Remarks on the a priori bound for the vorticity of the axisymmetric Navier-Stokes equations

Applications of Mathematics - We study the axisymmetric Navier-Stokes equations. In 2010, Loftus-Zhang used a refined test function and re-scaling scheme, and showed that $$left| {{omega...     

Preparation and electroluminescent application of iridium(III) complexes containing sulfur-containing phenylpyridazine ligands

Transition Metal Chemistry - Four iridium(III) complexes (1–4) with sulfur-containing phenylpyridazine ligands were successfully synthesized and characterized. The structure of complex 3 was...     

Pontrjagin空间上算子集合的两个稠密性定理

Ｋａｐｌａｎｓｋｙ稠密性定理￣［１］是ｖｏｎＮｅｕｍａｎｎ代数和Ｃ￣＊代数理论中一个基本而重要的定理。算子代数中许多深刻的结果都是以此为工具导出的。要在不定度规空间上探讨算子代数的性质，人们自然会关心在这类空间上是否存在同一类型的结果。本文的主要目的就是在Ｐｏｎｔｒｊａｇｉｎ空间上给出一个相应的稠密性定理。同时，我们还将给出关于完全正则自共轭算子的另一个稠密性的结果。     

Global existence and large time behavior of the asymmetric fluids

In this paper, we consider the asymptotic stability of the steady state with the constant equilibrium state. Under the assumptions that the \({H^3}\) norm of the initial data is small, but its higher-order derivatives could be large, we prove the global existence to the Cauchy problem for the asymmetric fluids in \({\mathbb{R}^3}\). Moreover, we obtain the time decay rates of the solutions and their higher-order spatial derivatives by introducing the negative Sobolev and Besov spaces.     

Di- and tetranuclear heterometallic CuII-LnIII complexes (Ln = Gd and Dy): Synthesis, structure and magnetic properties

Four 3d-4f heterometallic complexes, [CuⅡ LnⅢ (bpt) 2 (NO 3 ) 3 (MeOH)] (Ln = Gd, 1; Dy, 2; bptH = 3,5-bis(pyrid-2-yl)-1,2,4- triazole), [CuⅡ 2 LnⅢ 2 (μ-OH) 2 (bpt) 4 Cl 4 (H 2 O) 2 ]·6H 2 O (Ln = Gd, 3; Dy, 4), have been synthesized under solvothermal conditions. X-ray structural analyses reveal that 1 and 2 are isostructural while 3 and 4 are isostructural. In each complex, the copper and gadolinium or dysprosium ions are linked by two triazolate bridges and form a CuⅡ -LnⅢ dinuclear unit. The intramolecular Cu-Ln distances are 4.542, 4.525, 4.545 and 4.538 for 1, 2, 3 and 4, respectively. Two dinuclear CuLn units are bridged by two OH- groups into the zig-zag tetranuclear {CuⅡ 2 LnⅢ 2 } structures with the Ln(Ⅲ) Ln(Ⅲ) distances of 3.742 and 3.684 for 3 and 4, respectively. Magnetic studies show that the antiferromagnetic CuⅡ-LnⅢ interactions occur in 1 (J CuGd = 0.21 cm-1 ) and 2. The antiferromagnetic interaction occurs in complex 3 with J CuGd = 0.82 cm-1 and J GdGd = 0.065 cm-1 , while dominant ferromagnetic interaction occurs in complex 4.     

Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.     

Interfacial microstructure and reaction at the spin-coated fluorinated polyimide/Al interface: surface-enhanced X-ray diffraction and TEM studies

2 multilayers by means of X-ray diffraction, transmission electron microscopy, and an ellipsometer. The FPI precursor, a solution of PMDA/6FDA/TFMOB/PPD was spin-coated onto the Al layer and then cured at 400 °C for one hour. It is found that the moisture and oxygen from the FPI layer released during thermal treatment can lead to the oxidation of the interface between the Al and the FPI. The TEM cross-sectional images and the electron diffraction patterns indicate that the oxidized interface is amorphous. The oxidation product is identified to be Al₂O₃. The oxidation onset temperature is determined to be 415 °C, which is slightly higher than the curing temperature. The oxidation of the FPI/Al interface results in an increase in the electrical resistance of the Al layer, and thus may lead to a reduction in its effective electrical thickness. Received: 21 May 1997/Accepted: 27 May 1997