Chernoff approximations of Feller semigroups in Riemannian manifolds

Chernoff approximations of Feller semigroups and the associated diffusion processes in Riemannian manifolds are studied. The manifolds are assumed to be of bounded geometry, thus including all compact manifolds and also a wide range of non-compact manifolds. Sufficient conditions are established for a class of second order elliptic operators to generate a Feller semigroup on a (generally non-compact) manifold of bounded geometry. A construction of Chernoff approximations is presented for these Feller semigroups in terms of shift operators. This provides approximations of solutions to initial value problems for parabolic equations with variable coefficients on the manifold. It also yields weak convergence of a sequence of random walks on the manifolds to the diffusion processes associated with the elliptic generator. For parallelizable manifolds this result is applied in particular to the representation of Brownian motion on the manifolds as limits of the corresponding random walks.     

K3 surfaces,Picard numbers and Siegel disks

If a K3 surface admits an automorphism with a Siegel disk, then its Picard number is an even integer between 0 and 18. Conversely, using the method of hypergeometric groups, we are able to construct K3 surface automorphisms with Siegel disks that realize all possible Picard numbers. The constructions involve extensive computer searches for appropriate Salem numbers and computations of algebraic numbers arising from holomorphic Lefschetz-type fixed point formulas and related Grothendieck residues.     

Inverse scattering problem with Levinson formula for eigenparameter-dependent discrete Sturm–Liouville equation

In this paper, an inverse scattering problem for discrete Sturm–Liouville equation with eigenparameter-dependent boundary condition is investigated. In quest of finding scattering function and the main equation of this problem, the uniqueness of the kernel is proven. Also, an appropriate Levinson-type formula based on the continuity of scattering function is given.     

Extraction-condensation method for solving large sets of equations in FE analysis

In static and dynamic analysis of a large complex structure, one may merely be interested in the stresses and displacements at some important locations. A new solution technique for structural analysis with FEM is proposed in this paper by which those important unknowns are separated from the rest. In static analysis the important unknows can be found directly. In dynamic analysis all mass and exciting forces can be condensed onto a small number of predetermined points in order to make the dynamic analysis much simplified. A large scale problem can be solved with a small capacity computer quickly.     

等截面梁有限变形的传递函数增量算法

本文介绍了一种计算等截面梁有限变形的新方法－传递函数增量算法，它是一种半解析数值计算方法。此算法充分利用增量失空法Ｇａｕｓｓ求积公式计算非线性有限变形的特点，并将这些特点与传递函数方法，有效地结合起来，既避免了数值方法计算量大的困难，又使得求解高阶非线性微分方程的解析解成为可能，算例分析表明，这是一种易编程，计算量小，收敛快，求解精度高的行之有效的计算方法。     

Weissenberg-Rabinowitsch-Auswertung der mit dem Platte-Platte-Rotationsrheometer gemessenen Fließkurve mittels eines Fließgesetzes vom Carreauschen Typ

Zusammenfassung Basierend auf dem das Fließverhalten strukturviskoser Fluide sehr genau beschreibenden sogenannten Carreau-Ansatz wird eine Näherungsformel für die Drehmoment-Schergeschwindigkeit-Charakteristik (scheinbare Fließkurve) des Platte-Platte-Rotationsrheometers (PPR) im stationären Versuch vorgeschlagen. Die gewonnenen Resultate können in die Auswertungseinheit des Platte-Platte-Systems leicht integriert werden und damit das Anwendungsgebiet des PPR-Systems für konzentrierte Polymerlösungen und Polymerschmelzen beträchtlich erweitern.

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A new simplified, but very accurate, formula is proposed for the torque-rate characteristic (apparent flow curve) of the parallel-disk rotational rheometer (PDR) in steady-shear mode, based on the Carreau formula for the viscosity of pseudoplastic fluids. The results can easily be incorporated into the evaluation of the parallel-disk system and therefore the application field of the PDR-system can be extended considerably for concentrated polymer solutions and polymer melts.

     

不可压缩二维流动Navier—Stokes方程的有限元解

对不可压缩流体沿二维后台阶流动的Ｎ－Ｓ方程的流函数－涡量式用有限元方法加以求解，固壁上的涡量用时间迭代法加以确定。分别计算Ｒｅ＝２００，４００，８００和１０００时流动区域的流函数和涡量值，并在Ｒｅ＝８００时与有关文献的结果相比较，基本吻合。且在此基础上讨论了出口条件对计算结果的影响。本文的方法对分析流经液压阀口等流动问题具有借鉴意义。     

GENERALIZATION OF STEINER FORMULAFOR THE HOMOTHETIC MOTIONS ONTHE PLANAR KINEMATICS

The Steiner formula and the mixture area formula given by M(U|¨)ller were expressed under the one-parameter closed planar homothetic motions in the complex sense . Also, using the generalization of Steiner formula, the result of Holditch theorem for homothetic motions is got. In the case of the homothetic scale h≡1 the results given by M(U|¨)ller are obtained as a special case.     

Exterior cloaking with active sources in two dimensional acoustics

We cloak a region from a known incident wave by surrounding the region with three or more devices that cancel out the field in the cloaked region without significantly radiating waves. Since very little waves reach scatterers within the cloaked region, the scattered field is small and the scatterers are for all practical purposes undetectable. The devices are multipolar point sources that can be determined from Green's formula and an addition theorem for Hankel functions. The cloaking devices are exterior to the cloaked region.