双漏斗肥皂膜实验的研究

研究双漏斗肥皂膜实验中肥皂膜的形状、特性以及它随两漏斗距离的变化过程.从理论上导出并经实验验证一个重要结论:两漏斗口的最大距离等于其半径的1.325倍,然而这一点常常被忽视.     

Application of Bohmian Mechanics to Dynamics of Prices of Shares: Stochastic Model of Bohm–Vigier from Properties of Price Trajectories

We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Through comparing properties of trajectories we come to the conclusion that the only possibility to proceed with real financial data is to apply the stochastic version of the pilot wave theory—the model of Bohm–Vigier.     

Analysis of Laser-generated Rayleigh wave on viscoelastic materials

In order to understand the viscoelasticity of material, this research has been conducted to study the propagation characteristics of viscoelastic Rayleigh wave theoretically. A model is presented for the pulsed laser generation of ultrasound on viscoelastic medium surface. Referred to the Kelvin model, the frequency equation and the normal displacement of viscoelastic Rayleigh wave were derived, the influence of the viscoelastic modulus on dispersion and attenuation was discussed. From the theoretical calculation, it is shown that the effect of viscoelasticity on the attenuation of Rayleigh wave is more than that on its dispersion. In the case of a weak viscosity, the attenuation of viscoelastic Rayleigh wave is directly proportional to viscosity modulus; the effect of shear viscosity on the attenuation is much more than that of bulk viscosity. The transient response of viscoelastic Rayleigh wave was also simulated using Laplace and Hankel inversion transform, which are showed in good agreement with the theoretic predictions. The model provides a useful tool for the determination of viscoelastic parameters of medium.     

Compensation of gradient-induced magnetic field perturbations

Pulsed magnetic field gradients are essential for MR imaging and localized spectroscopy applications. However, besides the desired linear field gradients, pulsed currents in a strong external magnetic field also generate unwanted effects like eddy currents, gradient coil vibrations and acoustic noise. While the temporal magnetic field perturbations associated with eddy currents lead to spectral line shape distortions and signal loss, the vibration-related modulations lead to anti-symmetrical sidebands of any large signal (i.e. water), thereby obliterating the signals from low-concentration metabolites. Here the measurement, characterization and compensation of vibration-related magnetic field perturbations is presented. Following a quantitative evaluation of the various temporal components of the main magnetic field, a digital B0 magnetic field waveform is generated which reduces all temporal variations of the main magnetic field to within the spectral noise level.     

一种高效率小口径非球面数控抛光方法

自主设计研制的非球面数控抛光机采用气囊式抛光工具,可抛光100mm以下的非球面光学零件,针对口径35mm凹非球面透镜(顶点曲率半径R=-108.14mm的双曲面),研究了非球面的抛光工艺,并确定了相关工艺参数,抛光时间大约为20min,第二次次抛光后元件面形精度达到1.08μm,满足了该零件的使用要求。相对于现有设备美国Precitich公司的Microfinish 300型CNC非球面抛光机,该抛光设备实现了中等精度要求的小口径非球面元件的高效数控抛光。目前该抛光机已经成功地应用于某光学系统非球面零件的批量生产中。     

X射线相位成像的最佳衬度

根据Zernike相衬观察法的基本思想和Fresnel–Kirchhoff衍射理论,采用傅里叶变换和卷积处理,考虑到临床实际,利用振幅近似和相位缓变条件,将X射线经过生物组织产生的相位改变转换成强度分布.在所导出的理论公式的基础上,作出相位衬度和吸收衬度与物平面到像平面距离的关系曲线.分析得到X射线相位衬度成像的最佳物像距离,并通过微聚焦X射线成像装置对蟑螂成像的实验加以验证,其结果表明理论所预言的成像最佳位置符合度较高.     

Stability of stochastic integrals under change of filtration

Let (Ω, ,P) be a probability space equipped with two filtrations { _t} and { _t} satisfying the usual conditions. Assume that X is a semimartingale and that h is locally bounded and predictable for each of the two filtrations { _t} and { _t}. New examples of such processes are given. Utilizing and extending partial results of Zheng (1982), this paper extends the available results on the relationship between the stochastic integral processes ∫^th_s dX_s taken respectively in the sense of { _t} and of { _t}. In particular, it is shown that these stochastic integrals differ at most by a continuous process with quadratic variation defined and equal to 0. If both stochastic integrals are { _t∩ _t} semimartingales, then it is proved that the stochastic integral ∫^th_s dX _s taken in { _t} sense is indistinguishable from that taken in { _t} sense.     

我国的地磁生物学研究

概述了我国地磁生物学研究工作的现状，主要包括以下两个方面：（１）地球基本磁场生物效应研究；（２）地球变化磁场生物效应的研究。     

Tiling problems and undecidability in the cluster variation method

In cluster approximations for lattice systems the thermodynamic behavior of the infinite system is inferred from that of a relatively small, finite subsystem (cluster), approximations being made for the influence of the surrounding system. In this context we study, for translation-invariant classical lattice systems, the conditions under which a state for a cluster admits an extension to a global translation-invariant state. This extension problem is related to undecidable tiling problems. The implication is that restrictions of global translation-invariant states cannot be characterized purely locally in general. This means that there is an unavoidable element of uncertainty in the application of a cluster approximation.     

Sufficiency for Optimal Control Problems Involving Parameters

The optimal control problem is extended to the case where the performance index, the differential constraints, and the prescribed final conditions contain parameters. The sufficient condition for a minimum is derived for nonsingular problems using the sweep method. As expected, it involves the finiteness of a matrix or the location of the conjugate point. The minimum-time navigation problem is solved as a fixed final time problem to illustrate the application of the theory.