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.

     

The radioisotopic battery based on radio-voltaic effect

The radio-voltaic effect is investigated to be applied radioisotopic batteries in this work. The collection rates of the electron-hole pairs are 94 percent for the alpha particles emitted by²³⁹Pu source and 65 percent for the beta particles emitted by⁹⁰Sr-⁹⁰Y source. The maximum energy conversion efficiency got by the silicon element is about 16%. A prototype radioisotopic battery with¹⁴⁷Pm beta sources is constructed. Its maximum short-circuit current and off voltage are about 2 A and 190 mV respectively. The experimental data suggest that the life of the prototype battery may be more than three years.     

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。     

Synthesis and structure characterization of a novel series of N-alkylphthalimidylaminocarbonylmethoxylcalix [4] arenes

A novel series of N-alkylphthalimidylaminocarbonylmethoxylcalix[4]arenes with the reaction between 4-(N-bromoacetyla- mino)-phthalimide derivatives and calix[4]arene has been synthesized and structurally characterized by IR,~1HNMR and MS.From their analysis data,it was found that compounds 7a-7d adopted a cone conformation.