A Review of Results on Axially Symmetric Navier-Stokes Equations,with Addendum by X. Pan and Q. Zhang

In this paper, we give a brief survey of recent results on axially symmetric Navier-Stokes equations (ASNS) in the following categories: regularity criterion, Liouville property for ancient solutions, decay and vanishing of stationary solutions. Some discussions also touch on the full 3 dimensional equations. Two results, closing of the scaling gap for ASNS and vanishing of homogeneous D solutions in 3 dimensional slabs will be described in more detail.In the addendum, two new results in the 3rd category will also be presented, which are generalizations of recently published results by the author and coauthors.     

(Z)-1-[2-(Triarylstannyl)vinyl]-1-cycloheptanols: Synthesis, characterization, halodemetallation and crystal structures

The synthesis and characterization by ¹H, ¹³C, ¹¹⁹Sn NMR and ¹¹⁹Sn Mössbauer spectroscopy of (Z)-1-[2-(triphenylstannyl)vinyl]-1-cycloheptanol,

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(1), and (Z)-1-[2-tri-p-tolylstannyl)vinyl-1-cycloheptanol,

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(2), are described, together with their halodemetallation by I₂, Br₂ and ICIl to yield derivatives of the types

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(Ar = phenyl or p-tolyl, N = 1, 2; X = I, Br, Cl, respectively). The solid-state structures of four compounds have been determined by X-ray diffraction analysis. In the crystals of

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(1) and

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(2) the Sn atom has a tetrahedral geometry distorted towards trigonal bipyramid as a consequence of a close intramolecular contact with the hydroxyl O(1) atom of 2.742(3) Å and 2.768(3) Å, respectively. A trigonal bipyramidal geometry is found in

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(12) and

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(4), in which significant Sn---O(1) interactions are noted [2.437(8) Å and 2.407(8) Å, respectively].     

Oscillatory singular integrals on and Hardy spaces

We consider boundedness properties of oscillatory singular integrals on and Hardy spaces. By constructing a phase function, we prove that boundedness may fail while boundedness holds for all . This shows that the theory and theory for such operators are fundamentally different.

     

磺胺二甲嘧啶的极谱伏安行为

本文考察了磺胺二甲嘧啶在多种底液中的极谱伏安行为，发现其在ＢｒｉｔｏｎＲｏｂｉｎｓｏｎ（ＢＲ）缓冲溶液（ｐＨ２．２）中产生一个良好的还原峰，峰电位为－０．８５Ｖ（ｖｓ．ＳＣＥ），峰电流与磺胺二甲嘧啶浓度在１×１０－７３×１０－４ｍｏｌ／Ｌ范围内呈良好的线性关系，检出限为９×１０－８ｍｏｌ／Ｌ，大多数金属离子和无机阴离子不干扰测定，可望用于定量测定用多种电化学方法研究了该还原峰电流的性质，结果表明，它是具有吸附性质的不可逆还原峰     

预取向液晶单体光聚合反应

通过表面摩擦、施加外电场(或磁场)和应力剪切等手段使液晶单体取向后进行光聚合反应是制备高度取向、高度均匀和高度透明高分子液晶膜的重要方法。它在高分子非线性光学材料、导电商分子材料和光纤涂层等领域中具有广泛的应用前景。