A TVD Type Wavelet-Galerkin Method for Hamilton-Jacobi Equations

In this paper,we use Daubechies scaling functions as test functions for the Galerkin method,and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations.It can be proved that the schemesare TVD schemes.Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations.Furthermore,they have high-order accuracy in smooth regions and good resolution of singularities.     

An implicit method for linear ill‐posed problems with perturbed operators

An implicit iterative method is applied to solving linear ill‐posed problems with perturbed operators. It is proved that the optimal convergence rate can be obtained after choosing suitable number of iterations. A generalized Morozov's discrepancy principle is proposed for the problems, and then the optimal convergence rate can also be obtained by an a posteriori strategy. The convergence results show that the algorithm is a robust regularization method. Copyright © 2006 John Wiley & Sons, Ltd.     

通过平均场处理的严格重正化群变换方法对Potts模型的应用

本文运用作者所发展的严格docimation- 平均场近似方法对Potts 模型的临界指数作了计算.所得结果与严格解符合得很好, 而与计算工作量相当的重正化群方法相比, 精确度大为提高。 关键词：     

A gas-kinetic scheme for shallow-water equations with source terms

In this paper, the Kinetic Flux Vector Splitting (KFVS) scheme is extended to solving the shallow water equations with source terms. To develop a well-balanced scheme between the source term and the flow convection, the source term effect is accounted in the flux evaluation across cell interfaces. This leads to a modified gas-kinetic scheme with particular application to the shallow water equations with bottom topography. Numerical experiments show better resolution of the unsteady solution than conventional finite difference method and KFVS method with little additional cost. Moreover, some positivity properties of the gas-kinetic scheme is established.     

Synthesis of β-phenyl-δ,ε-unsaturated amino acids and stereoselective introduction of side chain groups into [4,3,0]-bicyclic β-turn dipeptides

(2S,3S)- and (2R,3R)-2-amino-3-phenyl-5-hexenoic acids have been synthesized in large scale by using Ni(II)-complexes as a template. The amino acids were used in the synthesis of [4,3,0]-bicyclic β-turn mimetics by a convergent methodology. The unique advantage of this strategy is the convenience of introducing side chain groups with predetermined chiralities on both the five- and six-membered heterocyclic rings.     

Relaxor behavior of (Ba,Sr)(Zr,Ti)O3 ferroelectric ceramics

We examine the ferroelectric-relaxor behavior of (Ba_0.65Sr_0.35)(Zr_0.35Ti_0.65)O₃ (BSZT) ceramics in the temperature range from 80 to 380 K. A broad dielectric maximum, which shifts to higher temperature with increasing frequency, signifies the relaxor-type behavior of these ceramics. The value of the relaxation parameter γ∼2 estimated from the linear fit of the modified Curie-Weiss law, indicates the relaxor nature of the BSZT ceramics. The dielectric relaxation rate follows the Vogel-Fulcher relation with T_VF=107 K, E_a=0.121 eV, and ν₀=6.83×10¹⁴ Hz, further supports such relaxor nature. The slim P-E hysteresis loop and ‘butterfly’ shape dc bias field dependence of permittivity at T>T_m (T_m, the temperature of permittivity maximum) clearly signifies the occurrence of nanopolar clusters, which is the typical characteristic of ferroelectric relaxor. At 300 K and 10 kHz, the dielectric constant and loss tan δ are ∼1100 and 0.0015, respectively. The high tunability (∼25%) and figure of merit (∼130) at room temperature show that the BSZT ceramics could be a promising candidate for tunable capacitor applications.     

利用相干渡越辐射测量电子束团长度的分析与计算

利用相干渡越辐射(CTR)测量短和超短电子束团长度是国际上束测领域新发展的频域测量技术.文中理论分析和数值计算了北京自由电子激光装置的皮秒级的射频电子束团序列产生的CTR,当辐射波长在长于束长(4ps)时,渡越辐射发生相干增强效应;与非相干渡越辐射相比,当λ≥2πσz时,增强的倍数约等于束团中粒子的数目(10⁸);CTR从亚毫米波到毫米波段呈宽带连续谱特性;渡越辐射能量主要集中在轴线附近,宏脉冲辐射能量高达几毫焦.设计采用偏振型束团长度测量系统,利用CTR自相关技术,实验测量该束团序列的纵向长度,并藉助傅里叶变换光谱法,推求束团电子分布.     

完全Rees矩阵半群的分解及性质

用等价关系Q^~出了完全Rees矩阵半群的一种分解．而且得到了它的每个Q^~一类的表示．