Full asymptotics and Laurent series of layer potentials for Laplace's equation on the half‐space

We combine the calculus of conormal distributions, in particular the Pull‐Back and Push‐Forward Theorems, with the method of layer potentials to solve the Dirichlet and Neumann problems on half‐spaces. We obtain full asymptotic expansions for the solutions, show that boundary layer potential operators are elements of the full b‐calculus and give a new proof of the classical jump relations. En route, we improve Siegel and Talvila's growth estimates for the modified layer potentials in the case of polyhomogeneous boundary data. The techniques we use here can be generalised to geometrically more complex settings, as for instance the exterior domain of touching domains or domains with fibred cusps. This work is intended to be a first step in a longer program aiming at understanding the method of layer potentials in the setting of certain non‐Lipschitz singularities that can be resolved in the sense of Melrose using manifolds with corners and at applying a matching asymptotics ansatz to singular perturbations of related problems.     

X射线与CsI:Na转换屏作用规律的研究

本文用MonteCarlo方法模拟了轫致辐射X光子与CsI:Na转换屏的作用过程.给出了正向散射光子的角分布以及正向出射光子的能谱分布,指出正向散射光子的主要成分是CsI:Na的特征辐射光子,其能量为33.17和35.98keV.此外,还对吸收光子数与管电压和CsI:Na层厚度的关系进行了说明.     

Performance analysis of OTDM system in the presence of FEC using symmetric Mach-Zehnder switch

Optical time division multiplexing is an emerging and promising alternative for future high-speed photonic networks because of its ability to accommodate higher bit rate and flexible bandwidth. SMZ have been found to be the most suitable switching element than all the available de-multiplexing switches because of compact size, thermal stability, and low-power operation. In this paper, we simulate four channel OTDM systems (all-channel multiplexer and de-multiplexer) with a Mach-Zehnder modulator and an SMZ de-multiplexer to investigate the impact of FEC on the OTDM system. It is observed that the presence of FEC in OTDM transmission can greatly improve the system performance.     

Operational retrieval algorithms for JEM/SMILES level 2 data processing system

To measure the thermal emission from stratospheric minor species with high sensitivity, the Superconducting Submillimeter-wave Limb-Emission Sounder (SMILES) aboard the Japanese Experiment Module (JEM) of the International Space Station (ISS) carries 4 K cooled Superconductor–Insulator–Superconductor (SIS) mixers. The major feature of the SMILES is its high-sensitive measurement ability with low system noise temperature less than 700 K.As a part of the ground system for the SMILES, a level 2 data processing system (DPS-L2) has been developed. It retrieves the density distributions of the target species from calibrated spectra in near-real-time. The retrieval process consists of two parts: the forward model, which computes radiative transfer, and the inverse model, which deduces atmospheric states. Since the forward model must provide the most accurate basis for results and be implemented under limited computing resources, the forward model algorithm for an operational system has to be accurate and fast. Hence, the algorithm is improved (1) by designing accurate instrument functions such as the instrumental field of view (FOV), sideband rejection ratio of sideband separator, and spectral responses of acousto-optic spectrometer (AOS) and (2) by optimizing radiative transfer calculation.This paper presents the development of the DPS-L2 along with the details on its algorithm and the algorithm performance. The accuracy of this algorithm is better than 1%, and the processing time for single-scan spectra is less than 1 min with eight parallel processings using a 3.16-GHz Quad-Core Intel Xeon processor. Thus, this algorithm is suitable for the SMILES measurement.     

Forward equations for reflected diffusions with jumps

In this paper we obtain the forward equations associated with the evolution of the density, if it exists, of reflected diffusions on the positive orthant with jumps which form a marked point process whose random jump measure possesses a stochastic intensity. These results generalize the so-called generalized Dynkin equations for piecewise deterministic jump processes due to Davis. We then consider the stationary case where the existence of a stochastic intensity is not needed. The techniques are based on local times and the use of random jump measures. We discuss the application of these results to problems arising in queuing and storage processes as well as stationary distributions of diffusions with delayed and jump reflections at the origin.This research was supported in part by the Quebec-France Cooperative Research Program and by the Natural Sciences and Engineering Research Council of Canada under Grant OGP 0042024.     

Classification of three-class association schemes using backtracking with dynamic variable ordering

We describe several techniques for the exhaustive computer generation of non-isomorphic association schemes with a given set of intersection numbers using a backtracking algorithm with forward checking and dynamic variable ordering. We have applied these techniques to the classification of certain open parameter sets for three-class association schemes listed by Van Dam in (Three-class association schemes, J. Algebraic Combin. 10 (1999) 69–107) for which we present several new results. Among these are some new (imprimitive) distance regular graphs of diameter 3.     

Bechtold-Jacobs generalized model for shift scheduling with extraordinary overlap

In constructing working shifts, the classical Dantzig (Operation Research 2:339–341, 1954) set covering model uses a great number of variables which makes computation very complicated for some cases that incorporate a high degree of break-placement flexibility. Bechtold and Jacobs (Management Science 36:1339–1351, 1990) proposed an implicit model under the assumption that there is no extraordinary overlap, which considerably reduced the number of variables. In this paper we give a generalization that is valid without this hypothesis by adding a minimal set of constraints. Also, in some cases where there is extraordinary overlap we reduce our constraint set to a subset with the same number or less than that of Bechtold and Jacobs. I. Addou’s current address is Département de Mathématiques et Statistique, Université de Montréal, Succ. Centre-ville, Montréal, Québec, Canada, H3C2J7; e-mail: addou@dms.umontreal.ca.     

Mathematical proof of closed form expressions for finite difference approximations based on Taylor series

Taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms, with explicit formulas for their coefficients. However, those formulas were not derived mathematically and were based on observation of numerical results. In this paper, we provide a mathematical proof of those formulas by deriving them mathematically from the Taylor series.     

Running error for the evaluation of rational Bézier surfaces through a robust algorithm

Running error analysis of the corner cutting algorithm for rational Bézier surfaces is carried out and the sharpness of the corresponding error bounds is shown.     

正渗透过程中纳米碳管膜的盐水通道行为

以纳米碳管(CNT)仿生构筑正渗透(FO)膜, 采用分子动力学模拟的方法考察水和盐在由CNT(6,6)、CNT(7,7)、CNT(8,8)、CNT(9,9)、CNT(10,10)、CNT(11,11)等不同尺寸纳米碳管构筑膜中, 于2.5、3.75、5.0mol·L^-1等不同汲取液浓度下的传递行为. 纳秒级的模拟得到水分子在不同尺寸纳米碳管膜内的分布, 水通量的变化以及盐截留等情况. 模拟结果表明, 由CNT(8,8)构筑的正渗透膜表现出优异的通水阻盐性能.