色散渐减光纤中Ginzburg-Landau方程的自相似脉冲演化的解析解

采用对称约简的分析方法，得出了变系数Ginzburg-Landau方程的抛物渐近自相似脉冲解析解的一般表达式.给出了二阶色散系数纵向双曲型变化和纵向指数型变化的色散渐减光纤中自相似脉冲的振幅、啁啾以及脉冲宽度的具体形式，并与数值解进行了对比，其结果符合得很好.从而证实了稀土元素掺杂的色散渐减光纤中，在增益色散因子的影响下，脉冲的演化具有抛物型自相似特性.     

A Mechanical Model for Analyzing the Runaway Solutions in the Radiation Reaction Problem

In order to understand the rise of runaway solutions in the radiation reaction problem a mechanical model is used. An alternative demonstration of Daboul’s theorem, through Hurwitz’s criterion, is given. The origin of runaway solutions in electrodynamics is discussed. They arise when the particle has a negative mechanical mass or when approximations are used in the equation of motion. In the 1-dimensional mechanical model an exact and linear equation of motion for the particle is obtained, the corresponding exact solution is again runaway when the mechanical mass is negative. The exact solution is not runaway when the mechanical mass is positive. However, the use of approximations leads to an equation of motion which has runaway solutions. It is exhibited that the use of approximations in the 3-dimensional mechanical model is completely necessary because the general equation of motion for the particle is non-linear. The analysis of this case proceeds in a very similar way to the one carried out in electrodynamics. This means that the number of dimensions also plays an important role in the analysis.     

Vibrational dynamics of the organometallic compound triarylorganoantimony (V) SbPh<Subscript>3</Subscript>[O<Subscript>2</Subscript>CC(OH)Ph<Subscript>2</Subscript>]<Subscript>2</Subscript>

A complete normal coordinate analysis was performed for five-coordinate non-rigid triarylantimony diester SbPh₃(O₂CR)₂, known to be a bioactive molecule, using Wilson G-F matrix method and Urey Bradley force field. The study of vibrational dynamics was performed using the concept of group frequencies and band intensities.      

在两个耦合的量子点和腔QED系统中的双模激子的压缩性质(英文)

本文研究了在两个耦合的量子点和腔QED系统中的双模激子的压缩性质.讨论了不同的初始光场对双模激子的正常压缩与和压缩的影响.计算表明,当初始态光场制备在相干态时,双模激子既不存在正常压缩,也不存在和压缩,这说明双模激子振辐的两个正交分量具有相同的量子涨落;然而,当初始腔场处于压缩真空态时,无论是正常压缩还是和压缩,双模激子振辐的两个正交分量总有一个存在压缩.这意味着量子噪声能被有效的得到抑制.此外,两种情形下的最大压缩都由初始腔场的压缩因子r决定.经过比较,我们还发现双模激子的正常压缩比和压缩大.     

Calculation of conformations and vibrational spectra of a monomeric fragment of the 2,6-carboxymethyl cellulose molecule

A theoretical conformational analysis has been carried out for the side substituents of a fragment of the molecule for 2,6-carboxymethyl cellulose (a water-soluble cellulose ether), and the frequencies and the potential energy distribution of the normal vibrations have been calculated for the most stable conformers of the ether groups of this fragment in the approximation of the molecular mechanics method. It has been shown that the most stable conformers are those that have the conformations gg, t, g⁻, g⁻, g⁻-for the groups of atoms on the bonds C5-C6, C6-O6, C13-O6, C10-C13, C10-O9 and the conformations g⁺g⁻, g⁺, g⁻, g⁻; g⁺g⁻, g⁻, g⁻, g⁻; g⁺g⁻, g⁻, g⁺, t for the groups of atoms on the bonds C2-O2, C11-O2, C7-C11, C7-O8. Comparative analysis of the calculated frequencies and the potential energy distribution of the normal vibrations for 13 of the most stable conformers showed, as in the case of the 2,6-hydroxyethyl cellulose molecule, that the frequencies and modes of the normal vibrations are highly sensitive to conformational transitions in the analyzed spectral region (800–1500 cm⁻¹). The characteristic patterns for the change in the frequencies and modes of the normal vibrations have been established in connection with conformational transitions within both side substituents. The observed conformational lability of the bulky substituents in the cellulose ether molecules and its manifestations in the vibrational spectrum provide a basis for hypothesizing that one of the major mechanisms for the process of their thermal gelation in aqueous solutions is conformational transitions within these substituents. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 1, pp. 5–15, January–February, 2007.     

Multivariate Normal Slice Sampling

By introducing auxiliary variables, the traditional Markov chain Monte Carlo method can be improved in certain cases by implementing a “slice sampler.” In the current literature, this sampling technique is used to sample from multivariate distributions with both single and multiple auxiliary variables. When the latter is employed, it generally updates one component at a time.

In this article, we propose two variations of a new multivariate normal slice sampling method that uses multiple auxiliary variables to perform multivariate updating. These methods are flexible enough to allow for truncation to a rectangular region and/or exclusion of any n-dimensional hyper-quadrant. We present results of our methods and existing state-of-the-art slice samplers by comparing efficiency and accuracy. We find that we can generate approximately iid samples at a rate that is more efficient than other methods that update all dimensions at once. Supplemental materials are available online.     

Multivariate Normal Probabilities: Implementing an Old Idea of Plackett's

This article describes a reduction formula for the computation of multivariate normal probabilities first developed by Plackett. The method is recursive and, despite very promising results, seems not to have been implemented before. Extensive numerical results are given to compare the effectiveness of the approach to other methods from the literature.     

Normal tracing deflectometry using a secondary light source

Scanning deflectometric profilers based on an f–gθ system are typical optical tools used to measure mirror profiles at many synchrotron facilities. Unlike these profilers, which are based on a pencil beam, here a secondary light source and a pinhole are used to construct a system that automatically selects a beam that will always pass through the pinhole and propagate along the normal direction of the measured area on the surface under test. By measuring the angle variation of the selected beam, slope variations of the surface under test can be measured. Systematic errors introduced by manufacturing defects or aberrations of an optical element, which greatly degrade the performance of traditional profilers, could be minimized by using the developed method. Simulation values of the proposed method and a conventional method are compared.     

Fast computation of Hermite normal forms of random integer matrices

This paper is about how to compute the Hermite normal form of a random integer matrix in practice. We propose significant improvements to the algorithm by Micciancio and Warinschi, and extend these techniques to the computation of the saturation of a matrix. We describe the fastest implementation for computing Hermite normal form for large matrices with large entries.     

Asymptotic exponential cones of Metzler matrices and their use in the solution of an algebraic problem

The aim of this paper is that of investigating the asymptotic exponential cone of a single Metzler matrix, introduced in [23], and of defining and analysing the new concept of asymptotic exponential cone of a family of Metzler matrices (along a certain direction). These results will provide necessary and/or sufficient conditions for the solvability of an interesting algebraic problem that arises in the context of continuous-time positive switched systems and, specifically, in the investigation of the reachability property [21,22,25].