Table of Content

20 January 1999, Volume 34 Issue 1

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The Sublimit Distribution of Small Random Perturbed Dynamic Systems

LI Yulin,QIAN Minping

1999, 35(1):  1-12. 

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In this article a general framework is given in order to study the large-time behavior of a dynamic system dX_t=b(X_t)dt perturbed by a small noise εdBt. The limit distribution of the perturbed system X^ε at time t ～exp(c/ε²) as ε→0 is roughly described through the hierarchy structure of attractors.

Impossibility of Difference Sets Depending on Certain Cyclotomic Equation

WAN Zhaoze

1999, 35(1):  13-17. 

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Let f=Ord_p(q), ε_pbe a primitive p-th root of unity，γ∈Z[ε_p]。Suppose that f is odd and γγ^-=n（where n∈Z, q|n）. By some assumption, K.T.Arasu and A.Pott obtain that γ can be written as the form γ＝∑^e_i=1a∑^f-1_j=0ε^iqj_p(where p-1=ef). And note that it would be nice if the condition "f is odd" could be removed. In this paper, the author will deal with the case "f is even" and get a corresponding results.

Regression Estimation Using Cluster Correlation

YANG Baohui,SUN Shanze

1999, 35(1):  18-22. 

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Some troubles emerge when we use regression estimator in such a case: in a continuous survey research, when the prior sample and the present sample are independent and they have different elements, we can not compute the regression coefficient. In this paper, we give a new regression estimator under the cluster correlation model. Simulation result shows that, in estimating the population mean, the new estimator is as good as the sample mean under the condition that the two samples are all from the whole population, and better than the sample mean when the prior sample is from the whole population and the present sample is from a subpopulation.

Confidence Limits about The Mean Time between the Failures (MTBF) in Assurance Test

ZHANG Xiao

1999, 35(1):  23-30. 

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On the basis of strict mathematical description about the assurance test, the optimal lower confidence limit and upper confidence limit are found out by the method of arranging order in the sample space.

Character Degrees of Finite Solvable Groups and Nilpotent Length

LU Ziqun

1999, 35(1):  31-34. 

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In this paper, we use n₁(G)=| {χ|χ∈Irr(G), χ(1) is a composite number}| and n₂(G)=|{χ(1)|χ∈Irr(G), χ(1) is a composite number}| to evaluate the nilpotent length of G, respectively.

Numerical Simulation of Drops Falling to and Splashing on Liquid Interfaces

XU Jun

1999, 35(1):  35-46. 

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The 2-D full Navier-Stokes equations are solved by second-order projection method coupled to level set technique to model the process of a drop falling to and impacting on a free surface of the same liquid. Striking discrepancies between the method and others are that the former includes the resistance and the upward-directed acceleration effects of the ambient liquid, and incorporates the effects of viscosity, gravity, and surface tension. Without applying any rejoining or repositioning techniques, the method can deal with singularities as cusps and corners appearing on the configuration, naturally, while main features of the procedures under various conditions observed in physical experiments can be captured in our numerical examples. As an updated version, the approach employs no reinitilization treatment.

Generalizations of Keldych-Sedov Formula and Their Applications

WEN Guochun,TIAN Maoying

1999, 35(1):  47-55. 

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It is known that the Keldych-Sedov formula gives the representation of solutions of the mixed boundary value problem for analytic functions in the upper half-plane the authors. But for many problems in mechanics and physics, one needs the more general formula of solutions of discontinuous Riemann-Hilbert boundary value problem for analytic functions in the upper half-plane and other special domains. In the present paper, the authors establish the representations of the general discontinuous boundary value problem for analytic functions in the upper half-plane and upper half-disk. Moreover the authors give their applications to some nonlinear elliptic complex equations. The results in present paper have the important applications to the equations of mixed type and nonlinear mechanics.

Frequency Dependence of The Properties about High Permeability Ferrite and Transformer

WANG Bo,PEI Xiedi,LIAO Shaobin

1999, 35(1):  56-59. 

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The research of the high initial permeability(6000-20000)ferrite and the frequency dependence of inductance of the ferrite transformer made by high permeability ferrite core are presented. When the driving frequency increases from 100Hz to 300kHz the inductance shows a V-shape L-f curve. The reasons forming such a V-shape curve are discussed in detail.

Microscopic Fluorescence Image Analysis System and Application on Optical Microcavity

GUO Chaohua,LIN Yong,XIN Yongchun,ZHANG Bei,ZHOU Dejian,HUANG Chunhui

1999, 35(1):  60-64. 

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The acquisition and digital analysis system of microscopic fluorescence image and their application on the study of organic optical microcavity were presented. A luminescence image of a rare-earth complex organic optical microdisk with radius of 0.000009m has been observed. The dominant Whispering-Gallery mode in this microdisk was demonstrated.

Effects of Charge Particles on The Fractal Structure

HOU Shimin,ZENG Yan,XUE Zengquan,WU Quande

1999, 35(1):  107-111. 

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We report the effects of charge particles on the fractal structure based on the Diffusion-Limited Aggregation(DLA) model. The dimensions of fractal structures become larger and the shapes of fractal structures alse change, in pace with the increase of the chargeability P in the scope of P≤30%. The reasons of the effects are discussed preliminarily.

A Special Case for Testing The Bond-responsive Relaxation Model

ZHAO Yufeng,XUE Zengquan,PANG Shijin

1999, 35(1):  119-124. 

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The electronic quenching energy arising from the splitting of the diamond Si into two half-infinite systems each with an ideal (111) surface is calculated using semiempirical tight-binding (SETB) method. In spite of the different sets of band structure parameters in the two independent SETB models employed, they reach the same conclusion which can be considered a test of the recently proposed bond-responsive relaxation model by us.

Determination on Size of Nanoclusters

WANG Dehuang,CHENG Humin,MA Jiming,LIANG Ruisheng,TANG Zhilie

1999, 35(1):  65-68. 

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The size of TiO₂, SnO₂ and CuCl nanoclusters are determined using the transmission electron microscopy and the X-ray diffraction spectrum. The measured results are analyzed comparably.

Calculation of The Electrostatic Field Distribution in RFQ Accelerator Ending Space

WU Yu

1999, 35(1):  69-73. 

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RFQ accelerator ending space voltage distribution is calculated by using the RELAX3D software for the first time. Discussion about the method for calculating the voltage of any point with interpolation is presented.

A Barotropic Quasi-geostrophic Model with Large-scale Orography, Friction and Heating

CHEN Jiong,LIU Shikuo

1999, 35(1):  74-80. 

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Starting from a barotropic model equations including large-scale orography, friction and heat factor, by means of scale analysis and small parameter method, then a barotropic quasi-geostrophic model with large-scale orography, friction and heating is obtained. It is shown that this equation is a basic one which is used to study the influence of the Tibetan Plateau on the large-scale flow in the atmosphere. If the dynamic effect, friction and heat effect of large-scale orography are disregarded, this model will degenerate to the general barotropic quasi-geostrophic one.

Observation Data Assimilation and Precipitation Prediction of The Limited-area Numerical Model in The Early Stage

ZHU Guofu

1999, 35(1):  81-88. 

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A series of forecast experiments on a heavy Mei-yu precipitation process in July 1991 are performed to reduce the spin-up error of the limited-area numerical weather prediction model by assimilating observation data in four dimensions. Two schemes of assimilation are designed to better initial states for the improvement of the model forecast in the early stage; one is Newtonian relaxation by nudging which is used for assimilating the observations of temperature and wind fields; the other is humidity-modifying scheme for assimilating precipitation observations. The results show: 1) the former is characterized by the initial state with large-scale weather situation and the initial field gains meso-scale information; 2) the latter develops low-pressure system and the initial field gains more and better mesoscale information; 3) As a result, the incorporation of two schemes improves the early 6h precipitation prediction. Newtonian relaxation by nudging is more important to the Mei-yu weather process by forming the large-scale environmental conditions.

Baroclinic Mesoscale Semi-balanced and Quasi-balanced Dynamic Models

ZHAO Qiang,LIU Shikuo

1999, 35(1):  89-100. 

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The physical characteristics of mesoscale are analyzed, and results show that the unbalanced forced motion is the fundamental cause, which lead to evolution of some important mesoscale weather systems. The mesoscale dynamics equations are the basis of the theoretical studies of mesoscale atmospheric dynamics. There fore, according to the characteristics of the mesoscale motion, the formal scaling analysis and the asymptotic theory are used to simplify the governing atmospheric dynamics equations which are based on fluid dynamics and thermodynamics, so they can describe the basic characteristics of the mesoscale motion more accurately. These procedures are essential for the development of the mesoscale dynamics. The semi-balanced and quasi-balanced models based on nonlinear balance equation are derived;they are in analogy with the semi-geostrophic and quasi-geostrophic models, respectively, and may be used as basis for the theoretical studies of the mesoscale atmospheric dynamics. The uasi-balanced model is also used to study the mesoscale balanced vortex system, and the conclusion has shown that the mesoscale vortex system is mainly controlled by the gradient wind, and the development of its wind and pressure fields are described by an evolution equation.

Some Theoretical Issues in Climate Studies

LI Xiaodong,ZHANG Qinghong,YE Jinlin

1999, 35(1):  101-106. 

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This paper discusses some theoretical issues in the following aspects: methodology, climatic model, climatic change and climate prediction.

AC Zeeman Effect of Atom

XING Aitang

1999, 35(1):  125-129. 

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The formula of level shifts in AC Zeeman effect is derived on the base of a simple semiclassical method. The theoretical predictions of this formula are qualitatively in good agreement with the phenomena observed in AC Zeeman experiment. Furthermore, two important properties of AC Zeeman effect are predicted in theory: the level shifts in AC Zeeman effect of atom are the transient courses concurring with transition; the level shifts have saturation property.

The Resonant Characteristics of Eccentric Circular and Concentric Circular-elliptical Ring Microstrip Antennas

RAO Qinjiang,GONG Zhonglin,XU Chenghe

1999, 35(1):  130-135. 

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To study the resonant characteristics of eccentric circular and concentric circular-elliptical ring microstrip antennas, the method, which is connected with the concentric ring microstrip antenna and based on the perturbation, is employed to calculate resonant wave numbers. Comparisons of calculations with reference for the fundamental mode are also presented, agreement is very good for small eccentricity.

Aliasing-free Discrete-time Time-frequency Distribution

GAO Qianli,ZHAO Qun,CHI Huisheng

1999, 34(1):  112-118. 

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Cohen's bilinear time-frequency distribution has received considerable attention as a powerful tool for analyzing nonstationary signals. In this paper, a new discrete-time time-frequency distribution is introduced. Unlike the existing analytic signal method, the new one utilizes all signal local autocorrelation information, so that, without computing analytic signal, one can avoid aliasing when the signal is sampled at one Nyquist's rate. Some desirable distribution properties and associated kernel requirements are also discussed.