On the existence of f-local subgroups in a group

We prove the existence of infinite subgroups with nontrivial locally finite radicals and of locally finite subgroups in the groups with almost finite almost solvable elements of prime orders and in the groups with generally finite elements.     

Efficient computation of mean drag for the subcritical flow past a circular cylinder using general Galerkin G2

General Galerkin (G2) is a new computational method for turbulent flow, where a stabilized Galerkin finite element method is used to compute approximate weak solutions to the Navier–Stokes equations directly, without any filtering of the equations as in a standard approach to turbulence simulation, such as large eddy simulation, and thus no Reynolds stresses are introduced, which need modelling. In this paper, G2 is used to compute the drag coefficient c_D for the flow past a circular cylinder at Reynolds number Re=3900, for which the flow is turbulent. It is found that it is possible to approximate c_D to an accuracy of a few percent, corresponding to the accuracy in experimental results for this problem, using less than 10⁵ mesh points, which makes the simulations possible using a standard PC. The mesh is adaptively refined until a stopping criterion is reached with respect to the error in a chosen output of interest, which in this paper is c_D. Both the stopping criterion and the mesh‐refinement strategy are based on a posteriori error estimates, in the form of a space–time integral of residuals times derivatives of the solution of a dual problem, linearized at the approximate solution, and with data coupling to the output of interest. Copyright © 2008 John Wiley & Sons, Ltd.     

Smooth and path connected Banach submanifold Σ r of B(E,F) and a dimension formula in B(ℝ n ,ℝ m )

Given two Banach spaces E,F, let B(E,F) be the set of all bounded linear operators from E into F, Σ _r the set of all operators of finite rank r in B(E,F), and Σ _r ^# the number of path connected components of Σ _r . It is known that Σ _r is a smooth Banach submanifold in B(E,F) with given expression of its tangent space at each A ∈ Σ _r . In this paper,the equality Σ _r ^# = 1 is proved. Consequently, the following theorem is obtained: for any nonnegative integer r, Σ _r is a smooth and path connected Banach submanifold in B(E,F) with the tangent space T _A Σ _r = {B ∈ B(E,F): BN(A) ⊂ R(A)} at each A ∈ Σ _r if dim F = ∞. Note that the routine method can hardly be applied here. So in addition to the nice topological and geometric property of Σ _r the method presented in this paper is also interesting. As an application of this result, it is proved that if E = ℝ ⁿ and F = ℝ ^m , then Σ _r is a smooth and path connected submanifold of B(ℝ ⁿ , ℝ ^m ) and its dimension is dimΣ _r = (m+n)r−r ² for each r, 0 <- r < min {n,m}. Supported by the National Science Foundation of China (Grant No.10671049 and 10771101).     

Energy relaxation method for chemical non‐equilibrium flow computations

In this paper, an algorithm for chemical non‐equilibrium hypersonic flow is developed based on the concept of energy relaxation method (ERM). The new system of equations obtained are studied using finite volume method with Harten–Lax–van Leer scheme for contact (HLLC). The original HLLC method is modified here to account for additional species and split energy equations. Higher order spatial accuracy is achieved using MUSCL reconstruction of the flow variables with van Albada limiter. The thermal equilibrium is considered for the analysis and the species data are generated using polynomial correlations. The single temperature model of Dunn and Kang is used for chemical relaxation. The computed results for a flow field over a hemispherical cylinder at Mach number of 16.34 obtained using the present solver are found to be promising and computationally (25%) more efficient. The present solver captures physically correct solution as the entropy conditions are satisfied automatically during the computations. Copyright © 2007 John Wiley & Sons, Ltd.     

Analysis of discrete techniques for image transformation

Let an image be distorted by a nonlinear transformationT, and then be restored back to its original by the inverse transformationT ^–1. Such a cycle conversion,T ^–1 T, of digital images can be facilitated by the combination (CSIM) given in [6] using the splitting-shooting method and the splitting-integrating method forT andT ^–1 respectively. Since there is no need to solve nonlinear equations, CSIM has been widely applied to specific areas of image processing and pattern recognition, even those with complicated transformations, e.g., the harmonic transformation [12]; however, no strict error analysis has been provided so far. In this paper, a priori error estimates and convergence rates are derived for pixel greyness obtained from CSIM; also the analytical results are extended to the harmonic transformation. Numerical and graphical experiments are provided to support the theoretical analysis.Some preliminary results of this paper were presented at the 40th anniversary meeting of SIAM, Los Angeles, July 20–24, 1992. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada, the Fonds pour la Formation de Chercheurs et l'Aide à la Recherche of Quebec by the Ministère de l'Enseignement Supérieur et de la Science (Action Structurante), and the Science Council of Republic of China under Grant No. NSC-85-2121-M-008.     

Estimate of the truncation error of finite volume discretization of the Navier–Stokes equations on colocated grids

A methodology is proposed for the calculation of the truncation error of finite volume discretizations of the incompressible Navier–Stokes equations on colocated grids. The truncation error is estimated by restricting the solution obtained on a given grid to a coarser grid and calculating the image of the discrete Navier–Stokes operator of the coarse grid on the restricted velocity and pressure field. The proposed methodology is not a new concept but its application to colocated finite volume discretizations of the incompressible Navier–Stokes equations is made possible by the introduction of a variant of the momentum interpolation technique for mass fluxes where the pressure part of the mass fluxes is not dependent on the coefficients of the linearized momentum equations. The theory presented is supported by a number of numerical experiments. The methodology is developed for two‐dimensional flows, but extension to three‐dimensional cases should not pose problems. Copyright © 2005 John Wiley & Sons, Ltd.     

On the efficiency of linearization schemes and coupled multigrid methods in the simulation of a 3D flow around a cylinder

This paper studies the efficiency of two ways to treat the non‐linear convective term in the time‐dependent incompressible Navier–Stokes equations and of two multigrid approaches for solving the arising linear algebraic saddle point problems. The Navier–Stokes equations are discretized by a second‐order implicit time stepping scheme and by inf–sup stable, higher order finite elements in space. The numerical studies are performed at a 3D flow around a cylinder. Copyright © 2005 John Wiley & Sons, Ltd.     

六西格玛管理中的网络计划技术及其应用

利用网络计划技术,对节点(事项)和箭条(作业活动)分别规定了六个时间值,讨论了他们之间的关系;结合实例应用,分析了资源的合理配置,得到了有一定参考意义的结果.     

Numerical solution of the heat equation with nonlinear boundary conditions in unbounded domains

The numerical solution of the heat equation in unbounded domains (for a 1D problem‐semi‐infinite line and for a 2D one semi‐infinite strip) is considered. The artificial boundaries are introduced and the exact artificial boundary conditions are derived. The original problems are transformed into problems on finite domains. The space semi‐discretization by finite element method and the full approximation by the implicit‐explicit Euler's method are presented. The solvability of the full discretization schemes is analyzed. Computational examples demonstrate the accuracy and the efficiency of the algorithms. Also, the behavior of blowing up solutions is examined numerically. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 379–399, 2007