A Nonconforming Arbitrary Quadrilateral Finite Element Method for Approximating Maxwell's Equations

The main aim of this paper is to provide convergence analysis of Quasi-Wilson nonconforming finite element to Maxwell's equations under arbitrary quadrilateral meshes.The error estimates are derived,which are the same as those for conforming elements under conventional regular meshes.     

Adaptive regulation for deterministic systems

For the linear deterministic system with unknown orders and coefficients adaptive controls are given so that the closed-loop system is stabilized and the unknown parameters are consistently estimated. Moreover, if the parameter estimation is ignored, then the system input and output can be reduced to zero with an exponential rate.This project is supported by the National Natural Science Foundation of China.In Commemoration of the 15th Anniversary of the Acta Mathematicae Applicatae Sinica.     

Cycle control functions and the number of limit cycles

The cycle control function is defined and used to estimate the number of limit cycles for some planar autonomous systems. Some sufficient conditions for the existence of no or at most one limit cycle are given.     

Discovery of a new long-lived isomeric state in 125Ce

A new long-lived isomeric state in the near proton dripline nucleus ¹²⁵Ce has been identified with Schottky mass spectrometry at GSI. The excitation energy E ^* = 103(12)keV and the decay time of 193(1)s have been obtained from a single stored fully ionized ^125m Ce⁵⁸⁺ ion. The data implies an E3 transition and a 1/2⁺ assignment for the spin of the isomer.     

Optimizing the optical field distribution of solid immersion lens system by a continuous phase filter

In solid immersion lens (SIL) microscopy systems with high numerical aperture (NA), there always exists the aberration produced by Fresnel effects at the interface between SIL and the sample. This aberration may cause the degradation of the image of sample. We design a continuous phase filter and optimize the optical field distribution of SIL system. The numerical results show that when the continuous phase filter is used, the field distribution of SIL system can be optimized, and the focal depth and intensity of transmitted light can be increased. At the same time, the intensity of side-lobe and the resolution are kept almost unchanged.     

关于半线性热方程的死角性质

本文考虑下述问题：这里，．本文证明了在发生死角时只有有限个死角点．     

粒子分辨CCT方法中的δ电子效应

提出了切伦科夫相关时间测量(CCT)中初始粒子在辐射体里产生的δ电子的干扰问题,以及降低干扰的方法. 通过模拟计算给出了北京τ-C工厂探测器初步设计中CCT的π/K分辨本领.     

On order-preservation and positive correlations for multidimensional diffusion processes

Summary As a continuation of the study by Herbst and Pitt (1991), this note presents two criteria. The first one is on the order-preservation for two (may be different) multidimensional diffusion processes. The second one is on the preservation of positive correlations for a diffusion process.Research supported in part by the Ying-Tung Fok Educational Foundation and the National Natural Science Foundation of China     

Deposition-evaporation stochastic systems in two and higher dimensions

We study the stochastic dynamics of deposition-evaporation cooperative processes of dimers, trimers, etc., in two- and higher-dimensional lattices. The dimer system in bipartite lattices allows for an exact solution of dynamic correlations and scaling functions by means of a quantum spin equivalence. Autocorrelations exhibit a diffusive asymptotic kinetics and crossovers of different dynamic regimes in highly anisotropic lattices. Monte Carlo simulations combined with finite-size scaling arguments support the validity of the diffusive picture in more general situations. Steady-state coverages and diffusion constants are obtained using mean-field approaches, spin wave calculations, and random walk analyses in nearly jammed configurations.     

Molecular Orbital Calculations on 2, 4, 6-Trinitrotoluene

Three ab initio calculations (HF/6-3IG, HF/6-3IG*, and HF/6-3IG**) on 2,4,6-trinitrotoluene were made, The results compare well with xray data, except dihedral angles of NO₂ relative to the plane of the benzene ring. The deviations are attributed to packing forces and steric effects in the crystal. The most stable structure was a torsional angle 10° of the methyl top with the benzene ring, unlike toluene. The rotational barriers of the methyl top and the 4-nitro group are small. Hydrogen bonding, dipole moments and total atomic charges arc calculated.