二阶椭圆型微分方程解的振动定理

考虑二阶非线性椭圆型微分方程∑^n_{i,j}∂/∂x_i{A_{i,j}(x,y)∂/∂x_j}+q(x)f(y)=0 (E)，其中q(x)在外区域 Ω∈R\+n上变号. 利用偏Riccati变换和积分平均技巧, 建立了方程(E)所有解振动的充分准则.     

Navier-Stokes方程带Backtracking技巧的两重网格算法

1 引 言考虑二维不可压 Navier-Stokes方程:     

Exact solutions and geometric phase factor of time-dependent three-generator quantum systems

There exist a number of typical and interesting systems and/or models, which possess three-generator Lie-algebraic structure, in atomic physics, quantum optics, nuclear physics and laser physics. The well-known fact that all simple 3-generator algebras are either isomorphic to the algebra sl (2, C) or to one of its real forms enables us to treat these time-dependent quantum systems in a unified way. By making use of both the Lewis-Riesenfeld invariant theory and the invariant-related unitary transformation formulation, the present paper obtains exact solutions of the time-dependent Schr?dinger equations governing various three-generator Lie-algebraic quantum systems. For some quantum systems whose time-dependent Hamiltonians have no quasialgebraic structures, it is shown that the exact solutions can also be obtained by working in a sub-Hilbert-space corresponding to a particular eigenvalue of the conserved generator (i.e., the time-independent invariant that commutes with the time-dependent Hamiltonian). The topological property of geometric phase factors and its adiabatic limit in time-dependent systems is briefly discussed. Received 6 July 2002 / Received in final form 21 October 2002 Published online 11 February 2003     

Natural Operators Lifting Vector Fields to Bundles of Weil Contact Elements

Let A be a Weil algebra. The bijection between all natural operators lifting vector fields from m-manifolds to the bundle functor K ^A of Weil contact elements and the subalgebra of fixed elements SA of the Weil algebra A is determined and the bijection between all natural affinors on K ^A and SA is deduced. Furthermore, the rigidity of the functor K ^A is proved. Requisite results about the structure of SA are obtained by a purely algebraic approach, namely the existence of nontrivial SA is discussed.     

Stability analysis of abnormal multiplication of plankton using parameter identification technique

This paper presents the mathematical approach for the abnormal multiplication of plankton. An abnormal multiplication can be expressed as an unstable problem and the stability of the system is investigated by introducing eigenvalues of a mathematical equation. The stability of the system can be judged by an eigenvalue based on the Lyapunov's stability theory. In this paper, the Arnoldi‐QR method is used to obtain eigenvalues and eigenvectors of the system. The mode superposition method is employed to create spatial distribution needed to analyse the stability. To obtain the objective eigenvalue, the parameter identification technique is employed. The finite element method is used for the discretization in space. Lake Kasumigaura, which is located in Ibaraki Prefecture in Japan, is selected and actual data in 1975, 1976, 1991 and 2000 are used in order to investigate the stability of the specified lake in Japan. Copyright © 2004 John Wiley & Sons, Ltd.     

Investigation on chaotic motion in hysteretic non-linear suspension system with multi-frequency excitations

This paper presents the investigation on possible chaotic motion in a vehicle suspension system with hysteretic non-linearity, which is subjected to the multi-frequency excitation from road surface. The Melnikov’s function is used to derive the critical condition for the chaotic motion, and then it is investigated that the effects of parameters in non-linear damping on the chaotic field. The path from quasi-periodic to chaotic motion is found via Poincaré map and Lyapunov exponents.     

Simultaneous Measurement of Droplet Size and Three-Components of Velocity in Spray

The combination of the optical diagnostics and image processing technique has produced various methods of practical measurement in engineering. The measurement of size and velocity of droplets in fuel spray is one typical example. In general, the spray is a complicated and three-dimensional two-phase flow; therefore multi-dimensional field measurement of the spray field is indispensable. In the present paper, a technique of simultaneous measurement of droplet size and three-components of velocity is proposed and applied to spray issuing from the swirl nozzle as a practical application. The focused image of glare points is captured by a stereoscopic arrangement, and droplet size and the three-components of velocity are evaluated from the doublet image. Fundamental optical arrangements to capture the image of the glare points with a stereo view are established, and the feasibility and the accuracy of the technique are confirmed. © 2004 The Optical Society of Japan     

Determination of optical nonlinearities in Cu(mpo)2 by Z-scan technique

The optical nonlinearities of Cu(mpo)₂ [formula = C₁₀H₈N₂CuO₂S₂] complex have firstly been investigated by using the Z-scan technique with a nanosecond-pulsed Nd:YAG laser at its second harmonic (532 nm) radiation. The nonlinear optical absorption and refraction coefficients of Cu(mpo)₂ have been measured with the different on-axial peak irradiances I ₀ at the waist ranging from 0.48 to 5.66 GW/cm². The nonlinear transmittance characteristics exhibit the near resonant two-photon absorption (TPA) at 532 nm and are explained by a population redistribution model. The nonlinear absorption originates from the near resonant TPA while the mechanism of the nonlinear refraction is the near resonant TPA transition enhancement. The linear increasing dependences of the optical nonlinearities on the incident irradiance arise from the population redistribution due to the near resonant TPA.     

An embedding domain approach for a class of 2-d shape optimization problems: mathematical analysis

This contribution combines a shape optimization approach to free boundary value problems of Bernoulli type with an embedding domain technique. A theoretical framework is developed which allows to prove continuous dependence of the primal and dual variables in the resulting saddle point problems with respect to the domain. This ensures the existence of a solution of a related shape optimization problem in a sufficiently large class of admissible domains.     

A DC excited waveguide multibeam CO2 laser using high frequency pre-ionization technique

High power industrial multibeam CO₂ lasers consist of a large number of closely packed parallel glass discharge tubes sharing a common plane parallel resonator. Every discharge tube forms an independent resonator. When discharge tubes of smaller diameter are used and the Fresnel numberN ≪ 1 for all resonators, they operate in waveguide mode. Waveguide modes have excellent discrimination of higher order modes. A DC excited waveguide multibeam CO₂ laser is reported having six glass discharge tubes. Simultaneous excitation of DC discharge in all sections is achieved by producing pre-ionization using an auxiliary high frequency pulsed discharge along with its other advantages. Maximum 170 W output power is obtained with all beams operating in EH₁₁ waveguide mode. The specific power of 28 W/m is much higher as compared to similar AC excited waveguide multibeam CO₂ lasers. Theoretical analysis shows that all resonators of this laser will support only EH₁₁ mode. This laser is successfully used for woodcutting