A second-order accurate numerical method for a fractional wave equation

We study a generalized Crank–Nicolson scheme for the time discretization of a fractional wave equation, in combination with a space discretization by linear finite elements. The scheme uses a non-uniform grid in time to compensate for the singular behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assuming that the spatial domain is convex or smooth, we show that the error is of order k ² + h ², where k and h are the parameters for the time and space meshes, respectively.     

Peritectic phase growth in directionally solidified Cu-70% Sn alloy

The growth mechanism of the peritectic η phase involving the peritectic reaction and peritectic transformation in Cu-70%Sn alloy was investigated under directional solidification. The results show that a major growth mechanism in thickening of the peritectic η-layer is not the peritectic reaction but the peritectic transformation. The transformation temperature and isothermal time play crucial roles in determining the volume fraction and the thickness of the peritectic η phase. With the increase of the temperature and isothermal time, the volume fraction of the peritectic η phase increases. The regressed data show that the relationship between the thickness of η phase (Δx) and the transformation temperature (T) meets the following equation In Δx=6.5−1673 1 / T. Additionally, there exists a relationship between the thickness of the η phase (Δx) and the isothermal time (t) at the 9 mm solidification distance below the peritectic reaction interface, Δx=0.72t ^1/2, which is consistent with the theoretical model. Supported by the National Science Foundation of China (Grant No. 50395102)     

离子束混合工艺对材料抗蚀性能的影响

本文介绍了离子束混合工艺方法。与直接注入相比较,离子束混合所使用的设备造价低1/4—1/2,而生产效率可提高1—2个数量级,因而使生产成本大幅度降低,这无疑对离子束工艺的实际应用将产生巨大的促进作用。 通过对轴承材料(GCr15和Cr4Mo4V)经Cr、N、Ta不同元素的混合处理后,在0.5M H_2SO_4和0.1M NaCl的缓冲溶液中的阳极极化曲线表明经混合处理后的两种材料试样,其抗蚀能力和抗点蚀能力均大大提高,这与直接注入的试样效果是一致的。 通过俄歇谱仪和透射电镜的分析结果表明混合是成功的,且在一定的条件下,形成非晶组织。 本文的结论是,无论是离子的直接注入还是离子束混合,对提高轴承材料的抗腐蚀性能都是有效的方法,特别是离子束混合技术具有更大的应用前景。     

Piezooptical optical bistability

A glass fiber piezooptical optical bistability device is reported.Basing on pho-toelastic and strain effects of single-mode fiber,we have realized piezooptical modulation andperformed experiments of optical bistability.     

约束Hamilton系统的Poincaré-Cartan不变量

从正则形式作用量出发,导出了约束Hamilton系统(奇异拉氏量)的Poincaré-Cartan不变量,证明了该不变量与约束Hamilton系统的正则方程之间的等价性,纠正了某些作者工作中的错误。     

New isothermal equation of state of solids applied to high pressures

In the present paper, a new two-parameter inverted equation of state (EOS) is developed which is found to be working very well in the high-pressure region. To check its success and validity, this EOS has been applied in a number of solids. The computed volume compression is found to be in very good agreement with the experimental data in the whole range of pressure in all the solids. The minimum and the maximum pressure range used in the present study is 0–320 kbar and 0–3000 kbar, respectively.     

Vanishing of local homology

 We study the vanishing properties of local homology of complexes of modules without assuming that its homology is artinian. Using vanishing results for local homology and cohomology we prove new vanishing results for Ext- and Tor-modules. Received: 1 August 2002; in final form: 23 September 2002 / Published online: 16 May 2003 Mathematics Subject Classification (1991): 13C12, 13D07, 13D45.     

A column generation approach for the timetabling problem of Greek high schools

A column generation (CG) approach for the solution of timetabling problems is presented. This methodology could be used for various instances of the timetabling problem, although in this paper the solution of the high-school situation in Greece is presented. The results obtained show clearly that the CG approach that has been extremely successful in recent years in the solution of airline crew scheduling problems could also be very efficient and robust for the solution of timetabling problems. Several large timetabling problems corresponding to real problems have been successfully solved, with the solutions obtained feasible and of very high quality in accordance with the problem definition. In addition, none of the solutions contained any idle hour for any of the teachers, which was one of the main goals of this optimization effort.     

光照下meso-四(4-磺基苯基)卟啉(H_2TPPS)形成锌配合物的光-极谱研究

在氨性溶液中,光照射对ZnTPPS的形成影响很大。光-极谱试验表明:光电流(i_p)与浓度(c)间有以下的关系:对Zn(NH_3)_4~(2+),i_p∝C_((Zn)(NH_3)_4)~(2+)_~(1/2),对H_2TPPS,i_p∝C_(H_2TPPS),ZnTPPS络合物还原波的i_p不明显。本文对其差异性和光电流产生的原因做了初步探讨。