Some ratio inequalities for iterated stochastic integrals

Let X = (X_t, ?_t) be a continuous local martingale with quadratic variation 〈X〉 and X₀ = 0. Define iterated stochastic integrals I_n(X) = (I_n(t, X), ?_t), n ≥ 0, inductively by $$ I_{n} (t, X) = \int ^{t} _{0} I_{n-1} (s, X)dX_{s} $$ with I₀(t, X) = 1 and I₁(t, X) = X_t. Let (??^x_t(X)) be the local time of a continuous local martingale X at x ∈ ?. Denote ??*t(X) = sup_x∈? ??^x_t(X) and X* = sup_t≥0 |X_t|. In this paper, we shall establish various ratio inequalities for I_n(X). In particular, we show that the inequalities $$ c_{n,p} \, \left\Vert (G ( \langle X \rangle _{\infty} )) ^{n/2} \right\Vert _{p} \; \le \; \left\Vert {\mathop \sup \limits _{t \ge 0}} \; {\left\vert I_{n} (t, X) \right\vert \over {(1+ \langle X \rangle _{t} ) ^{n/2}}} \right\Vert _{p} \; \le C_{n, p} \, \left\Vert (G ( \langle X \rangle _{\infty} )) ^{n/2} \right\Vert _{p} $$ hold for 0 < p < ∞ with some positive constants c_n,p and C_n,p depending only on n and p, where G(t) = log(1+ log(1+ t)). Furthermore, we also show that for some γ ≥ 0 the inequality $$ E \left[ U ^{p}_{n} \exp \left( \gamma {U ^{1/n} _{n} \over {V}} \right) \right] \le C_{n, p, \gamma} E [V ^{n, p}] \quad (0 < p < \infty ) $$ holds with some positive constant C_n,p,γ depending only on n, p and γ, where U_n is one of 〈I_n(X)〉^1/2_∞ and I*_n(X), and V one of the three random variables X*, 〈X〉^1/2_∞ and ??*_∞(X). (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Regularity properties of semigroups generated by some Fleming-Viot type operators

We study different qualitative properties of the semigroup generated by some degenerate differential elliptic operators on the standard simplex of Rd. Some methods are new and are based on the representation formulas of the semigroup in terms of iterates of suitable positive operators. The main result is the ultracontractivity property which is obtained in the setting of weighted Lp-spaces. We describe the asymptotic behavior of the semigroup and obtain the compactness property in the same setting and also in spaces of continuous functions.     

Improved formulation,branch-and-cut and tabu search heuristic for single loop material flow system design

The single loop material flow system design is a combinatorial optimization problem, arising in material handling system design, which amounts to designing an unidirectional loop flow pattern as well as to locate pickup and delivery stations. The objective is to minimize the time required to carry out all material flow movements between cells. In this paper, we develop valid inequalities for a previously proposed formulation. The valid inequalities are then embedded into a branch-and-cut framework which is shown to solve much larger instances to optimality than those reported in the literature. A tailored tabu search heuristic is also illustrated and computationally assessed.     

抛物泛函微分方程解的振动

该文讨论一类抛物泛函微分方程解的振动性质，得到了不同边界条件下方程解振动的充分条件，并给出了实例．     

带有可测系数的二阶非线性抛物型方程组的初—混合边值问题

在多连通区域上研究带有可测系数的二阶非线性抛物型方程组的初－混合边值问题，首先我们将其化为复形式的方程组，并给出在一定条件下的上述初－这值问题解的先验估计，然后利用解的估计和列紧性原理，证明了这种初－边值问题解的存在性。在论证过程中，我们始终用复分析方法讨论文中所提出的问题，没有看到国外有人使用这种方法处理此类问题。     

Φ630石英轻质抛物面反射镜的二维动态哈特曼检验

简要介绍二维动态哈特曼波前探测仪检测波面形的基本原理、方法及其特点。首次运用该方法对φ630石英轻质抛物面反射镜实现了定量检测，给出了镜面面形测量结果。     

Properties of the Fast Diffusion Equation and Its Multidimensional Exact Solutions

We prove invariance of the fast diffusion equation in the two-dimensional coordinate space and give its reduction to a one-dimensional analog in the space variable. Using these results, we construct new exact multidimensional solutions which depend on arbitrary harmonic functions. As a consequence, we obtain new exact solutions to the well-known Liouville equation, the stationary analog of the fast diffusion equation with a linear source. We consider some generalizations to the case of systems of quasilinear parabolic equations.     

Blow-up properties for a degenerate parabolic system with nonlinear localized sources

This paper deals with blow-up properties for a degenerate parabolic system with nonlinear localized sources subject to the homogeneous Dirichlet boundary conditions. The main aim of this paper is to study the blow-up rate estimate and the uniform blow-up profile of the blow-up solution. Our conclusions extend the results of [L.L. Du, Blow-up for a degenerate reaction-diffusion system with nonlinear localized sources, J. Math. Anal. Appl. 324 (2006) 304-320]. At the end, the blow-up set and blow up rate with respect to the radial variable is considered when the domain Ω is a ball.     

Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems

We study the existence theory for parabolic variational inequalities in weighted L ² spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L ² setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coefficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.