57Fe Mössbauer spectroscopic study of (25−x)MnO–xZnO–15Fe2O3–60B2O3 glasses

The ⁵⁷Fe Mössbauer technique has been used to investigate the effect of zinc oxide substitution in (25???x)MnO–xZnO–15Fe₂O₃–60B₂O₃ glass system (x?=?0, 5, 10, 15 and 20 mol% of ZnO ). Mössbauer absorption spectra for all the samples recorded at room temperature suggest the existence of the two paramagnetic quadrupole doublets. The observed variations in hyperfine parameters have been explained on the basis of cations distribution and exchange interaction at the lattice sites and it is concluded that B–B interaction increases while the metal–metal interaction decreases due to replacement of manganese oxide by zinc oxide. These results suggest that the present glass system exhibits a paramagnetic behaviour that changes towards the weak paramagnetic when manganese oxide was replaced with zinc oxide.     

Analytic Independence of an Ideal Relative to Certain Injective Module Over a Commutative Noetherian Ring

In this paper we will introduce the concepts of analytic independence and analytic spread for ideals relative to certain injective module over a commutative Noetherian ring.     

光刻机硅片表面不平度原位检测技术

随着光刻特征尺寸的不断减小,硅片表面不平度对光刻性能的影响越来越显著.该文提出了一种新的硅片表面不平度的原位检测技术本文在分析特殊测试标记成像规律的基础上,讨论了测试标记的对准位置偏移量与硅片表面起伏高度的变化规律,提出了一种新的硅片表面不平度原位检测技术.实验表明,该技术可实现硅片表面不平度及硅片表面形貌的高准确度原位测量.该技术考虑了光刻机承片台吸附力的非均匀性对硅片表面不平度的影响,更真实反映曝光工作状态下的硅片表面不平度大小.与现有的原位检测方法相比,硅片表面不平度的测量空间分辨率提高了1.67%倍,可实现硅片表面形貌的原位检测.     

唯一分解整半群上的Mobius函数及其反演公式

陈兆斗首先在文献[1]中定义出了有单位元并满足消去律的唯一分解交换半群上的Mbius函数.本文我们首先证明了Mbius函数作为半群(M1,*)上的元素是常值函数ζ(·)的逆函数.其后获得了该Mbius函数的一些相关结果并给出了三个Mbius反演公式.     

Simultaneous Measurement of Particle Size and Particle Velocity by the Spatial Filtering Technique

The objective of this study was to compare the measuring results of a fiber‐optical probe based on a modified spatial filtering technique with given size distributions of different test powders and also with particle velocity values of laser Doppler measurements. Fiber‐optical spatial filtering velocimetry was modified by fiber‐optical spot scanning in order to determine simultaneously the size and the velocity of particles. The fiber‐optical probe system can be used as an in‐line measuring device for sizing of particles in different technical applications. Spherical test particles were narrow‐sized glass beads in the range 30–100 μm and irregularly shaped test particles were limestone particles in the range 10–600 μm. Particles were dispersed by a brush disperser and the measurements were carried out at a fixed position in a free particle‐laden air stream. Owing to the measurement of chord lengths and to the influence of diffraction and divergent angle, the probe results show differences from the given test particle sizes. Owing to the particle‐probe collisions, the mean velocity determined by the probe is smaller than the laser Doppler mean velocity.     

Accelerating Galerkin BEM for linear elasticity using adaptive cross approximation

The adaptive cross approximation (ACA) algorithm (Numer. Math. 2000; 86 :565–589; Computing 2003; 70 (1):1–24) provides a means to compute data‐sparse approximants of discrete integral formulations of elliptic boundary value problems with almost linear complexity. ACA uses only few of the original entries for the approximation of the whole matrix and is therefore well‐suited to speed up existing computer codes. In this article we extend the convergence proof of ACA to Galerkin discretizations. Additionally, we prove that ACA can be applied to integral formulations of systems of second‐order elliptic operators without adaptation to the respective problem. The results of applying ACA to boundary integral formulations of linear elasticity are reported. Furthermore, we comment on recent implementation issues of ACA for non‐smooth boundaries. Copyright © 2006 John Wiley & Sons, Ltd.     

Flow in a waterfall with large Froude number

An approximate method is developed to solve the full nonlinear equations governing two-dimensional irrotational flow in a free waterfall, falling under the influence of gravity, at high Froude number based on conditions far upstream. Schwarz—Christoffel transformation is used to map the region, in the complex potential-plane, onto the upper half-plane. The Hilbert transformation as well as the perturbation technique, for large Froude number, are used as a basis for the approximate solution of the problem. A complete solution, up to second-order approximation, for the downstream free-surfaces profiles, for different Froude number, is discussed and illustrated. The obtained approximate solutions are compared with those of other authors. Favourable agreement with other results suggests that this method is effective in dealing with flow problems strongly influenced by gravity and high Froude number. The results obtained by this method are sufficiently accurate for practical purposes.     

ON DIRECT METHOD OF SOLUTION FOR A CLASS OF SINGULAR INTEGRAL EQUATIONS

In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.