A proof of zelevinski’s structure theorem for psh algebras 1

We give a new proof of the structure theorem for PSH—algebras, and of a formula for primitives     

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.     

类氖钛X射线激光实验研究

在“星光”装置上采用预脉冲技术和透-反射线聚焦系统成功地进行了类氛钛x射线激光实验.测量了TiXⅢ,3s-3p,J=0～1激光线的增益系数.首次实验研究了预脉冲能量不同时,激光线强度随泵浦激光能量的变化及其发散角和偏转角.     

Limits of minimal surfaces and Scherk's Fifth Surface

Communicated by J. C. C. Nitsche     

On the singularity of Green's tensor for a perfectly conducting semi-infinite cone

This paper is intended to clarify a misunderstanding concerningthe source singularity of the electric Green's tensor for aperfectly conducting semi-infinite cone of circular cross-section.Tai's series expansion of the Green's tensor is known to lacka singular term at the source region. Jones has reconstructedthe solution to this problem and has pointed out the differencebetween his result and that of Tai. The aim of our paper isto demonstrate that, although Jones's closed-form solution iscorrect, there is a mistake in his comparison with Tai's seriessolution. We conclude that one of the two additional singularterms that Jones claims as missing from Tai's formula must beomitted. Besides, we compare Jones's closed-form solution withSmyshlyaev's solution to the very same problem. We concludethat the magnetic field expressions given by Jones and Smyshlyaevcoincide, but a singular term is missing from Smyshlyaev's expressionfor the electric field.     

Spin-cluster effects and frustration in the uniaxial spin glass Fe2−xTi1+xO5

Transverse-field (TF) muon-spin-relaxation (μSR) and Mössbauer experiments on the uniaxial insulating spin glass Fe_2?xTi_1+xO₅ (x=0.25) have been performed near and below the spin-glass temperature (T _g). The effect of a transverse field on the spin-freezing process and spin-glass state has been investigated by measuring the field-and temperature-dependencies of the μSR parameters. Spin-cluster effects signaled by anomalous μ-spin relaxation have been observed in a temperature region just aboveT _g. An interpretation supported by recently developed theoretical models addressing non-linear relaxation in an intermediate Griffiths phase is offered.     

On the limiting profile arising from orthonormalizing shifts of exponentially decaying functions

It is shown that, under certain conditions, orthonormalizingthe positive integer shifts of an exponentially decaying functionon the half line by the Gram-Schmidt process leads to a limitingprofile given by orthonormalizing all their integer shifts onthe whole line. These results derive from properties of Choleskyfactorization of bi-infinite and semi-infinite matrices. Anexample is provided by the negative exponential function andconjectures are given, supported by numerical evidence, forthe Gaussian and Lorentz function.