Character of the thermal motion of water molecules according to the data on quasielastic incoherent scattering of slow neutrons

The paper discusses the applicability of quasi-crystalline approximation to describing the thermal motion of water molecules in their normal and supercooled states. The problem is subjected to the critical analysis of experimental data on incoherent scattering of slow neutrons based on theories developed by Singwi-Sjolander [1] and Oskotsky [2] modified to duly take into account the limited applicability range of diffusion approximation. The applicability conditions of quasi-crystalline approximation are shown to be consistently satisfied only when water is in supercooled state and within a narrow temperature range above the melting temperature.     

Using multi-exposure of color fringes to measure the beating motion of a moth

A multi-exposure of color fringes method has been developed to improve the capture speed of a conventional color CCD camera. In the method, four groups of projected fringe patterns encoded with different colors and different directions are stored in one CCD frame. Therefore the capture frequency of the conventional CCD can be improved to 200 Hz. It is available to measure the insect wings with low beating frequency, such as dragonfly, moth, or butterfly, whose beating frequency is about 30–40 Hz. We have used the method to measure the beating motion of a moth successfully.     

空气/水界面水分子的取向和运动

对四种不同的实验构型下空气／水界面自由O-H键在3700cm~(-1)的和频振动光谱的分析表明,水分子在空气／水界面的取向运动只可能是在平衡位置附近有限角度之内的受限转动。界面水分子的自由O-H键取向距界面法线约33°,而取向分布或运动的宽度不超过15°。这一图像显著地不同于Wei等人(Phys. Rev. Lett.86,4799(2001))只通过单一的SFG实验构型所得出结论,即：空气／水界面的水分子在超快的振动弛豫时间内在很大的角度范围内运动。     

Estimation of integrated volatility in stochastic volatility models

In the framework of stochastic volatility models we examine estimators for the integrated volatility based on the pth power variation (i.e. the sum of pth absolute powers of the log‐returns). We derive consistency and distributional results for the estimators given high‐frequency data, especially taking into account what kind of process we may add to our model without affecting the estimate of the integrated volatility. This may on the one hand be interpreted as a possible flexibility in modelling, for example adding jumps or even leaving the framework of semimartingales by adding a fractional Brownian motion, or on the other hand as robustness against model misspecification. We will discuss possible choices of p under different model assumptions and irregularly spaced data. Copyright © 2005 John Wiley & Sons, Ltd.     

论恒力作用下质点的相对论运动

在相对论情况下，讨论了受恒力作用的质点的运动规律。     

On Weak Solutions of an Integral Equation Driven by a p-Semimartingale of Special Type

We consider the integral equation driven by a standard Brownian motion and by a fractional Brownian motion. Sufficient conditions under which the equation has a weak solution are obtained.     

In-time motion adjustment in laser cladding manufacturing process for improving dimensional accuracy and surface finish of the formed part

This paper presents in-time motion adjustment in laser cladding manufacturing process as a means to improve dimensional accuracy and surface finish of the built part. Defects occurring during laser cladding degrade the part quality such as dimensional accuracy and surface finish. In this paper, in-time motion adjustment strategy was presented to remedy and eliminate defects occurring during laser cladding to improve the dimensional accuracy and surface finish. Based on the relationship between the motion of laser head relative to the growing part and other parameters in effects on clad profile, the laser traverse speed, stand-off distance and laser approach orientation to the existing clad layer were adjusted by instructions from a close-loop control system in real time to remedy and eliminate defects. The results of the experiments verified the effects of in-time motion adjustment on dimensional accuracy and surface finish.     

Some Notes about Tanaka''''s Equation

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The Clock Paradox in a Static Homogeneous Gravitational Field1

The gedanken experiment of the clock paradox is solved exactly using the general relativistic equations for a static homogeneous gravitational field. We demonstrate that the general and special relativistic clock paradox solutions are identical and in particular that they are identical for finite acceleration. Practical expressions are obtained for proper time and coordinate time by using the destination distance as the key observable parameter. This solution provides a formal demonstration of the identity between the special and general relativistic clock paradox with finite acceleration and where proper time is assumed to be the same in both formalisms. By solving the equations of motion for a freely falling clock in a static homogeneous field elapsed times are calculated for realistic journeys to the stars. ¹ Both authors contributed equally to this paper.     

A Joint Integral Test for the Locations of Extrema for Brownian Motion

Let μ⁺(t) and μ⁻(t) be the locations of the maximum and minimum, respectively, of a standard Brownian motion in the interval [0,t]. We establish a joint integral test for the lower functions of μ⁺(t) and μ⁻(t), in the sense of Paul Lévy. In particular, it yields the law of the iterated logarithm for max(μ⁺(t),μ⁻(t)) as a straightforward consequence. Our result is in agreement with well-known theorems of Chung and Erdős [(1952) Trans. Amer. Math. Soc. 72, 179–186.], and Csáki, F?ldes and Révész [(1987) Prob. Theory Relat. Fields 76, 477–497].