A finite point method for adaptive three‐dimensional compressible flow calculations

The finite point method (FPM) is a meshless technique, which is based on both, a weighted least‐squares numerical approximation on local clouds of points and a collocation technique which allows obtaining the discrete system of equations. The research work we present is part of a broader investigation into the capabilities of the FPM to deal with 3D applications concerning real compressible fluid flow problems. In the first part of this work, the upwind‐biased scheme employed for solving the flow equations is described. Secondly, with the aim of exploiting the meshless capabilities, an h‐adaptive methodology for 2D and 3D compressible flow calculations is developed. This adaptive technique applies a solution‐based indicator in order to identify local clouds where new points should be inserted in or existing points could be safely removed from the computational domain. The flow solver and the adaptive procedure have been evaluated and the results are encouraging. Several numerical examples are provided in order to illustrate the good performance of the numerical methods presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Gauss legendre quadrature formulas over a tetrahedron

In this article we consider the Gauss Legendre Quadrature method for numerical integration over the standard tetrahedron: {(x, y, z)|0 ≤ x, y, z ≤ 1, x + y + z ≤ 1} in the Cartesian three‐dimensional (x, y, z) space. The mathematical transformation from the (x, y, z) space to (ξ, η, ζ) space is described to map the standard tetrahedron in (x, y, z) space to a standard 2‐cube: {(ξ, η, ζ)| ? 1 ≤ ζ, η, ζ ≤ 1} in the (ξ, η, ζ) space. This overcomes the difficulties associated with the derivation of new weight coefficients and sampling points. The effectiveness of the formulas is demonstrated by applying them to the integration of three nonpolynomial, three polynomial functions and to the evaluation of integrals for element stiffness matrices in linear three‐dimensional elasticity. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

The use of geometric meshes in product integration Simpson''s rules

This paper concerns with the use of geometric meshes in product integration Simpson's rules for the numerical evaluation of weakly singular weighted integrals. We provide a criterion for selecting the mesh in order to achieve a desired accuracy with a low amount of computation. Numerical experiments indicate a reduction in computational costs with respect to the same rules with uniform meshes.     

高精度数值积分公式的构造及其应用

通过对一个给定的数值积分公式进行加速、改进,得到了两类新的精度更高的数值积分公式.然后将其进行复合,得到复合公式,并将复合公式推广到计算二重积分.最后进行了数值实验,数值计算结果表明:两类新的数值积分公式都具有比给定的公式更高阶的精度和更快的收敛速度.     

各向异性Besov函数的最优积分误差

1 引言设f(x)=f(x1,…,xd)是D=[0,2π]d上关于每一个变量以2π为周期的实函数．我们记f∈Lp(D)(1≤p≤∞)如果     

Flat Circle Planes as Integrals of Flat Affine Planes

In a previous article (Arch. Math. {64} (1995), 75–85) we showed that flat Laguerre planes can be constructed by'integrating' flat affine planes. It turns out that'most' of the known flat Laguerre planes arise in this manner. In this paper we show that similar constructions are also possible in the case of the other two kinds of flat circle planes, that is, the flat Möbius planes and the flat Minkowski planes. In particular, we show that many of the known flat Möbius planes can be constructed by integrating a closed strip taken from a flat affine plane. We also show how flat Minkowski planes arise as integrals of two flat affine planes. All known flat Minkowski planes can be constructed in this manner.     

Gaussian Versus Optimal Integration of Analytic Functions

We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the constant weight function and arguments outside the interval of integration. September 7, 1995. Date revised: October 25, 1996.     

Nodal type bound states of Schrödinger equations via invariant set and minimax methods

For nonlinear Schrödinger equations in the entire space we present new results on invariant sets of the gradient flows of the corresponding variational functionals. The structure of the invariant sets will be built into minimax procedures to construct nodal type bound state solutions of nonlinear Schrödinger type equations.     

硅基光电集成器件研究进展

随着器件结构与制作工艺的不断创新与完善，硅基发光器件已经可以实现室温下的有效工作，外量子效率可达到0．1％；低功耗的硅基高速调制器件的调制速率达到1GHz以上；而硅基光探测器对1300nm与1550nm波长的探测响应度也已分别达到了0．16mA／W和0．08mA／W．文章对硅基光电器件的研究进展情况进行了概述，并着重对几种器件的结构及工作原理进行了分析．     

The importance of the voice in male-to-female transsexualism.

Transsexuality is a complex, permanent transposition involving a paradoxical feeling of belonging to the opposite sex. Furthermore, in the case of male-to-female transsexuals, the unchanged male voice, which is at odds with the female outward appearance, poses a serious obstacle to full social integration of the woman. One way of permanently raising the fundamental frequency, requiring little effort, is modified cricothyroidopexy via miniplates, which has been used in our hospital since 1993 following a technique developed by Isshiki (thyroplasty type IV). Until now, this operation has been performed on 67 female patients. To record the anatomical-morphological and functional data, preoperatively, post-operatively, and a year after the operation, a detailed voice diagnosis was made, laryngoscopy was carried out, X-rays were taken, and computer-assisted tomography was used to examine the larynx. Thus far, the functional results have been good. On average, the fundamental frequency has been raised by about one fourth. Whereas none of the female patients had a female-speaking voice before the operation, after the operation, about 30% of the patients' voices were in the female range, and 32% had at least a neutral-sounding voice.