Indestructibility of compact spaces

In this article we investigate which compact spaces remain compact under countably closed forcing. We prove that, assuming the Continuum Hypothesis, the natural generalizations to _ω1${\omega }_1$-sequences of the selection principle and topological game versions of the Rothberger property are not equivalent, even for compact spaces. We also show that Tall and Usuba?s “_ℵ1${\aleph }_1$-Borel Conjecture” is equiconsistent with the existence of an inaccessible cardinal.     

A fractional credit model with long range dependent default rate

Motivated by empirical evidence of long range dependence in macroeconomic variables like interest rates we propose a fractional Brownian motion driven model to describe the dynamics of the short and the default rate in a bond market. Aiming at results analogous to those for affine models we start with a bivariate fractional Vasicek model for short and default rate, which allows for fairly explicit calculations. We calculate the prices of corresponding defaultable zero-coupon bonds by invoking Wick calculus. Applying a Girsanov theorem we derive today’s prices of European calls and compare our results to the classical Brownian model.     

Stochastic optimal multi-modes switching with a viscosity solution approach

We consider the problem of optimal multi-modes switching in finite horizon, when the state of the system, including the switching cost functions are arbitrary (_gij(t,x)≥0$g_{ij}(t,x)\ge 0$). We show existence of the optimal strategy, via a verification theorem. Finally, when the state of the system is a Markov process, we show that the vector of value functions of the optimal problem is the unique viscosity solution to the system of m$m$ variational partial differential inequalities with inter-connected obstacles.     

Asymptotic analysis for a downside risk minimization problem under partial information

We give an analytic characterization of a large-time “downside risk” probability associated with an investor’s wealth. We assume that risky securities in our market model are affected by “hidden” economic factors, which evolve as a finite-state Markov chain. We formalize and prove a duality relation between downside risk minimization and the related risk-sensitive optimization. The proof is based on an analysis of an ergodic-type Hamilton–Jacobi–Bellman equation with large (exponentially growing) drift.     

AZ31B镁合金I型材室温弯曲成型研究

由于镁合金AZ31B材料在拉伸与压缩时的力学性能差异,使AZ31B型材在室温下成型规律很难掌握.文章以AZ31B镁合金I型材为研究对象,通过对I型材弯曲过程的数值分析,研究了I型材成型过程与加强筋的高度与厚度的关系,同时对成型过程中的受力、回弹现象及翘曲做了深入的分析,得出了对工程有实用性的结论,可以指导工程实际.     

On the Cauchy-Rassias stability of a generalized additive functional equation

Let X and Y be Banach spaces and f:X→Y an odd mapping. We solve the following generalized additive functional equation