谱元方法求解二维不可压缩Navier-Stokes方程

利用有限元的思想并结合谱方法的精度提出求解偏微分方程的谱元方法,在元素内插值函数使用伪谱Chebyshev逼近,并将此方法应用于求解不可压Navier-Stokes方程,具体求解了二维方腔顶盖驱动流,与公认基准解对比获得了较好的结果。     

Linearized inverse scattering for elastic parameters in a half-space with reflection data

ＩｎｔｒｏｄｕｃｔｉｏｎＭｕｌｔｉｐａｒａｍｅｔｅｒｉｎｖｅｒｓｅｓｃａｔｔｅｒｉｎｇｆｏｒｅｌａｓｔｉｃｍｅｄｉｕｍｉｓａｆｏｕｎｄａｔｉｏｎａｌｐｒｏｂｌｅｍｉｎｓｅｉｓｍｏｌｏｇｙａｎｄｎｏｎｄｅｓｔｒｕｃｔｉｖｅｔｅｓｔｉｎｇ .ＷｉｔｈｉｎｔｈｅＢｏｒｎａｐｐｒｏｘｉｍａｔｉｏｎ ,ｔｈｉｓｐｒｏｂｌｅｍｈａｓｂｅｅｎｉｎｖｅｓｔｉｇａｔｅｄｂｙｓｅｖｅｒａｌａｕｔｈｏｒｓ.Ｂｌａｃｋｌｅｄｇｅｅｔａｌ.[1]ｈａｖｅｅｘｔｅｎｄｅｄｔｈｅＸ＿ｒａｙｔｏｍｏｇｒａｐｈｙｓｃｈｅｍｅｔｏｔｈｅｄ…     

Canonical form of a nonlinear monetary system

This paper addresses an autonomous system of quadratic ordinary differential equations, which describes a monetary system involving interest rate, investment demand and price index. The canonical form of this system is derived, which is dependent on a single parameter. On this basis, it is proved that this system is not smoothly equivalent to the generalized Lorenz canonical form.     

Gradient regularity for elliptic equations in the Heisenberg group

We give dimension-free regularity conditions for a class of possibly degenerate sub-elliptic equations in the Heisenberg group exhibiting super-quadratic growth in the horizontal gradient; this solves an issue raised in [J.J. Manfredi, G. Mingione, Regularity results for quasilinear elliptic equations in the Heisenberg group, Math. Ann. 339 (2007) 485-544], where only dimension dependent bounds for the growth exponent are given. We also obtain explicit a priori local regularity estimates, and cover the case of the horizontal p-Laplacean operator, extending some regularity proven in [A. Domokos, J.J. Manfredi, C1,α-regularity for p-harmonic functions in the Heisenberg group for p near 2, in: Contemp. Math., vol. 370, 2005, pp. 17-23]. In turn, using some recent techniques of Caffarelli and Peral [L. Caffarelli, I. Peral, On W1,p estimates for elliptic equations in divergence form, Comm. Pure Appl. Math. 51 (1998) 1-21], the a priori estimates found are shown to imply the suitable local Calderón-Zygmund theory for the related class of non-homogeneous, possibly degenerate equations involving discontinuous coefficients. These last results extend to the sub-elliptic setting a few classical non-linear Euclidean results [T. Iwaniec, Projections onto gradient fields and Lp-estimates for degenerated elliptic operators, Studia Math. 75 (1983) 293-312; E. DiBenedetto, J.J. Manfredi, On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems, Amer. J. Math. 115 (1993) 1107-1134], and to the non-linear case estimates of the same nature that were available in the sub-elliptic setting only for solutions to linear equations.     

On Regularity for Measures in Multiplicative Free Convolution Semigroups

Given a probability measure  μ on the real line, there exists a semigroup μ _t with real parameter t > 1 which interpolates the discrete semigroup of measures μ _n obtained by iterating its free convolution. It was shown in (Math. Z. 248(4):665–674, 2004) that it is impossible that μ _t have no mass in an interval whose endpoints are atoms. We extend this result to semigroups related to multiplicative free convolution. The proofs use subordination results.     

Two new triterpenoid saponins from Rhaponticum uniflorum

Two new triterpenoid saponins were isolated from the roots of Rhaponticum uniflorum.Their structures were elucidated as 3-O-[β-D-glucopyranosyl] -ilexolic acid-28-O-[β-D-glucopyranosyl]ester 1 and 3-O-[β-D-glucopyranosyl]-urs-12,19(29)-dien-oic acid-28-O-[β-D-glucopyranosyl]ester 2 mainly by 1D,2D NMR techniques and chemical methods.     

TiN涂层的径向微动行为

对ＧＣｒ１５／４５＃钢和ＧＣｒ１５／离子镀ＴｉＮ涂层的４５钢摩擦副进行了径向微动试验,试验的最大载荷从２００Ｎ到８００Ｎ,循环次数为１０＾５。摩擦磨损试验结果表明,ＴｉＮ涂层的抗塑性变形能力和抗么向微动损伤能力比基体好,ＳＥＭ分析表明,ＴｉＮ涂层的磨屑呈现剥层特征钢试样表现出粘着现象。     

Permanence of a delayed discrete mutualism model with feedback controls

This paper discusses a two species discrete model of mutualism with delays and feedback controls. Sufficient conditions are obtained for the permanence of the system. The results show that feedback control variables have no influence on the persistence property of the system.     

A vanishing theorem on Kaehler Finsler manifolds

Let M be a connected compact complex manifold endowed with a strongly pseudoconvex complex Finsler metric F. In this paper, we first define the complex horizontal Laplacian □_h and complex vertical Laplacian □_v on the holomorphic tangent bundle T^1,0M of M, and then we obtain a precise relationship among □_h,□_v and the Hodge–Laplace operator on (T^1,0M,,), where , is the induced Hermitian metric on T^1,0M by F. As an application, we prove a vanishing theorem of holomorphic p-forms on M under the condition that F is a Kaehler Finsler metric on M.     

An Inexact Newton Method Derived from Efficiency Analysis

We consider solving an unconstrained optimization problem by Newton-PCG like methods in which the preconditioned conjugate gradient method is applied to solve the Newton equations. The main question to be investigated is how efficient Newton-PCG like methods can be from theoretical point of view. An algorithmic model with several parameters is established. Furthermore, a lower bound of the efficiency measure of the algorithmic model is derived as a function of the parameters. By maximizing this lower bound function, the parameters are specified and therefore an implementable algorithm is obtained. The efficiency of the implementable algorithm is compared with Newtons method by theoretical analysis and numerical experiments. The results show that this algorithm is competitive.Mathematics Subject Classification: 90C30, 65K05.This work was supported by the National Science Foundation of China Grant No. 10371131, and Hong Kong Competitive Earmarked Research Grant CityU 1066/00P from Hong Kong University Grant Council