Joint Distribution of Rises and Falls

The marginal distributions of the number of rises and the number of falls have been used successfully in various areas of statistics, especially in non-parametric statistical inference. Carlitz (1972, Duke Math. J.39, 268–269) showed that the generating function of the joint distribution for the numbers of rises and falls satisfies certain complex combinatorial equations, and pointed out that he had been unable to derive the explicit formula for the joint distribution from these equations. After more than two decades, this latter problem remains unsolved. In this article, the joint distribution is obtained via the probabilistic method of finite Markov chain imbedding for random permutations. A numerical example is provided to illustrate the theoretical results and the corresponding computational procedures.     

On Copure Projective Modules and Copure Projective Dimensions

Let R be any ring. A right R-module M is called n-copure projective if Ext¹(M, N) = 0 for any right R-module N with fd(N) ≤ n, and M is said to be strongly copure projective if Ext ⁱ (M, F) = 0 for all flat right R-modules F and all i ≥ 1. In this article, firstly, we present some general properties of n-copure projective modules and strongly copure projective modules. Then we define and investigate copure projective dimensions of modules and rings. Finally, more properties and applications of n-copure projective modules, strongly copure projective modules and copure projective dimensions are given over coherent rings with finite self-FP-injective dimension.     

Euler configurations and quasi-polynomial systems

Consider the problem of three point vortices (also called Helmholtz’ vortices) on a plane, with arbitrarily given vorticities. The interaction between vortices is proportional to 1/r, where r is the distance between two vortices. The problem has 2 equilateral and at most 3 collinear normalized relative equilibria. This 3 is the optimal upper bound. Our main result is that the above standard statements remain unchanged if we consider an interaction proportional to r ^b, for any b < 0. For 0 < b < 1, the optimal upper bound becomes 5. For positive vorticities and any b < 1, there are exactly 3 collinear normalized relative equilibria. The case b = −2 of this last statement is the well-known theorem due to Euler: in the Newtonian 3-body problem, for any choice of the 3 masses, there are 3 Euler configurations (also known as the 3 Euler points). These small upper bounds strengthen the belief of Kushnirenko and Khovanskii [18]: real varieties defined by simple systems should have a simple topology. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.     

Controllability of neutral functional integrodifferential systems in abstract space

In this paper, by using fractional power of operators and Sadovskii fixed point theorem, we study the controllability of abstract neutral functional integrodifferential systems with infinite delay. As application, an example is provided to illustrate the obtained results.     

Study on size-dependent optical property of 4,4′-dibromobiphenyl nanocrystals

4,4^′-dibromobiphenyl nanocrystals with different sizes in the range from 20 nm to 300 nm were prepared by the reprecipitation method. It was found that their absorption peaks experienced a red shift while the size of the nanocrystals increased. Through analyzing these spectra of the nanocrystals with different sizes, it is suggested that this size-dependent optical property is contributed by two factors, the size effect and the J-aggregate formation. Received: 28 August 2000 / Accepted: 2 March 2001 / Published online: 23 May 2001     

Anisotropy of sound velocity for a new PbB4O7 crystal as determined by the laser ultrasonic technique

4 O₇ crystal is a new nonlinear optical crystal. For the first time the anisotropy of the velocities of its longitudinal and surface acoustic waves (SAWs) are determined by laser ultrasonic technique. The velocities of surface waves for X-, Y-, and Z-cut crystals are also calculated. The theoretical calculations of slowness curves are in good agreement with experimental results. The SAW slowness curve is elliptical for Y- or Z-cut crystal wafers, and circular for an X-cut wafer. Received: 27 January 1997/Accepted: 30 July 1997     

Beam reception and data transmission performance analysis of optical taper used in a mobile wireless optical communication

Mobile wireless optical communication system was demonstrated experimentally by using a special solid coupling optical taper. The performance of special solid coupling optical taper and the data transmission performance with 240 Mbit/s were investigated on the rectilinear orbit between the mobile terminal and the fixed terminal. The experimental results shown that the scheme used in the mobile wireless optical communication system is reliable and quite simple, which could be widely used in future.     

角分辨光电子能谱光束线1200line/mm光栅研制

国家同步辐射实验室新建了覆盖5～40 eV的低能区高分辨率角分辨光电子能谱光束线.其球面光栅单色仪包含了三块光栅,即300,600和1200 line/mm球面层式(Laminar)光栅.采用全息离子束刻蚀工艺,在硅光栅基片上成功地刻蚀出1200 line/mm、占空比0.35、槽深35 nm、有效刻划面积大于120 ...     

Dual-wavelength laser operation at 1061 and 942 nm in Nd:GSAG

A dual-wavelength continuous-wave (CW) diode end-pumped gadolinium scandium aluminum garnet (Nd:GSAG) laser that generates simultaneous laser action at the wavelengths 1061 and 942 nm is demonstrated. A total output power of 589 mW (476 mW at 1061 nm and 113 mW at 942 nm) for the dual-wave-length was achieved at the incident pump power of 18.2 W. The M ² values for 942 and 1061 nm lights were found to be around 1.18 and 1.37, respectively.