Third order nonoscillatory central scheme for hyperbolic conservation laws

Summary. A third-order accurate Godunov-type scheme for the approximate solution of hyperbolic systems of conservation laws is presented. Its two main ingredients include: 1. A non-oscillatory piecewise-quadratic reconstruction of pointvalues from their given cell averages; and 2. A central differencing based on staggered evolution of the reconstructed cell averages. This results in a third-order central scheme, an extension along the lines of the second-order central scheme of Nessyahu and Tadmor \cite{NT}. The scalar scheme is non-oscillatory (and hence – convergent), in the sense that it does not increase the number of initial extrema (– as does the exact entropy solution operator). Extension to systems is carried out by componentwise application of the scalar framework. In particular, we have the advantage that, unlike upwind schemes, no (approximate) Riemann solvers, field-by-field characteristic decompositions, etc., are required. Numerical experiments confirm the high-resolution content of the proposed scheme. Thus, a considerable amount of simplicity and robustness is gained while retaining the expected third-order resolution. Received April 10, 1996 / Revised version received January 20, 1997     

Small generators of number fields

If K is a number field of degree n over Q with discriminant D _K and if α∈K generates K, i.e. K=Q(α), then the height of α satisfies with . The paper deals with the existence of small generators of number fields in this sense. We show: (1) For each $n$ there are infinitely many number fields K of degree $n$ with a generator α such that . (2) There is a constant d ² such that every imaginary quadratic number field has a generator α which satisfies .?(3) If K is a totally real number field of prime degree n then one can find an integral generator α with . Received: 10 January 1997 / Revised version: 13 January 1998     

FULL DISCRETE NONLINEAR GALERKIN METHOD FOR THE NAVIER-STOKES EQUATIONS

This paper deals with the inertial manifold and the approximate inertial manifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore, we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.     

嵌套病例对照研究中的两步估计方法（英）

本文讨论嵌套病例对照研究中相对危险率的估计问题，引入了相对危险率的两步估计，并在一般嵌套病例对照抽样的假设下讨论了相对危险率的两步估计的相合性问题，最后给出了几个例子。     

Exact groups and Fell bundles

Kirchberg and Wasserman's Theorem, according to which a group is exact if and only if its reduced C*-algebra is exact, is extended to the context of Fell bundles. Received: 31 December 2000 / Revised version: 7 August 2001 / Published online: 4 April 2002     

Solving the Gleason problem on linearly convex domains

Let be a bounded, connected linearly convex set in with boundary. We show that the maximal ideal (both in ) and ) consisting of all functions vanishing at is generated by the coordinate functions . Received: 2 July 2001; in final form: 26 September 2001 / Published online: 28 February 2002