Operation of the quasi-optical gyrotron at harmonics of the gyrofrequency

This paper investigates the performance of a quasioptical gyrotron, when the electron beam interacts with the radiation fields at harmonics of the gyrofrequency. The nonlinear equations of motion are obtained in the slow-timescale. The expression for the linear gain is derived and the conditions for excitation are given (frequency threshold, optimal operating point, bean current and resonator quality thresholds). In the nonlinear regime, it is shown that maximum efficiencies comparable to those at the fundemental (50%) are possible, albeit at a prohitively high radiation field amplitude, while realistically feasible field amplitudes can give somewhat smaller, but nevertheless still high efficiencies (15%). Finally, the results are suplemented by empirical scaling laws, useful for experimental designs.     

Evolution and characterization of fluorite-like nano-SrBi2Nb2O9 phase in the SrO-Bi2O3-Nb2O5-Li2B4O7 glass system

Transparent glasses of various compositions in the system (100−x)Li₂B₄O₇−x(SrO-Bi₂O₃-Nb₂O₅) (where x=10, 20, 30, 40, 50 and 60, in molar ratio) were fabricated via splat quenching technique. The glassy nature of the as-quenched samples was established by differential thermal analyses. X-ray powder diffraction (XRD) and transmission electron microscopic studies confirmed the amorphous nature of the as-quenched and crystallinity in the heat-treated samples. Fluorite phase formation prior to the perovskite SrBi₂Nb₂O₉ phase was analyzed by both the XRD and high-resolution transmission electron microscopy. Dielectric and the optical properties (transmission, optical band gap and Urbach energy) of these samples have been found to be compositional dependent. Refractive index was measured and compared with the values predicted by Wemple-Didomemenico and Gladstone-Dale relations. The glass nanocomposites comprising nanometer-sized crystallites of fluorite phase were found to be nonlinear optic active.     

关于两两NQD列的若干极限性质

本文讨论了两两ＮＱＤ列的Ｍａｒｃｉｎｋｉｅｗｉｃｚ型弱大数律及Ｊａｍｉｓｏｎ型加权和的强稳定性，指出了两两ＮＱＤ列与独立列的一个本质性区别，从而提出了解决两两ＮＱＤ旬几乎处处收敛和完全收敛的一种方式。     

神光-Ⅱ装置三倍频实验中靶场单元技术的改进

 主要介绍为了满足神光-Ⅱ高功率激光装置三倍频光（351nm，3ω）的物理实验要求，靶场三倍频模拟光源和瞄准监视系统两个主要单元技术的改进，即三倍频模拟光源由基频光（1 053nm，3ω）通过腔外的KTP+BBO晶体倍频获得，再经八路分光系统和主激光耦合；瞄准监视系统由透射式光学系统改进为反射式光学系统，避免原系统存在较大的色差，提高瞄准精度。     

再谈Minc-Sathre不等式的上下界

用调和平均值、均值不等式之间的关系及对数平均不等式,对Minc-Sathre不等式的上下界进行改进,使结论更精确.     

Harmonic and attosecond pulse enhancement in the presence of noise

<正>In this paper,we theoretically investigate the effect of noise on the photoionization,the generation of the high-order harmonic and the attosecond pulse irradiated from a model He~+ ion.It shows that by properly adding noise fields,such as Gaussian white noise,random light or colored noise,both the ionization probabilities(IPs) and the harmonic yields can be enhanced by several orders of magnitude.Further,by tuning the noise intensity,a stochastic resonance-like curve is observed,showing the existence of an optimal noise in the ionization enhancement process.Finally,by superposing a properly selected harmonic,an intense attosecond pulse with a duration of 67 as is directly generated.     

Numerical simulation and convergence analysis for a system of nonlinear singularly perturbed differential equations arising in population dynamics

In this article, we consider a system of nonlinear singularly perturbed differential equations with two different parameters. To solve this system, we develop a weighted monotone hybrid scheme on a nonuniform mesh. The proposed scheme is a combination of the midpoint scheme and the upwind scheme involving the weight parameters. The weight parameters enable the method to switch automatically from the midpoint scheme to the upwind scheme as the nodal points start moving from the inner region to the outer region. The nonuniform mesh in particular the adaptive grid is constructed using the idea of equidistributing a positive monitor function involving the solution gradient. The method is shown to be second order convergent with respect to the small parameters. Numerical experiments are presented to show the robustness of the proposed scheme and indicate that the estimate is optimal.     

Interbasis expansions for isotropic harmonic oscillator

The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n.     

Gauss–Seidel Estimation of Generalized Linear Mixed Models With Application to Poisson Modeling of Spatially Varying Disease Rates

Generalized linear mixed models (GLMMs) are often fit by computational procedures such as penalized quasi-likelihood (PQL). Special cases of GLMMs are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints make it difficult to apply these iterative procedures to datasets having a very large number of records.

We propose a computationally efficient strategy based on the Gauss–Seidel algorithm that iteratively fits submodels of the GLMM to collapsed versions of the data. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status, and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. For Poisson and binomial regression models, the Gauss–Seidel approach is found to substantially outperform existing methods in terms of maximum analyzable sample size. Remarkably, for both models, the average time per iteration and the total time until convergence of the Gauss–Seidel procedure are less than 0.3% of the corresponding times for the IWLS algorithm. Platform-independent pseudo-code for fitting GLMS, as well as the source code used to generate and analyze the datasets in the simulation studies, are available online as supplemental materials.