On Generating Discrete Orthogonal Bivariate Polynomials

In this paper we present an algorithm for recursively generating orthogonal bivariate polynomials on a discrete set S ². For this purpose we employ commuting pairs of real symmetric matrices H, K ^n×n to obtain, in a certain sense, a two dimensional Hermitian Lanczos method. The resulting algorithm relies on a recurrence having a slowly growing length. Practical implementation issues an applications are considered. The method can be generalized to compute orthogonal polynomials depending on an arbitrary number of variables.     

On G 2 Continuous Spline Interpolation of Curves in ℝ d

In this paper the problem of G ² continuous interpolation of curves in ^d by polynomial splines of degree n is studied. The interpolation of the data points and two tangent directions at the boundary is considered. The case n = r + 2 = d, where r is the number of interior points interpolated by each segment of the spline curve, is studied in detail. It is shown that the problem is uniquely solvable asymptotically, e., when the data points are sampled regularly and sufficiently dense, and lie on a regular, convex parametric curve in ^d . In this case the optimal approximation order is also determined.     

增量式轴角编码器的电子细分及零位处理

使用单片机对增量式光电轴角编码器产生的叠栅条纹信号进行计数和电子细分,便可将轴的机械转动模拟量转换成数字量;加上固定参考零位后,可使编码器具有"记忆"功能,因此对如何解决零位技术问题做了详细分析说明,并给出了实际解决方案.     

Field of View Increase for Optical Heterodyne Receivers

The field of view of optical heterodyne systems are usually limited by a simple criterion- namely, that A_RR ², where A_R is an effective aperture, _R the corresponding field of view and the optical wavelength. This paper will demonstrate that with a simple change of systems geometry and the possible use of array detectors, this severe restriction can be alleviated considerably and, in some cases, eliminated. Both coherent sources and thermal radiation sources are considered. This might suggest that heterodyne systems that were eliminated in the past because of that criterion alone, could turn out to be, not only possible, but even advantageous compared to other techniques.     

基于LAGRANGE插值的高阶微分中值定理

本文基于LAGRANGE插值，将微积分中非常重要的中值定理推广到了高阶的情形。     

任意三角形单元上的三次Lagrange型插值逼近

本文推广了文［２］中的结果，对于任意三角形单元的三次Ｌａｇｒａｎｇｅ型插值多项式给出了原函数ｕ与被插函数Ｕ之间的误差估计     

Parallel Calculation of Accurate Path Lines in Virtual Environments through Exploitation of Multi-Block CFD Data Set Topology

The use of Virtual Reality (VR) techniques for the investigation of complex flow phenomena offers distinct advantages in comparison to conventional visualization techniques. Especially for unsteady flows, VR methodology provides an intuitive approach for the exploration of simulated fluid flows. However, the visualization of Computational Fluid Dynamics (CFD) data is often too time-consuming to be carried out in real-time, and thus violates essential constraints concerning real-time interaction and visualization. To overcome this obstacle, we make use of the fact that typically a multi-block approach is employed for domain decomposition, and we use the corresponding data structures for the computation of path lines and for parallelization. In this paper, we present the synthesis of fragmented multi-block data sets and our implementation of an accurate path line integration scheme in order to speed up path line computations. We report on the results of our efforts and describe a combination of this algorithm with a highly efficient visualization approach of large amounts of particle traces, thus considerably improving interactivity when exploring large scale CFD data sets.Mathematics Subject Classifications (2000) 76Mxx, 76M27, 76M28, 65M55, 65L05, 65L06, 65D05, 65Y05, 68U05.     

A half-moment model for radiative transfer in a 3D gray medium and its reduction to a moment model for hot, opaque sources

We present in this paper a new 3D half-moment model for radiative transfer in a gray medium, called the model, which uses maximum entropy closure. This model is a generalization to 3D of the 1D version recently proposed in (J. Comp. Phys. 180 (2002) 584). The direction space Ω is divided into two pieces, Ω⁺ and Ω^-, in a dynamical way by the plane perpendicular to the total radiative flux, and the half moments are defined from these subspaces. The model closure and the integrations of the radiative transfer equation performed on the moving Ω^± spaces are detailed. 1D planar results, which have motivated the extension of the model of (J. Comp. Phys. 180 (2002) 584) to multi-dimensions, are shown. These results are very good. The model is thereafter derived for 3D spherically symmetric geometry, where the correctness of the non-trivial border terms can be checked. Two 3D spherically symmetric problems are numerically solved in order to show the accuracy of the closure and the role of the border terms. Once again, compared to the solution obtained with a ray tracing solver, results are very good. From the 3D half-moment model, a new moment model, called , is derived for the particular case of a 3D hot and opaque source radiating into a cold medium, for applications such as simulations of stellar atmospheres and fires. Two-dimensional numerical results are presented and compared to those obtained solving the RTE and with other moment models. They demonstrate the very good accuracy of the model, its good convergence properties, and better prediction compared to all other existing moment models in its domain of applicability.     

Experimental and theoretical analyses on the microwave backscattering ability and differential radar reflectivity of non-spherical hydrometeors

This paper experimentally and theoretically examines the scattering properties of simulated non-spherical hydrometeors including water oblates, ice oblates and ice sphere-cone-oblates, in terms of the backscattering cross-section and the differential reflectivity. The experimental measurements of the backscattering cross-sections of non-spherical hydrometeor samples were performed in the Electromagnetic Scattering Laboratory of China National Space Industrial Corporation. Meanwhile, the backscattering cross-sections have been computed with the transition (T) matrix method. The theoretical results are compared with the experimental data, showing that the calculations are consistent with the observations in general. Experimental and theoretical analyses indicate that the backscattering cross-section of non-spherical particles increases as the particle size parameter increases, and fluctuates when the sizes are larger under the effect of resonance scattering. Differential reflectivity Z_DR of water oblates in natural rainfall is always greater than 0 dB whereas Z_DR of hailstones may be negative. There is a good linear relationship between differential reflectivity and aspect ratio of a particle. These derivations agree with the literature and can be used to identify the presence of hail particles and distinguish between plate-type and columnar-type hydrometeors. In this study, the measuring experiment and the T-matrix method calculations for the scattering of simulated raindrop and ice particles are also briefly described.