非线性一致同时逼近

设Ω是紧Ｈａｕｓｄｏｒｆｆ空间,Ｃ（Ω）表示定义在Ω上取值于实数域的所有实连续函数全体组成的空间,在Ｃ（Ω）上定义一致范数则Ｃ（Ω）构成一个Ｂａｎａｃｈ空间．定义其中 ｜｜· ｜｜Ｂ是Ｒｍ中给定的范数． 设Ｇ是Ｃ（Ω）的一个非空子集,ｆ１,…,ｆｍ是Ｃ（Ω）中给定的ｍ个函数．若存在ｆ∈Ｇ,满足那么称这样的ｆ是Ｇ对Ｆ的最佳一致同时逼近,其全体记为ＰＧ（Ｆ）． 近年来．最佳同时逼近问题作为单元最佳逼近问题的推广,受到了广泛的关注．文［１－６］在一般的Ｂａｎａｃｈ空间中研究了各种意义下的最佳同时逼近的特征…     

二维变系数反应扩散方程的紧交替方向差分格式

1 引言 在研究热传导过程、气体扩散现象和电磁场的传播等问题时,常常遇到抛物型偏微分方程。用有限差分方法研究这类问题的数值解法目前已经有了许多工作。对于二维、三维抛物方程的数值求解比较理想的方法是交替方向法。     

Stability of symmetric closed characteristics on symmetric compact convex hypersurfaces in ℝ<Superscript>2<Emphasis Type="Italic">n</Emphasis></Superscript> under a pinching condition

In this paper, let Σ R2n be a symmetric compact convex hypersurface which is ( r, R )- pinched with R/r (5/3)1/2 . Then Σ carries at least two elliptic symmetric closed characteristics; moreover, Σ carries at least E [ n-1/2 ] + E [ n-1/3 ] non-hyperbolic symmetric closed characteristics.     

近严格凸与最佳逼近

本文研究近严格凸与最佳逼近的关系．证明了Ｂａｎａｃｈ空间Ｘ是近严格凸的当且仅当Ｘ的每个子空间是紧－半－切比晓夫空间．     

High‐order compact schemes for fractional differential equations with mixed derivatives

In this article, we consider two‐dimensional fractional subdiffusion equations with mixed derivatives. A high‐order compact scheme is proposed to solve the problem. We establish a sufficient condition and show that the scheme converges with fourth order in space and second order in time under this condition.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2141–2158, 2017     

Compact finite difference schemes of the time fractional Black-Scholes model

In this paper, three compact difference schemes for the time-fractional Black-Scholes model governing European option pricing are presented. Firstly, in order to obtain the fourth-order accuracy in space by applying the Pad\''{e} approximation, we eliminate the convection term of the B-S equation by an exponential transformation. Then the time fractional derivative is approximated by $L1$ formula, $L2 - 1_\sigma$ formula and $L1 - 2$ formula respectively, and three compact difference schemes with oders $O(\Delta t^{2-\alpha}+h ^4)$, $O(\Delta t^{2}+h ^4)$ and $O(\Delta t^{3-\alpha}+h ^4)$ are constructed. Finally, numerical example is carried out to verify the accuracy and effectiveness of proposed methods, and the comparisons of various schemes are given. The paper also provides numerical studies including the effect of fractional orders and the effect of different parameters on option price in time-fractional B-S model.     

The Huber theorem for non-compact conformally flat manifolds

It was proved in 1957 by Huber that any complete surface with integrable Gauss curvature is conformally equivalent to a compact surface with a finite number of points removed. Counterexamples show that the curvature assumption must necessarily be strengthened in order to get an analogous conclusion in higher dimensions. We show in this paper that any non compact Riemannian manifold with finite -norm of the Ricci curvature satisfies Huber-type conclusions if either it is a conformal domain with volume growth controlled from above in a compact Riemannian manifold or if it is conformally flat of dimension 4 and a natural Sobolev inequality together with a mild scalar curvature decay assumption hold. We also get partial results in other dimensions. Received: April 14, 2000; revised version: March 20, 2001     

A compact HL-space need not have a monolithic hyperspace

We show that Kunen's example of a compact L-space, constructed under CH, can be modified so that it has a non-monolithic hyperspace. This answers a question of Bell's. This example is also relevant to a question of Arhangel'skii's.

     

矩阵代数收敛至球面与非交换度量几何

介绍了Rieffel定义的紧致量子度量空间与量子Gromov-Hausdorff距离和近来Latrémolière定义的量子Gromov-Hausdorff邻距,分别讨论了矩阵代数如何在这两种量子距离下收敛至球面.     

A Residual-Based Compact Scheme for the Compressible Navier–Stokes Equations

A simple and efficient time-dependent method is presented for solving the steady compressible Euler and Navier–Stokes equations with third-order accuracy. Owing to its residual-based structure, the numerical scheme is compact without requiring any linear algebra, and it uses a simple numerical dissipation built on the residual. The method contains no tuning parameter. Accuracy and efficiency are demonstrated for 2-D inviscid and viscous model problems. Navier–Stokes calculations are presented for a shock/boundary layer interaction, a separated laminar flow, and a transonic turbulent flow over an airfoil.