A comparison of master equation and Fokker-Planck equation in the thermodynamic limit

The master equation and the Fokker-Planck equation are compared thoroughly in both of the stationary and the time-dependent cases for a one-dimensional system. The comparison includes the master equation without detailed balance.     

纯生跳跃扩散型交换期权定价公式

在假定标的资产价格服从纯生跳跃过程的条件下,研究一类多资产期权——资产权重不同的交换期权,并在风险中性的条件下建立相应的定价方程,运用条件期望等相关知识得出交换期权的解析公式。文中最后列出一些特殊纯生跳跃扩散型交换期权的定价的例子.     

Studies on self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals

The use of Cu-doped (K_0.5Na_0.5)_0.2(Sr_0.61Ba_0.39)_0.9Nb₂O₆ as self-pumped phase conjugators using internal reflection is reported. Reflectivities as high as 63% at 5145.5 nm and 60% at 632.8 nm were realized. It was found that the photorefractive response changes significantly at different doping concentration. The responses of the crystals to the laser wavelength, incident angle and dopant concentration are studied.     

Matrix representation of three-dimensional astigmatic resonators

Three-dimensional astigmatic resonators, typical examples of which are the resonators bounded by cylindrical-spherical mirrors and cylindrical-cylindrical mirrors oriented at an arbitrary crossed angle, are investigated in detail by using a complex curvature tensor concept and generalized tensor ABCD law. Computerized numerical calculations illustrate some interesting characteristics of these astigmatic resonators.     

Super-Wavelets and Decomposable Wavelet Frames

A wavelet frame is called decomposable whenever it is equivalent to a superwavelet frame of length greater than one. Decomposable wavelet frames are closely related to some problems on super-wavelets. In this article we first obtain some necessary or sufficient conditions for decomposable Parseval wavelet frames. As an application of these conditions, we prove that for each n > 1 there exists a Parseval wavelet frame which is m-decomposable for any 1 < m ≤ n, but not k-decomposable for any k > n. Moreover, there exists a super-wavelet whose components are non-decomposable. Similarly we also prove that for each n > 1, there exists a Parseval wavelet frame that can be extended to a super-wavelet of length m for any 1 < m ≤ n, but can not be extended to any super-wavelet of length k with k > n. The connection between decomposable Parseval wavelet frames and super-wavelets is investigated, and some necessary or sufficient conditions for extendable Parseval wavelet frames are given.     

Effect of carbon content on the microstructure and the cracking susceptibility of Fe-based laser-clad layer

The laser cladding of Fe-based alloys on a medium carbon steel substrate was performed using a CO₂ laser and Ar shielding gas that was blown into a molten pool. The microstructure and cracking susceptibility of the laser-clad layers were studied in terms of carbon additions. Results show that the small change of the carbon content in the alloy powders can obviously change the microstructure and properties of the layers. When the carbon content is in the range of 0.3–0.4 wt.%, the decrease of the carbon content in alloy powders will increase the hardness and toughness of the layers simultaneously under the same process parameters. As a result, crack-free coatings with high hardness can be obtained. As the carbon content increases from 0.2 wt.% to 0.4 wt.%, the segregation ratio of chromium increases, while the segregation ratios of nickel, manganese, and silicon first decrease and then increase. At the same time, a new designing principle concerning the composition and microstructure has been put forward, and the principal mechanisms of strengthening and toughening of the layers are fine-grain strengthening and low carbon martensitic phase transformation strengthening.     

矩阵方程（A^TXA，B^TXB=（C，D）的反对称解及其最佳逼近

本利用矩阵对的标准相关分解，得到了矩阵方程(A^TXB，B^TXB)=(C，D)反对称解存在的充分必要条件及通解表达式，同时给出了解关于已知矩阵的最佳逼近．     

InAs/GaSb/AlSb resonant tunneling spin device concepts

We discuss device concepts for creating spin-polarized current sources without external magnetic fields, using non-magnetic 6.1 Å semiconductor resonant tunneling structures. Spin filters, spin pumps, and spin transistors that exploit structural and bulk inversion asymmetries will be examined.     

BOUNDEDNESS OF VECTOR-VALUED CALDERN-ZYGMUND OPERATORS ON HERZ SPACES WITH NON-DOUBLING MEASURES

In the paper we obtain vector-valued inequalities for Calder6n-Zygmund operator, simply CZO on Herz space and weak Herz space. In particular.we obtain vector-valued inequalities for CZO on Lq(Rd, |x|αdμ) space, with 1< q <∞, -n <α< n(q -1), and on L1,∞(Rd,|x|αdμ) space, with -n <α< 0.     

Grid‐free surface vorticity method applied to flow induced vibration of flexible cylinders

In order to study cross flow induced vibration of heat exchanger tube bundles, a new fluid–structure interaction model based on surface vorticity method is proposed. With this model, the vibration of a flexible cylinder is simulated at Re=2.67 × 10⁴, the computational results of the cylinder response, the fluid force, the vibration frequency, and the vorticity map are presented. The numerical results reproduce the amplitude‐limiting and non‐linear (lock‐in) characteristics of flow‐induced vibration. The maximum vibration amplitude as well as its corresponding lock‐in frequency is in good agreement with experimental results. The amplitude of vibration can be as high as 0.88D for the case investigated. As vibration amplitude increases, the amplitude of the lift force also increases. With enhancement of vibration amplitude, the vortex pattern in the near wake changes significantly. This fluid–structure interaction model is further applied to simulate flow‐induced vibration of two tandem cylinders and two side‐by‐side cylinders at similar Reynolds number. Promising and reasonable results and predictions are obtained. It is hopeful that with this relatively simple and computer time saving method, flow induced vibration of a large number of flexible tube bundles can be successfully simulated. Copyright © 2004 John Wiley & Sons, Ltd.