非线性力学场论的几个基本课题

最近10年,在变形体转动的描述和应用,应变的度量和应用,以及应力,应变的客观性导数这三个非线性力学场论中互相关联的基本课题方面,提出了许多新问题,作出了大量的研究工作.本文综合介绍了其中一些方面的情况,并概述了笔者的相应工作.      

基础滑移隔震体系的地震响应计算

利用随机振动理论求出了基础滑移隔震房屋在无频谱过程的白噪声过程作用下的响应特性，探讨了基础滑移隔震的振动时最佳阻尼系数取值，提出了基础最大滑移量在白噪声过程作用下的计算公式，并进行了基础滑移隔震位移量的试验测定。计算结果与试验结果表明，本文提出的基础滑移隔震体系的计算公式是可行的，为滑移隔震房屋设计证结构安全、合理提供了理论依据。     

地震作用下基于ADMF和系统参数组合的最优MTMD

多重调谐质量阻尼器 ( MTMD)是由许多频率成线性分布的调谐质量阻尼器组成。可能的系统参数组合形成 5种 MTMD,即 MTMD-1～MTMD-5。基于在基底加速度作用下具有一般 MTMD时结构的加速度传递函数 ,建立了 MTMD-1～ MTMD-5加速度动力放大系数 ( ADMF)的统一模式。利用 ADMF和数值寻优技术进行了详细的最优参数研究。最优参数包括 :最优频率间隔、最优阻尼比、最优调谐频率比。大量的数值比较表明 :在MTMD地震反应控制工程中 ,应优先选择 MTMD-1。     

An efficient and stable structure preserving algorithm for computing the eigenvalues of a Hamiltonian matrix

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Mo-X(B, C, N, O, F)共掺杂TiO2体系的光催化协同效应研究

采用密度泛函理论平面波超软赝势方法, 计算并分析了Mo/X(B, C, N, O, F)共掺杂TiO₂体系的形成能、电子结构和光学性质, 研究了共掺杂协同效应对于计算体系光催化性能的影响机制. 首先计算出不同掺杂体系的态密度及能带结构, 利用能带理论分析了共掺杂效应对于禁带宽度的调控作用, 进而分析了共掺杂对TiO₂光催化能力和稳定性的协同作用. 结合电荷密度图, 分析原子间的电荷转移情况, 得到计算体系中各原子成键状态. 最后, 结合光吸收谱线分析得出Mo/C共掺杂类型在调制TiO₂体系中可见光波段的光催化性能上优势明显, 在催化作用上表现出协同效应. 本文的理论研究对共掺杂方法在TiO₂光催化领域有着一定的指导意义.     

Chiral derivatization coupled with liquid chromatography/mass spectrometry for determining ketone metabolites of hydroxybutyrate enantiomers

With PMP chiral derivatization, the D/L-2HB and D/L-3HB enantiomers can be distinctly determined by reversed-phase chromatographic separation. In addition, the detection sensitivities were greatly enhanced by LC-ESI-MS analysis due to the introduction of easily ionizable tertiary amino group from PMP.     

Defects and microvoids in a-Si and a-Si:H

We report the first measurements of positron-annihilation spectra of samples of both pure and hydrogenated amorphous silicon. Comparison of these spectra with that of crystalline silicon indicates that the lowest-lifetime component can be identified as the contribution mainly from valence-band electrons. Both the pure (a-Si) and the hydrogenated (a-Si:H) samples exhibit a component with intermediate lifetime, which we attribute to small vacancies consisting of about 4 missing atoms. Finally, only a-Si:H shows a significant long-lived line (τ > 5 ns), which arises from large microvoids, with ～ 100 missing atoms. The existence of these microvoids in a-Si:H is consistent with recent reports of the presence of occluded H₂ gas under high pressure in such films.     

Modular synthesis of candidate indole-based insulin mimics by Claisen rearrangement

A modular synthetic route to (indolyl)kojic acid anti-diabetes agents has been developed. Sonogashira coupling of a protected iodoaniline with a propargyl kojate was used to construct an (indole)methyl kojate. Its heteroaromatic Claisen rearrangement, followed by tautomerization to return the indole and pyrone rings, was used to create the biaryl C-C bond. This route should enable collections of insulin mimic drug candidates to be prepared from a few basic building blocks.     

Distribution of Selmer groups of quadratic twists of a family of elliptic curves

We study the distribution of the size of the Selmer groups arising from a 2-isogeny and its dual 2-isogeny for quadratic twists of elliptic curves with full 2-torsion points in Q. We show that one of these Selmer groups is almost always bounded, while the 2-rank of the other follows a Gaussian distribution. This provides us with a small Tate-Shafarevich group and a large Tate-Shafarevich group. When combined with a result obtained by Yu [G. Yu, On the quadratic twists of a family of elliptic curves, Mathematika 52 (1-2) (2005) 139-154 (2006)], this shows that the mean value of the 2-rank of the large Tate-Shafarevich group for square-free positive integers n less than X is , as X→∞.     

Brookite-type TiO(2) nanotubes

Brookite-type TiO(2) nanotubes with crystalline multilayer walls have been synthesized for the first time via a simple hydrothermal route.