Legendre Transformation for Regularizable Lagrangians in Field Theory

Hamilton equations based not only upon the Poincaré–Cartan equivalent of a first-order Lagrangian, but also upon its Lepagean equivalent are investigated. Lagrangians which are singular within the Hamilton–De Donder theory, but regularizable in this generalized sense are studied. Legendre transformation for regularizable Lagrangians is proposed and Hamilton equations, equivalent with the Euler–Lagrange equations, are found. It is shown that all Lagrangians affine or quadratic in the first derivatives of the field variables are regularizable. The Dirac field and the electromagnetic field are discussed in detail.     

Observation of room temperature negative differential resistance in solution synthesized ZnO nanorod

We report the observation of negative differential resistance (NDR) in solution synthesized ZnO nanorod. The ZnO nanorod was fabricated as a two terminal planar device using lithographically patterned Au electrodes. The measured current–voltage response of the device has shown a negative differential resistance behavior. The peak-to-valley current ratio of the NDR is found to be greater than 4. The mechanism of this observed NDR effect has been explained based on charge trapping and de-trapping at the nanoscale contacts. It is the first observation of negative differential resistance effect in solution synthesized ZnO nanorod.     

Separation of Variables for Bi-Hamiltonian Systems

We address the problem of the separation of variables for the Hamilton–Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called N manifolds, to give intrisic tests of separability (and Stäckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel'fand–Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations.     

An Approximated Solution of the Einstein Equations for a Rotating Body with Negligible Mass

The paper considers the problem of finding the metric of space time around a rotating, weakly gravitating body. Both external and internal metric tensors are consistently found, together with an appropriate source tensor. All tensors are calculated at the lowest meaningful approximation in a power series. The two physical parameters entering the equations (the mass and the angular momentum per unit mass) are assumed to be such that the mass effects are negligible with respect to the rotation effects. A non zero Riemann tensor is obtained. The order of magnitude of the physical effects is discussed.     

Stationary optimal control of a stochastic system with stable environmental interferences

In this paper, we consider a class of nonstationary control systems. We obtain some conditions for stationary optimal controls of such systems. The results are then applied to a linear-quadratic system.     

用图解法拟合线性方程时其不确定度的计算

本文给出了用图解法拟合线性方程时其不确定度的计算过程,并讨论了图解法的使用方法。     

Trends in microdisk laser research and linear optical modelling

Research into microdisk lasers demonstrates new achievements both in the technology and in the associated physical effects and applications. Melting and rounding of the disk edge boosts the Q-factors due to improved surface smoothness. In-plane cavity shape is widely used as a design instrument. Optimal shaping of pumped area lowers the threshold power. Photonic molecules made of several microdisks as “photonic atoms” show lasing at several closely spaced frequencies. A microdisk with a single quantum dot as an active region is considered as the most promising system for realisation of a single photon emitter necessary for quantum computing. These new effects and devices can be simulated with accurate numerical techniques, developed recently for “warm-cavity” linear modelling, that are able to bring a new vision of the physics of lasing.     

图像的微分处理与相关识别

介绍了小波图像微分原理,并对图像的微分处理与相关识别进行了实验分析和研究。实验结果表明,对图像进行小波微分预处理后,可以有效地减少图像中的低频成份,这就使图像相关运算更多地比较了图像的细节变化,增加了相关图像的信息量,可以有效地提高图像的识别能力。