A microscopic phase-field model was used to investigate a directional coarsening mechanism caused by the anisotropic growth of long period stacking and different effects of phases on precipitation in Ni-Al-V alloy.The...A microscopic phase-field model was used to investigate a directional coarsening mechanism caused by the anisotropic growth of long period stacking and different effects of phases on precipitation in Ni-Al-V alloy.The results show that DO22 mainly coarsens along its short axis,which may press the neighboring L12,leading to the interaction among atoms.Diffusion channels of Al are formed in the direction where the mismatch between γ' and γ reduces;the occupation probabilities are anisotropic in space;and direction coarsening of L12 occurs finally.With a rise of ageing temperature,phases appear later and DO22 is much later at a higher temperature,the average occupation probabilities of Al and V reduce,and Al changes more than V.展开更多
In this study,the micro-failure process and failure mechanism of a typical brittle rock under uniaxial compression are investigated via continuous real-time measurement of wave velocities.The experimental results indi...In this study,the micro-failure process and failure mechanism of a typical brittle rock under uniaxial compression are investigated via continuous real-time measurement of wave velocities.The experimental results indicate that the evolutions of wave velocities became progressively anisotropic under uniaxial loading due to the direction-dependent development of micro-damage.A wave velocity model considering the inner anisotropic crack evolution is proposed to accurately describe the variations of wave velocities during uniaxial compression testing.Based on which,the effective elastic parameters are inferred by a transverse isotropic constitutive model,and the evolutions of the crack density are inversed using a self-consistent damage model.It is found that the propagation of axial cracks dominates the failure process of brittle rock under uniaxial loading and oblique shear cracks develop with the appearance of macrocrack.展开更多
Experimental evidence has indicated that clay exhibits strain-softening response under undrained compression following anisotropic consolidation.The purpose of this work was to propose a modeling method under critical...Experimental evidence has indicated that clay exhibits strain-softening response under undrained compression following anisotropic consolidation.The purpose of this work was to propose a modeling method under critical state theory of soil mechanics.Based on experimental data on different types of clay,a simple double-surface model was developed considering explicitly the location of critical state by incorporating the density state into constitutive equations.The model was then used to simulate undrained triaxial compression tests performed on isotropically and anisotropically consolidated samples with different stress ratios.The predictions were compared with experimental results.All simulations demonstrate that the proposed approach is capable of describing the drained and undrained compression behaviors following isotropic and anisotropic consolidations.展开更多
Photodissociation dynamics of ketene at 218 nm has been investigated using the velocity map ion-imaging method. Both angular and translational energy distributions for the CO products at different rotational and vibra...Photodissociation dynamics of ketene at 218 nm has been investigated using the velocity map ion-imaging method. Both angular and translational energy distributions for the CO products at different rotational and vibrational states have been obtained. The 2+1 REMPI spectrum of CO products is also obtained. The results are as bellow: (i) CO products in the first two vibrational states ( v"=0 and v"=1 ) exhibit significant rotational excitation. Furthermore the rotational excitation of CO at the v"=0 level is noticeably higher than that at the v"=1 level. (ii) It was found that the major photodissociation pathway of ketene at 218 nm is the CH2(ǎ^1A1)+CO(X^1∑^+) channel, while the CH2(b^1B1)+CO(X^1∑^+) channel and the CH2(X^3B1)+CO(X^1E^+) channel are also likely present, (iii) The anisotropy parameters β of CO different rovibronic states all appear to be larger than zero. No significant difference is observed at the two vibrational states,展开更多
Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel m...Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel method was proposed to estimate the equivalent strain hardening exponent of anisotropic materials based on an equivalent energy method. By performing extensive finite element (FE) simulations of the spherical indentation on anisotropic materials, dimensionless function was proposed to correlate the strain hardening exponent of anisotropic materials with the indentation imprint parameters. And then, a mathematic expression on the strain hardening exponent of anisotropic materials with the indentation imprint was established to estimate the equivalent strain hardening exponent of anisotropic materials by directly solving this dimensionless function. Additionally, Meyer equation was modified to determine the yield stress of anisotropic materials. The effectiveness and reliability of the new method were verified by the numerical examples and by its application on the TC1M engineering material.展开更多
Despite the high amount of scientific work dedicated to the gold nanoparticles in catalysis, most of the research has been performed utilising supported nanoparticles obtained by traditional impreg‐nation of gold sal...Despite the high amount of scientific work dedicated to the gold nanoparticles in catalysis, most of the research has been performed utilising supported nanoparticles obtained by traditional impreg‐nation of gold salts onto a support, co‐precipitation or deposition‐precipitation methods which do not benefit from the recent advances in nanotechnologies. Only more recently, gold catalyst scien‐tists have been exploiting the potential of preforming the metal nanoparticles in a colloidal suspen‐sion before immobilisation with great results in terms of catalytic activity and the morphology con‐trol of mono‐and bimetallic catalysts. On the other hand, the last decade has seen the emergence of more advanced control in gold metal nanoparticle synthesis, resulting in a variety of anisotropic gold nanoparticles with easily accessible new morphologies that offer control over the coordination of surface atoms and the optical properties of the nanoparticles (tunable plasmon band) with im‐mense relevance for catalysis. Such morphologies include nanorods, nanostars, nanoflowers, den‐dritic nanostructures or polyhedral nanoparticles to mention a few. In addition to highlighting newly developed methods and properties of anisotropic gold nanoparticles, in this review we ex‐amine the emerging literature that clearly indicates the often superior catalytic performance and amazing potential of these nanoparticles to transform the field of heterogeneous catalysis by gold by offering potentially higher catalytic performance, control over exposed active sites, robustness and tunability for thermal‐, electro‐and photocatalysis.展开更多
Exchange anisotropy in FM/AFM bilayers has given a lot of static magnetization properties such as enhanced coercivity and magnetization loop shifts. These phenomena are primarily from the effective anisotropies introd...Exchange anisotropy in FM/AFM bilayers has given a lot of static magnetization properties such as enhanced coercivity and magnetization loop shifts. These phenomena are primarily from the effective anisotropies introduced into a ferromagnet by exchange coupling with a strongly anisotropic antiferromagnet. These effective anisotropies can also be used to explain the dynamic consequences of exchange-biased bilayers. In this article, the dynamic consequences such as exchange-induced susceptibility, exchange-induced permeability, and the corresponding domain wall characteristics in the exchange-biased structures of ferromagnet/antiferromagnetl/antiferromagnet2 are studied. The results show that the second antiferromagnetic layer can largely affect the dynamic consequences of exchange-blazed bilayers. Especially in the case of critical temperature, the effects become more obvious. Practically, the exchange anisotropy of biased bilayer system can be tuned by exchange coupling with the second antiferromagnetic layer.展开更多
Some materials form better than others, moreover, a material that has the best formability for one stamping may behave very poorly in a stamping of another Configuration. The forming limit of a metal sheet is generall...Some materials form better than others, moreover, a material that has the best formability for one stamping may behave very poorly in a stamping of another Configuration. The forming limit of a metal sheet is generally given in terms of the limiting principal strains under different loading conditions and represented by the so-called FLD (forming limit diagram). In view of the difficulty to experimentally determine the forming limits, many researchers have sought to predict FLD. The formability of sheet metal has frequently been expressed by the value of strain hardening exponent and plastic anisotropy ratio. The stress-strain and hardening behaviour of a material is very important in determining its resistance to plastic instability. For these reasons, extensive test programs are often carried out in an attempt to correlate material formability with value of some mechanical properties. In this study, mechanical properties and the FLD of the AMS 5596 sheet metal was determined by using uniaxial tensile test and Marciniak's flat bottomed punch test respectively.展开更多
A novel rcgularization-based approach is presented for super-resolution reconstruction in order to achieve good tradeoff between noise removal and edge preservation. The method is developed by using L1 norm as data fi...A novel rcgularization-based approach is presented for super-resolution reconstruction in order to achieve good tradeoff between noise removal and edge preservation. The method is developed by using L1 norm as data fidelity term and anisotropic fourth-order diffusion model as a regularization item to constrain the smoothness of the reconstructed images. To evaluate and prove the performance of the proposed method, series of experiments and comparisons with some existing methods including bi-cubic interpolation method and bilateral total variation method are carried out. Numerical results on synthetic data show that the PSNR improvement of the proposed method is approximately 1.0906 dB on average compared to bilateral total variation method, and the results on real videos indicate that the proposed algorithm is also effective in terms of removing visual artifacts and preserving edges in restored images.展开更多
Silicon bulk etching is an important part of micro-electro-mechanical system(MEMS) technology. In this work, a novel etching method is proposed based on the vapor from tetramethylammonium hydroxide(TMAH) solution heat...Silicon bulk etching is an important part of micro-electro-mechanical system(MEMS) technology. In this work, a novel etching method is proposed based on the vapor from tetramethylammonium hydroxide(TMAH) solution heated up to boiling point. The monocrystalline silicon wafer is positioned over the solution surface and can be anisotropically etched by the produced vapor. This etching method does not rely on the expensive vacuum equipment used in dry etching. Meanwhile, it presents several advantages like low roughness, high etching rate and high uniformity compared with the conventional wet etching methods. The etching rate and roughness can reach 2.13 μm/min and 1.02 nm, respectively. Furthermore,the diaphragm structure and Al-based pattern on the non-etched side of wafer can maintain intact without any damage during the back-cavity fabrication. Finally, an etching mechanism has been proposed to illustrate the observed experimental phenomenon. It is suggested that there is a water thin film on the etched surface during the solution evaporation. It is in this water layer that the ionization and etching reaction of TMAH proceed, facilitating the desorption of hydrogen bubble and the enhancement of molecular exchange rate. This new etching method is of great significance in the low-cost and high-quality micro-electromechanical system industrial fabrication.展开更多
In this paper we mainly discuss the nonconforming fimte element method for second order elliptic boundary value problems on anisotropic meshes. By changing thediscretization form(i.e., by use of numerical quadrature ...In this paper we mainly discuss the nonconforming fimte element method for second order elliptic boundary value problems on anisotropic meshes. By changing thediscretization form(i.e., by use of numerical quadrature in the procedure of computing the left load), we obtain the optimal estimate O(h), which is as same as in the traditionalfinite element analysis when the load f ∈ H1 (Ω)η Co(Ω) which is weaker than the previousstudies. The results obtained in this paper are also valid to the conforming triangular elementand nonconforming Carey's element.展开更多
In a previous study, structure of silica gels prepared in a high magnetic field was investigated. While a direct application of such anisotropic silica gels is for an optical anisotropic medium possessing chemical res...In a previous study, structure of silica gels prepared in a high magnetic field was investigated. While a direct application of such anisotropic silica gels is for an optical anisotropic medium possessing chemical resistance, we show here their possibility of medium in materials processing. In this direction, for example, silica hydrogels have so far been used as media of crystal growth. In this paper, as opposed to the soft-wet state, dried silica gels have been investigated. We have found that lead (II) nanocrystallites were formed induced by electron irradiation to lead (ll)-doped dried Hydrogels made from a sodium metasilicate solution doped with silica gels prepared in a high magnetic field such as B = 10 T. lead (II) acetate were prepared. The dried specimens were irradiated by electrons in a transmission electron microscope environment. Electron diffraction patterns indicated the crystallinity of lead (II) nanocrystallites depending on B. An advantage of this processing technique is that the crystallinity can be controlled through the strength of magnetic field B applied during gel preparation. Specific skills are not required to control the strength of magnetic field.展开更多
In this paper, we study the following degenerate critical elliptic equation with anisotropic coefficients-div(|x N | 2α▽u) = K(x)|x N | α·2 * (s)-s |u| 2 * (s)-2 u in R N ,where x = (x 1 , . . . , x N ) ∈ R N...In this paper, we study the following degenerate critical elliptic equation with anisotropic coefficients-div(|x N | 2α▽u) = K(x)|x N | α·2 * (s)-s |u| 2 * (s)-2 u in R N ,where x = (x 1 , . . . , x N ) ∈ R N , N≥3, α > 1/2, 0≤ s ≤2 and 2 * (s) = 2(N-s)/(N-2). Some basic properties of the degenerate elliptic operator -div(|x N |2α▽u) are investigated and some regularity, symmetry and uniqueness results for entire solutions of this equation are obtained. We also get some variational identities for solutions of this equation. As consequences, we obtain some nonexistence results for this equation.展开更多
文摘由于受数据采集时间、照射剂量、成像系统扫描的几何位置等因素的约束,计算机断层成像(CT)技术目前只能在有限角度范围或在较少的投影角度得到数据,这些都属于不完全角度重建问题。图像重建问题中的总变分(Total-Variation, TV)最小化模型使用基于交替方向法(alternating direction method, ADM)的稀疏优化算法能够在不完全角度的图像重建中获得较优的重建结果。然而,在极稀疏的角度数量下,各向同性TV最小化算法的重建精度不是很理想,存在进一步改善空间。本文针对该问题,通过基于稀疏优化的交替方向方法推导基于各向异性TV最小化的CT图像重建算法。实验结果表明,在稀疏角度重建中,本文提出的基于各向异性TV最小化重建算法与各向同性TV最小化重建算法相比,在稀疏性保持良好的基础上,重建精度上存在优势,综合性能方面表现更优异。
基金Projects(51075335,10902086,50875217) supported by the National Natural Science Foundation of ChinaProject(JC201005) supported by the Northwestern Polytechnical University Foundation for Fundamental Research,ChinaProject(CX201007) supported by the Doctorate Foundation of Northwestern Polytechnical University,China
文摘A microscopic phase-field model was used to investigate a directional coarsening mechanism caused by the anisotropic growth of long period stacking and different effects of phases on precipitation in Ni-Al-V alloy.The results show that DO22 mainly coarsens along its short axis,which may press the neighboring L12,leading to the interaction among atoms.Diffusion channels of Al are formed in the direction where the mismatch between γ' and γ reduces;the occupation probabilities are anisotropic in space;and direction coarsening of L12 occurs finally.With a rise of ageing temperature,phases appear later and DO22 is much later at a higher temperature,the average occupation probabilities of Al and V reduce,and Al changes more than V.
基金Projects(41502283,41772309)supported by the National Natural Science Foundation of ChinaProject(2017YFC1501302)supported by the National Key Research and Development Program of ChinaProject(2017ACA102)supported by the Major Program of Technological Innovation of Hubei Province,China。
文摘In this study,the micro-failure process and failure mechanism of a typical brittle rock under uniaxial compression are investigated via continuous real-time measurement of wave velocities.The experimental results indicate that the evolutions of wave velocities became progressively anisotropic under uniaxial loading due to the direction-dependent development of micro-damage.A wave velocity model considering the inner anisotropic crack evolution is proposed to accurately describe the variations of wave velocities during uniaxial compression testing.Based on which,the effective elastic parameters are inferred by a transverse isotropic constitutive model,and the evolutions of the crack density are inversed using a self-consistent damage model.It is found that the propagation of axial cracks dominates the failure process of brittle rock under uniaxial loading and oblique shear cracks develop with the appearance of macrocrack.
基金Project(SKLGP2011K013)supported by the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection,ChinaProject(20110073120012)supported by the Research Fund for the Doctoral Program of Higher Education of China+1 种基金Project(11PJ1405700)supported by the the Shanghai Pujiang Talent Plan,ChinaProject(41002091)supported by the National Natural Science Foundation of China
文摘Experimental evidence has indicated that clay exhibits strain-softening response under undrained compression following anisotropic consolidation.The purpose of this work was to propose a modeling method under critical state theory of soil mechanics.Based on experimental data on different types of clay,a simple double-surface model was developed considering explicitly the location of critical state by incorporating the density state into constitutive equations.The model was then used to simulate undrained triaxial compression tests performed on isotropically and anisotropically consolidated samples with different stress ratios.The predictions were compared with experimental results.All simulations demonstrate that the proposed approach is capable of describing the drained and undrained compression behaviors following isotropic and anisotropic consolidations.
基金This work is suppotted by the Chinese Academy of Sciences,the Ministry of Science and Technology,and the National Natural Science Foundation of China.
文摘Photodissociation dynamics of ketene at 218 nm has been investigated using the velocity map ion-imaging method. Both angular and translational energy distributions for the CO products at different rotational and vibrational states have been obtained. The 2+1 REMPI spectrum of CO products is also obtained. The results are as bellow: (i) CO products in the first two vibrational states ( v"=0 and v"=1 ) exhibit significant rotational excitation. Furthermore the rotational excitation of CO at the v"=0 level is noticeably higher than that at the v"=1 level. (ii) It was found that the major photodissociation pathway of ketene at 218 nm is the CH2(ǎ^1A1)+CO(X^1∑^+) channel, while the CH2(b^1B1)+CO(X^1∑^+) channel and the CH2(X^3B1)+CO(X^1E^+) channel are also likely present, (iii) The anisotropy parameters β of CO different rovibronic states all appear to be larger than zero. No significant difference is observed at the two vibrational states,
基金Project(51675431)supported by the National Natural Science Foundation of China
文摘Uniaxial strain hardening exponent is not suitable for describing the strain hardening behaviors of the anisotropic materials, especially when material deforms in the multi-axial stress states. In this work, a novel method was proposed to estimate the equivalent strain hardening exponent of anisotropic materials based on an equivalent energy method. By performing extensive finite element (FE) simulations of the spherical indentation on anisotropic materials, dimensionless function was proposed to correlate the strain hardening exponent of anisotropic materials with the indentation imprint parameters. And then, a mathematic expression on the strain hardening exponent of anisotropic materials with the indentation imprint was established to estimate the equivalent strain hardening exponent of anisotropic materials by directly solving this dimensionless function. Additionally, Meyer equation was modified to determine the yield stress of anisotropic materials. The effectiveness and reliability of the new method were verified by the numerical examples and by its application on the TC1M engineering material.
基金supported by the Project from Institute of Chemical and Engineering Sciences (ICES), Singapore (ICES/15-1G4B01)~~
文摘Despite the high amount of scientific work dedicated to the gold nanoparticles in catalysis, most of the research has been performed utilising supported nanoparticles obtained by traditional impreg‐nation of gold salts onto a support, co‐precipitation or deposition‐precipitation methods which do not benefit from the recent advances in nanotechnologies. Only more recently, gold catalyst scien‐tists have been exploiting the potential of preforming the metal nanoparticles in a colloidal suspen‐sion before immobilisation with great results in terms of catalytic activity and the morphology con‐trol of mono‐and bimetallic catalysts. On the other hand, the last decade has seen the emergence of more advanced control in gold metal nanoparticle synthesis, resulting in a variety of anisotropic gold nanoparticles with easily accessible new morphologies that offer control over the coordination of surface atoms and the optical properties of the nanoparticles (tunable plasmon band) with im‐mense relevance for catalysis. Such morphologies include nanorods, nanostars, nanoflowers, den‐dritic nanostructures or polyhedral nanoparticles to mention a few. In addition to highlighting newly developed methods and properties of anisotropic gold nanoparticles, in this review we ex‐amine the emerging literature that clearly indicates the often superior catalytic performance and amazing potential of these nanoparticles to transform the field of heterogeneous catalysis by gold by offering potentially higher catalytic performance, control over exposed active sites, robustness and tunability for thermal‐, electro‐and photocatalysis.
基金the Natural Science Foundation of Educational Commission of Jiangsu Province under Grant No.06KJB140133National Natural Science Foundation of China under Grant No.10347118
文摘Exchange anisotropy in FM/AFM bilayers has given a lot of static magnetization properties such as enhanced coercivity and magnetization loop shifts. These phenomena are primarily from the effective anisotropies introduced into a ferromagnet by exchange coupling with a strongly anisotropic antiferromagnet. These effective anisotropies can also be used to explain the dynamic consequences of exchange-biased bilayers. In this article, the dynamic consequences such as exchange-induced susceptibility, exchange-induced permeability, and the corresponding domain wall characteristics in the exchange-biased structures of ferromagnet/antiferromagnetl/antiferromagnet2 are studied. The results show that the second antiferromagnetic layer can largely affect the dynamic consequences of exchange-blazed bilayers. Especially in the case of critical temperature, the effects become more obvious. Practically, the exchange anisotropy of biased bilayer system can be tuned by exchange coupling with the second antiferromagnetic layer.
文摘Some materials form better than others, moreover, a material that has the best formability for one stamping may behave very poorly in a stamping of another Configuration. The forming limit of a metal sheet is generally given in terms of the limiting principal strains under different loading conditions and represented by the so-called FLD (forming limit diagram). In view of the difficulty to experimentally determine the forming limits, many researchers have sought to predict FLD. The formability of sheet metal has frequently been expressed by the value of strain hardening exponent and plastic anisotropy ratio. The stress-strain and hardening behaviour of a material is very important in determining its resistance to plastic instability. For these reasons, extensive test programs are often carried out in an attempt to correlate material formability with value of some mechanical properties. In this study, mechanical properties and the FLD of the AMS 5596 sheet metal was determined by using uniaxial tensile test and Marciniak's flat bottomed punch test respectively.
基金Projects(60963012,61262034)supported by the National Natural Science Foundation of ChinaProject(211087)supported by the Key Project of Ministry of Education of ChinaProjects(2010GZS0052,20114BAB211020)supported by the Natural Science Foundation of Jiangxi Province,China
文摘A novel rcgularization-based approach is presented for super-resolution reconstruction in order to achieve good tradeoff between noise removal and edge preservation. The method is developed by using L1 norm as data fidelity term and anisotropic fourth-order diffusion model as a regularization item to constrain the smoothness of the reconstructed images. To evaluate and prove the performance of the proposed method, series of experiments and comparisons with some existing methods including bi-cubic interpolation method and bilateral total variation method are carried out. Numerical results on synthetic data show that the PSNR improvement of the proposed method is approximately 1.0906 dB on average compared to bilateral total variation method, and the results on real videos indicate that the proposed algorithm is also effective in terms of removing visual artifacts and preserving edges in restored images.
基金supported by the National Natu-ral Science Foundation of China(No.51675493 and No.51975542)the National Key R&D Program of China(No.2018YFF0300605,No.2019YFF0301802,and No.2019YFB2004802)Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi and Shanxi"1331 Project"Key Subject Construction(1331KSC).
文摘Silicon bulk etching is an important part of micro-electro-mechanical system(MEMS) technology. In this work, a novel etching method is proposed based on the vapor from tetramethylammonium hydroxide(TMAH) solution heated up to boiling point. The monocrystalline silicon wafer is positioned over the solution surface and can be anisotropically etched by the produced vapor. This etching method does not rely on the expensive vacuum equipment used in dry etching. Meanwhile, it presents several advantages like low roughness, high etching rate and high uniformity compared with the conventional wet etching methods. The etching rate and roughness can reach 2.13 μm/min and 1.02 nm, respectively. Furthermore,the diaphragm structure and Al-based pattern on the non-etched side of wafer can maintain intact without any damage during the back-cavity fabrication. Finally, an etching mechanism has been proposed to illustrate the observed experimental phenomenon. It is suggested that there is a water thin film on the etched surface during the solution evaporation. It is in this water layer that the ionization and etching reaction of TMAH proceed, facilitating the desorption of hydrogen bubble and the enhancement of molecular exchange rate. This new etching method is of great significance in the low-cost and high-quality micro-electromechanical system industrial fabrication.
基金Supported by NNSF of China(10371113)Supported by Foundation of Overseas Scholar of Chin&((2001)119)Supported by the project of Creative Engineering of Henan Province of China
文摘In this paper we mainly discuss the nonconforming fimte element method for second order elliptic boundary value problems on anisotropic meshes. By changing thediscretization form(i.e., by use of numerical quadrature in the procedure of computing the left load), we obtain the optimal estimate O(h), which is as same as in the traditionalfinite element analysis when the load f ∈ H1 (Ω)η Co(Ω) which is weaker than the previousstudies. The results obtained in this paper are also valid to the conforming triangular elementand nonconforming Carey's element.
文摘In a previous study, structure of silica gels prepared in a high magnetic field was investigated. While a direct application of such anisotropic silica gels is for an optical anisotropic medium possessing chemical resistance, we show here their possibility of medium in materials processing. In this direction, for example, silica hydrogels have so far been used as media of crystal growth. In this paper, as opposed to the soft-wet state, dried silica gels have been investigated. We have found that lead (II) nanocrystallites were formed induced by electron irradiation to lead (ll)-doped dried Hydrogels made from a sodium metasilicate solution doped with silica gels prepared in a high magnetic field such as B = 10 T. lead (II) acetate were prepared. The dried specimens were irradiated by electrons in a transmission electron microscope environment. Electron diffraction patterns indicated the crystallinity of lead (II) nanocrystallites depending on B. An advantage of this processing technique is that the crystallinity can be controlled through the strength of magnetic field B applied during gel preparation. Specific skills are not required to control the strength of magnetic field.
基金supported by National Natural Science Foundation of China (Grant Nos. 10901112, 11001255)Beijing Natural Science Foundation (Grant No. 1102013)China Postdoctoral Science Foundation (Grant No. 20090460548)
文摘In this paper, we study the following degenerate critical elliptic equation with anisotropic coefficients-div(|x N | 2α▽u) = K(x)|x N | α·2 * (s)-s |u| 2 * (s)-2 u in R N ,where x = (x 1 , . . . , x N ) ∈ R N , N≥3, α > 1/2, 0≤ s ≤2 and 2 * (s) = 2(N-s)/(N-2). Some basic properties of the degenerate elliptic operator -div(|x N |2α▽u) are investigated and some regularity, symmetry and uniqueness results for entire solutions of this equation are obtained. We also get some variational identities for solutions of this equation. As consequences, we obtain some nonexistence results for this equation.