Comparison of solutions of stochastic equations and applications

Pathwise comparison of solutions to a class of stochastic systems of differential equations is proved which extends the existing result of Geiβ and Manthey. When the diffusion coefficients are defferent, the Gal’?huk-Davis method is extended to establish the comparision results. We illustrate our results with several examples some of which arise in stochastic finance theory     

On some configurations related to the Shelah Weak Hypothesis

We show that some cardinal arithmetic configurations related to the negation of the Shelah Weak Hypothesis and natural from the forcing point of view are impossible. Received: 8 September 1999 / Published online: 3 October 2001     

On dimensional properties of the generalized Smirnov's spaces

We show that the transfinite inductive dimensions modulo PP-trind and P-trInd introduced in M.G. Charalambous (1997) [2] differ by simple spaces, where P is the absolutely additive Borel class A(α) or the absolutely multiplicative Borel class M(α), 0?α<ω₁.     

Isoperimetric inequalities for special classes of curves

In this paper the classical Banchoff-Pohl inequality, an isoperimetric inequality for nonsimple closed curves in the Euclidean plane, involving the square of the winding number, is sharpened for homothetic or Abresch-Langer solutions of curve shortening. For a larger class of curves and for rotationally symmetric curves, further isoperimetric inequalities containing the rotation number and the winding number, are presented.     

7A04铝合金的本构关系和失效模型

使用万能材料试验机、扭转试验机和Taylor撞击实验研究了高强铝合金7A04在常温至250 ℃的 准静态、动态本构关系和失效模型。基于实验结果,修改了Johnson-Cook强度模型中的应变强化项以及 Johnson-Cook失效模型中的温度软化项,并结合数值模拟标定了模型参数。实验结果表明,7A04铝合金的 应变和应变率强化效应不显著,失效应变随温度的增加、应力三轴度的减小和应变率的减小而增加。     

A partition relation for partially ordered sets

We introduce a partition relation which is an alternate for measuring how badly the ordinary partition relation fails, we develop its corresponding partition calculus and we determine its status for various typical partially ordered sets.     

Geometrically induced discrete spectrum in curved tubes

The Dirichlet Laplacian in curved tubes of arbitrary cross-section rotating w.r.t. the Tang frame along infinite curves in Euclidean spaces of arbitrary dimension is investigated. If the reference curve is not straight and its curvatures vanish at infinity, we prove that the essential spectrum as a set coincides with the spectrum of the straight tube of the same cross-section and that the discrete spectrum is not empty.     

Infinite products of relations, set-valued series and uniform openness of multifunctions

Using the notations of convergent series of sets and convergent products of relations, general open mapping theorems are presented which encompass classical results of Banach, Ptak, Khanh, and others.     

On Sums of Units

It is shown that if R is a finitely generated integral domain of zero characteristic, then for every n there exist elements of R which are not sums of at most n units. This applies in particular to rings of integers in finite extensions of the rationals. On the other hand there are many infinite algebraic extensions of the rationals in which every integer is a sum of two units.