On the Derivations of Filiform Leibniz Algebras

The algebras of derivations of naturally graded Leibniz algebras are described. The existence of characteristically nilpotent Leibniz algebras in any dimension greater than 4 is proved.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 733–742.Original Russian Text Copyright ©2005 by B. A. Omirov.     

Lie Atoms and Their Deformations

A Lie atom is essentially a pair of Lie algebras and its deformation theory is that of a deformation with respect to the first algebra, endowed with a trivialization with respect to the second. Such deformations occur commonly in algebraic geometry, for instance as deformations of subvarieties of a fixed ambient variety. Here we study some basic notions related to Lie atoms, focussing especially on their deformation theory, in particular the universal deformation. We introduce Jacobi–Bernoulli cohomology, which yields the deformation ring, and show that, under suitable hypotheses, infinitesimal deformations are classified by certain Kodaira–Spencer data. Received: May 2006 Revision: January 2007 Accepted: March 2007     

Effects of lattice dispersion and elastic anisotropy on the thermal properties of bcc metals

Two new parameters which take into account the effects of elastic anisotropy and phonon dispersion on lattice specific heat in the case of sodium and potassium have been evaluated. A new graded mesh method which uses a 162-direction approximation in (1/16) part of the Brillouin Zone (BZ) has been considered to evaluate the two parameters.     

Propagation of partially coherent Gaussian laser beams in graded-index fibres

Using statistical approach the author has solved the equations for the mutual coherence function of partially coherent Gaussian laser beams in graded-index fibres. The expressions for the complex degree of coherence and the intensity distribution have also been shown that the self-focusing length inside the fibre depends upon the degree of coherence. The result have been discussed for both conical and cylindrical guides.     

渐变折射率光波导的精确分析

本文利用转移矩阵理论和等效衰减系数的概念，导出了渐变折射率光波导的色散方程，数值计算的结果，赢余方程的精度优于目前存在的所有近似方法。     

Microprobe analysis of low alloyed sintered steels

Homogenization of Mo, W and Cr in alloyed P/M carbon steels during sintering with a transient liquid phase has been investigated by microscopic and microanalytical means. The reaction was found to start with carburization of the VIa metal, continues with the formation of different carbides, and generation of a liquid phase between the carbide and -Fe. The steady state equilibrium remains stable until all VIa metal has been consumed. Microprobe analysis was found to yield optimum results if selected model samples, in which homogenization should not proceed too fast, are investigated.Dedicated to Professor Günther Tölg on the occasion of his 60th birthday     

不同盖层对InAs/GaAs量子点结构和光学性质的影响

利用金属有机化合物气相沉积设备生长了不同盖层结构的InAs/GaAs量子点,采用原子力显微镜和光致发光光谱仪对量子点的结构和光学性质进行了研究.量子点层之间的盖层由一个低温层和一个高温层组成.对不同材料结构的低温盖层的对比研究表明,In组分渐变的InGaAs低温盖层有利于改善量子点均匀性、减少结合岛数目、提高光致发光强度;当组分渐变InGaAs低温盖层厚度由6.8 nm增加到12 nm,发光波长从1256.0 nm红移到1314.4 nm.另外,还对不同材料结构的高温盖层进行了对比分析,发现高温盖层采用In组分渐变的InGaAs材料有利于光致发光谱强度的提高. 关键词： 半导体量子点 盖层 组分渐变     

梯度颗粒复合介质的光学双稳

重点研究了组分的梯度构形对带壳球形颗粒复合介质的光学双稳特性的影响.其中球形颗粒是由非线性核和介电函数具有梯度分布的线性壳组成.对于壳层介电函数具有幂指数分布的情况,通过求解麦克斯韦方程,得到各区域的势能分布函数,从而求得核内电场的数学表达式.数值研究发现,该复合介质的光学双稳阈值和区域与壳层的厚度及壳层的介电幂指数有关,随着壳层厚度增大或幂指数增大,双稳阈值将变宽.此外,还研究了正入射情况下复合材料体系的反射系数随外电场的变化情况, 发现其关系曲线是一条回线. 关键词： 梯度颗粒 复合介质 光学双稳     

三级炮加载技术在超高压状态方程研究中的应用

根据阻抗梯度飞片设计原则和超高速数值模拟技术设计出一种新的叠层波阻抗梯度飞片,并利用三级炮加载技术将Ta飞片加速至9 km/s以上,测量了Ta在超高压下的状态方程。三级炮实验实现了冲击波速度与粒子速度的同时测量,Ta的Hugoniot数据与文献中发表的数据具有很好的线性关系,说明三级炮加载技术适合于材料超高压状态方程研究。     

Gabriel Dimension for Graded Rings

Using techniques of localization for Grothendieck categories with a family of projective generators, we show that for a graded ring R = ⊕ _σ∈G R _σ with finite support if R _e has Gabriel dimension then has Gabriel dimension. Moreover, adding some lattice results, we prove that if has Gabriel dimension then also has Gabriel dimension. This research has been supported by grant MTM2005-3227 from MEC.