An expansion in the exponent for compound binomial approximations

The purpose of this paper is two-fold. First, we introduce a new asymptotic expansion in the exponent for the compound binomial approximation of the generalized Poisson binomial distribution. The dependence of its accuracy on the symmetry and shifting of distributions is investigated. Second, for compound binomial and compound Poisson distributions, we present new smoothness estimates, some of which contain explicit constants. Finally, the ideas used in this paper enable us to prove new precise bounds in the compound Poisson approximation. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 1, pp. 67–110, January–March, 2006.     

An Alternative Approach to Obtain the Exact Wave Functions of Time-Dependent Hamiltonian Systems Involving Quadratic, Inverse Quadratic, and (1/x)p+p(1/x) Terms

By using the Lewis-Riesenfeld theory and algebraic method, we present an alternative approach to obtain the exact solution of time-dependent Hamiltonian systems involving quadratic, inverse quadratic and (1/x)p+p(1/x) terms. This solution is discussed and compared with that obtained by Choi, J. R. (2003). International Journal of Theoretical Physics 42, 853]. PACS: 03.65Ge; 03.65Fd; 03.65Bz     

CH分子束的强度与CH_4/He混合配比的关系及CH(A~2Δ)振转温度的计算

为了获得CH分子束及其相关特性,以氦气为载气,利用直流脉冲放电技术产生了CH分子束。实验记录了放电时间相对于脉冲分子束不同延时CH光谱信号强度的变化,放电相对延时为460μs左右获得最大的信号强度。研究了在保持CH4/He总气压3 atm和放电电压-4 kV不变的条件下CH分子束强度与不同配比的关系,建立了理论模型,对实验数据进行了理论拟合,拟合曲线与实验结果符合较好,配比为1%(甲烷与氦的气压比为1∶99)左右能够维持较稳定的放电现象和较强的放电强度而获得较强的CH自由基束流。在这一配比下对CH(A2Δ-X2Π)(0,0)带发射光谱进行探测和分析,获得CH(A2Δ)转动温度和振动温度分别为2455 K和4575 K,并估计此时每个脉冲中大约包含1013~1014个CH自由基。     

Assessment of thermal expansion coefficient of methylsilsesquioxane thin film

For the methylsilsesquioxane film whose optical birefringence is almost zero, it was recently reported that its vertical thermal expansion coefficient (CTE) was approximately one order of magnitude larger than the lateral CTE. Though the birefringence is not an absolute predictor of anisotropic behavior, the discrepancy in both the CTEs was so remarkable that it was essential to investigate whether the anisotropy was intrinsic property or not. If the effect of Poisson's ratio is considered in the calculation of the vertical CTE and when elastic modulus measured by surface acoustic wave spectroscopy is used in the assessment of the lateral CTE, both the CTEs are coincident with each other. Therefore, it can be concluded that the discrepancy in the CTEs can be attributed to a higher in‐plane polymer chain orientation but it can also arise from the misleadingly assumed modulus and Poisson's ratio. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3109–3120, 2006     

四阶半线性椭圆型积分微分方程的奇摄动

本文研究了一个四阶椭圆型积分微分方程的奇摄动问题。证明了相应的比较定理并得到了解的一致有效的渐近展开式。     

Multi-cracks problem for piezoelectric materials strip subjected to dynamic loading

This paper analyses and models the dynamic interaction among permeable multi-cracks in a piezoelectric strip under anti-plane shear waves by the Schmidt method. The Fourier transform is applied and then two pairs of triple integral equations can be solved using the Schmidt method. The results show that the stress and the electric displacement intensity factors of cracks depend on not only the crack length and the piezoelectric coefficient, but also the thickness of the piezoelectric strip, the distance between multi-cracks and the frequency of incident wave.     

Effect of the three-body force on triton asymptotic normalization constants by the hyperspherical harmonics expansion method

We investigate the change in the calculated value of asymptotic normalization constant (ANC) by the hyperspherical harmonics expansion method with the inclusion of three nucleon force (3BF) in addition to two nucleon force. We see that ANC does not change very much with the inclusion of 3BF indicating that the 3BF does not alter the asymptotic behaviours of HHE wavefunction significantly.     

Effect of nonlinear wave-current interaction on flow fields and hydrodynamic forces

A fifth-order theory for solving the problem of interaction between Stokes waves and exponential profile currents is proposed. The calculated flow fields are compared with measurements. Then the errors caused by the linear superposition method and approximate theory are discussed. It is found that the total wavccurrent field consists of pure wave, pure current and interaction components. The shear current not only directly changes the flow field, but also indirectly does so by changing the wave parameters due to wave-current interaction. The present theory can predict the wave kinematics on shear currents satisfactorily. The linear superposition method may give rise to more than 40% loading error in extreme conditions. When the apparent wave period is used and the Wheeler stretching method is adopted to extrapolate the current, application of the approximate theory is the best. Project supported by the Chinese Academy of Sciences.     

A note about the Gaussian property of the Brownian bridge

The Gaussian property of the Brownian bridge is characterized as an application of Ramachandran's theorem in terms of the independence of the random variables that appear in the Karhunen-Loéve expansion of the process. A reference about the construction of the Brownian bridge by means of functional transformations is also included.     

An analysis of the radiation reaction in a charged dumbbell

We make a thorough non-covariant analysis of the derivation of the equation of motion for a charged particle, including radiation reaction, by means of a simple model for the charge: a dumbbell. This model and our method to expand retarded quantities, based on complex-variable theory, allow us to avoid some of the usual approximations, so we can show several features of the radiation reaction problem.