program of Beijing Municipal Commission of Educationthe Scientific Research Foundation for the Returned Overseas Chinese ScholarsState Education Ministry (SRF for ROCS, SEM)
文摘This paper addresses the aliasing error in multiresolution analysis associated with a 2× 2 dilation expression of the Fourier transform of the aliasing error optimal L^2（R^2）-norm estimation of the aliasing error. the setting of a class of bidimensional matrix of determinant ±2. The explicit is established, from which we obtain an
基金supported by 973 Program(2011CB711100)supported by NSFC (11171229)
文摘In this paper, we mainly study the global L2 stability for large solutions to the MHD equations in three-dimensional bounded or unbounded domains. Under suitable conditions of the large solutions, it is shown that the large solutions are stable. And we obtain the equivalent condition of this stability condition. Moreover, the global existence and the stability of two-dimensional MHD equations under three-dimensional perturbations are also established.
基金Supported by the National Natural Science Foundation of China under Grant No 10390160.
文摘Terahertz time-domaln spectroscopy （THz-TDS） is used to study the spectral response of lithium niobate crystals （LiNbO3） in the far infrared region. The optical constants are derived from the measured complex refractive index. A giant birefringence is observed in this material, and the average refractive-index difference between the ordinary wave and the extraordinary wave, no - ne, can reach up to about 1.6. Such a large birefrlngence is attributed to the different p honon modes orAl（z） and E （ x , y ）. This unusual property makes LiNbO3 a promising material to be used as a functional material in the terahertz region, e.g. employed as wave-plates and polarization separators.
基金supported by the National Natural Science Foundation of China(Grant Nos.51301008 and 51171003)the Beijing Natural Science Foundation,China(Grant No.1112005)
文摘In this paper, we study the effects of Pr substitution on the hydrogenating process and magnetocaloric properties of La（1-x）PrxFe11.4Si1.6Hy hydrides. The powder x-ray diffraction patterns of the La1-xPrxFe11.4Si1.6 and its hydrides show that each of the alloys is crystallized into the single phase of cubic Na Zn13-type structure. There are hydrogen-absorbing plateaus under 0.4938 MPa and 0.4882 MPa in the absorbing curves for the La0.8Pr0.2Fe11.4Si1.6 and La0.6Pr0.4Fe11.4Si1.6 compounds. The releasing processes lag behind the absorbing process, which is obviously different from the coincidence between absorbing and releasing curves of the La Fe11.4Si1.6 compound. The remnant hydrogen content for La0.6Pr0.4Fe11.4Si1.6 is significantly more than that for La0.8Pr0.2Fe11.4Si1.6 after hydrogen desorption, indicating that more substitutions of Pr for La are beneficial to retaining more hydrogen atoms in the alloys. The values of maximum magnetic entropy change are 14.91 J/kg·K and 17.995 J/kg·K for La0.8Pr0.2Fe11.4Si1.6H0.13 and La0.6Pr0.4Fe11.4Si1.6H0.87,respectively.
文摘In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model.Different from others studies,we consider the physical case that the mobilities of the charges are different..The quasi-neutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multi-scaling asymptotic expansions.
基金The project supported by National Natural Science Foundation of China under Grant No. 10375038, the Natural Science Foundation of Beijing under Grant No. 1042004
文摘We investigate the entanglement of formation for a class of high-dimensional quantum mixed states. We present a kind of generalized concurrence for a class of high-dimensional quantum pure states such that the entanglement of formation is a monotonically increasing convex function of the generallzed concurrence, from the monotonicity and convexity the entanglement of formafion for a class of high-dimensional mixed states has been calculated analytically,
文摘Dynamics of ions in biological ion channels has been classically analyzed using several types of Poisson-Nernst Planck (PNP) equations. However, due to complex interaction between individual ions and ions with the channel walls, minimal incorporation of these interaction factors in the models to describe the flow phenomena accurately has been done. In this paper, we aim at formulating a modified PNP equation which constitutes finite size effects to capture ions interactions in the channel using Lennard Jonnes (LJ) potential theory. Particularly, the study examines existence and uniqueness of the approximate analytical solutions of the mPNP equations, First, by obtaining the priori energy estimate and providing solution bounds, and finally constructing the approximate solutions and establishing its convergence in a finite dimensional subspace in <em>L</em><sup>2</sup>, the approximate solution of the linearized mPNP equations was found to converge to the analytical solution, hence proof of existence.
基金supported by the National Basic Research Program of China (2006CB705601)the National Natural Science Foundation of China (50771002)
文摘The structures,grain sizes and magnetism were analyzed and computed for three typical samples:the stock of polycrystalline metal Gd(sample 1),the bulk nanocrystalline Gd prepared by spark plasma sintering(SPS) technique and subjected to the annealing process of 623 K for 0.5 h(sample 2) and the bulk nanocrystalline Gd prepared by the SPS technique at 573 K(sample 3).The computation results indicated that the sample 3 had the efficiency of space filling up to 99.38%.The computation results of magnetization i...
