多线性算子的各向异性Hardy空间估计

文中我们证明了一类由Calderón-Zygmund奇异积分算子生成的从乘积空间Lp1(Rn)×Lp2(Rm)×…×LpJ(Rn)到各向异性Hardy空间Hq(Rn)和各向异性弱Hardy空间Hq,∞(Rn)的多线性算子是有界的.作为上述结果的应用,得到了一类由Calderón-Zygmund奇异积分算子和各向异性BMO函数生成的交换子Lp(1相似文献   

Rational Design and Development of Anisotropic and Mechanically Strong Gelatin‐Based Stress Relaxing Hydrogels for Osteogenic/Chondrogenic Differentiation

Rational design and development of tailorable simple synthesis process remains a centerpiece of investigational efforts toward engineering advanced hydrogels. In this study, a green and scalable synthesis approach is developed to formulate a set of gelatin‐based macroporous hybrid hydrogels. This approach consists of four sequential steps starting from liquid‐phase pre‐crosslinking/grafting, unidirectional freezing, freeze‐drying, and finally post‐curing process. The chemical crosslinking mainly involves between epoxy groups of functionalized polyethylene glycol and functional groups of gelatin both in liquid and solid state. Importantly, this approach allows to accommodate different polymers, chitosan or hydroxyethyl cellulose, under identical benign condition. Structural and mechanical anisotropy can be tuned by the selection of polymer constituents. Overall, all hydrogels show suitable structural stability, good swellability, high porosity and pore interconnectivity, and maintenance of mechanical integrity during 3‐week‐long hydrolytic degradation. Under compression, hydrogels exhibit robust mechanical properties with nonlinear elasticity and stress‐relaxation behavior and show no sign of mechanical failure under repeated compression at 50% deformation. Biological experiment with human bone marrow mesenchymal stromal cells (hMSCs) reveals that hydrogels are biocompatible, and their physicomechanical properties are suitable to support cells growth, and osteogenic/chondrogenic differentiation, demonstrating their potential application for bone and cartilage regenerative medicine toward clinically relevant endpoints.     

新修正偶应力层合板理论中的几个基本假设对自由振动计算的影响

基于新修正偶应力理论,在对微细观尺度的复合材料层合梁/板进行力学响应计算时,往往采用一系列假设来简化模型。现有文献都全部或部分应用了这些假设,但对这些假设是否会对计算结果造成影响尚未进行充分讨论分析。本文建立了未经简化的新修正偶应力Reddy层合板模型,并对其自由振动进行了分析。通过数值算例的对比,讨论了常用的几个简化假设对微细观复合材料四边简支方板自振频率的影响以及适用范围。算例结果表明,常用的几个简化假设对于微尺度层合薄板自由振动的影响很小,对于厚板的低阶频率影响也很小,但对厚板的高阶频率影响显著。     

A new interpretation of Hund's first rule

The diagonal elements of the first and second order spinless density matrices have been calculated for the lowest excited¹ P and³ P terms of Be, B⁺ and C⁺⁺ using wavefunctions at different levels of approximations published in the literature. The analysis of these functions has resulted in a new interpretation of Hund's first rule in terms of an anisotropic screening effect.     

Analyzing Anisotropic Exchange in a Pentanuclear Os2Ni3 Complex

Spin Hamiltonian parameters of a pentanuclear Os Ni cyanometallate complex are derived from ab initio wave function based calculations, namely valence-type configuration interaction calculations with a complete active space including spin-orbit interaction (CASOCI) in a single-step procedure. While fits of experimental data performed so far could reproduce the data but the resulting parameters were not satisfactory, the parameters derived in the present work reproduce experimental data and at the same time have a reasonable size. The one-centre parameters (local matrices and single-ion zero field splitting tensors) are within an expected range, the anisotropic exchange parameters obtained in this work for an Os−Ni pair are not exceedingly large but determine the low-T part of the experimental χT curve. Exchange interactions (both isotropic and anisotropic) obtained from CASOCI have to be scaled by a factor of 2.5 to obtain agreement with experiment, a known deficiency of such types of calculation. After scaling the parameters, the isotropic Os−Ni exchange coupling constant is cm⁻¹ and the D parameter of the (nearly axial) anisotropic Os−Ni exchange is ⁻¹, so anisotropic exchange is larger in absolute size than isotropic exchange. The negative value of the isotropic J (indicating antiferromagnetic coupling) seemingly contradicts the large-temperature behaviour of the temperature dependent susceptibility curve, but this is caused by the negative g value of the Os centres. This negative g value is a universal feature of a pseudo-octahedral coordination with configuration and strong spin-orbit interaction. Knowing the size of these exchange interactions is important because Os(CN) is a versatile building block for the synthesis of / magnetic materials.     

基于MATLAB软件对不同偏振光在不同介质中的传播过程的动态模拟

利用MATLAB软件对不同偏振光在真空、各向同性介质、线型各向异性介质以及圆型各向异性介质中的传播过程进行了三维动态模拟,能够加深学生对光的偏振概念以及各种偏振光与不同介质之间相互作用原理的理解。     

一种高灵敏度石英微机械陀螺敏感器件

针对石英晶体各向异性的特点,设计了一种驱动梁为双"W"截面形状的石英音叉微机械陀螺,通过在驱动梁表面凹槽两端设置深凹槽,有效提高了凹槽侧壁的陡直性,进而提高了驱动梁内部电场的激励效率和陀螺灵敏度。采用有限元仿真的方法,分析了不同截面形状的驱动梁压电激励力的相对大小,优化设计了陀螺芯片结构参数。依据陀螺芯片的结构,设计了合理的工艺方案并在3英寸石英圆片上制作出了三种驱动梁截面形状的陀螺器件,测试结果表明,相对于矩形驱动梁截面的陀螺芯片,双"W"形驱动梁截面的陀螺芯片的灵敏度提高约60%。     

点支承四边自由各向异性平行四边形板自由振动、屈曲和弯曲分析

一个精确的重富立叶级数解析解用于分析四边形自由的点支横观各向异性平行四边形板的自由振动、屈曲和弯曲。解析解用叠加法得到,此解收敛迅速。与现有结果的比较证实了由本法得到的解析解的精确性。文后用图表给出高精度的自由振动、屈曲和弯曲计算结果。     

Robust Schur complement method for strongly anisotropic elliptic equations

We present robust and asymptotically optimal iterative methods for solving 2D anisotropic elliptic equations with strongly jumping coefficients, where the direction of anisotropy may change sharply between adjacent subdomains. The idea of a stable preconditioning for the Schur complement matrix is based on the use of an exotic non‐conformal coarse mesh space and on a special clustering of the edge space components according to the anisotropy behavior. Our method extends the well known BPS interface preconditioner [2] to the case of anisotropic equations. The technique proposed also provides robust solvers for isotropic equations in the presence of degenerate geometries, in particular, in domains composed of thin substructures. Numerical experiments confirm efficiency and robustness of the algorithms for the complicated problems with strongly varying diffusion and anisotropy coefficients as well as for the isotropic diffusion equations in the ‘brick and mortar’ structures involving subdomains with high aspect ratios. Copyright © 1999 John Wiley & Sons, Ltd.     

低阶煤热萃取物与瘦煤共炭化焦炭的微观结构及显微强度研究

以众唯瘦煤作为主炼焦煤,大同长焰煤萃取物作为添加剂,进行共炭化处理制备坩埚焦。利用偏光显微镜法定量研究焦炭光学显微组分,获得焦炭的各向异性指数(DRAS);采用XRD及分峰拟合的方法研究了焦炭的微晶粒径(L_c)、芳香缩合度(I_a)、石墨化度(g);利用Raman光谱结合分峰拟合的方法研究了焦炭中理想石墨微晶含量(I_g)。对所得焦炭的光学显微组分进行定量分析发现:大同长焰煤热解萃取产物的添加对共炭化焦炭的光学显微组分有显著的影响,利用偏光显微镜法计算出焦炭的DRAS与XRD和Raman计算的焦炭微晶参数呈现很好一致性。并且,焦炭的显微强度与其微观结构关联性极大。