On the Regularity for Stationary Harmonic Maps

We prove a compactness theorem for k-indexed stationary harmonic maps, and show a regularity theorem for this kind of maps which says that the singular set of a k-indexed stationary harmonic map is of Hausdorff dimension at most m-3.     

Small stable generic graphs with infinite weight. Digraphs without furcations

Grounding on Herwig’s generic construction that modifies Hrushovski’s construction, we give some examples of small stable theories of digraphs without furcations which have an infinite weight.     

求解双温热传导方程的一类新的加权隐格式

提出了一个解双温热传导方程U1 Ux Uxx-δUxxt=0(δ＞0)的一种新的具有二阶精度的两层加权隐格式,其截断误差阶为o(τ^2 h^2),此格式是条件稳定的,特别是当θ=1/2时,此格式绝对稳定.为了简单起见,我们选取参数θ=1/2,对该问题进行求解,获得了较满意的数值结果.     

Synthesis of diblock copolymers by combining stable free radical polymerization and atom transfer radical polymerization

A stable nitroxyl radical functionalized with an initiating group for atom transfer radical polymerization (ATRP), 4‐(2‐bromo‐2‐methylpropionyloxy)‐2,2,6,6‐tetramethyl‐1‐piperidinyloxy (Br‐TEMPO), was synthesized by the reaction of 4‐hydroxyl‐2,2,6,6‐tetramethyl‐1‐piperidinyloxy with 2‐bromo‐2‐methylpropionyl bromide. Stable free radical polymerization of styrene was then carried out using a conventional thermal initiator, dibenzoyl peroxide, along with Br‐TEMPO. The obtained polystyrene had an active bromine atom for ATRP at the ω‐end of the chain and was used as the macroinitiator for ATRP of methyl acrylate and ethyl acrylate to prepare block copolymers. The molecular weights of the resulting block copolymers at different monomer conversions shifted to higher molecular weights and increased with monomer conversion. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2468–2475, 2006     

Study of the stability in the problem on flowing around a wedge. The case of strong wave

We consider the flow of an inviscid nonheatconducting gas in the thermodynamical equilibrium state around a plane infinite wedge and study the stationary solution to this problem, the so-called strong shock wave; the flow behind the shock front is subsonic.We find a solution to a mixed problem for a linear analog of the initial problem, prove that the solution trace on the shock wave is the superposition of direct and reflected waves, and, the main point, justify the Lyapunov asymptotical stability of the strong shock wave provided that the angle at the wedge vertex is small, the uniform Lopatinsky condition is fulfilled, the initial data have a compact support, and the solvability conditions take place if needed (their number depends on the class in which the generalized solution is found).     

Stable intersections of affine cantor sets

We construct open sets of pairs of affine Cantor sets (K, K′) with the simplest possible combinatorics (i. e., defined by two affine increasing maps) which have stable intersection, while the product of lateral thicknesses τ_R(K) • τ_L (K′) is smaller than one. Thus, in a strong form, the converse to the following classic result due to Newhouse is not true: if the product of the thicknesses of two Cantor sets is bigger than one then there are translations of them which have stable intersection. We also describe the topological structure of K—K′ for typical pairs (K, K′) in this open set.     

A new risk model based on policy entrance process and its weak convergence properties

In this paper, we construct a new risk model based on the policy entrance process. The model is concerned with n kinds of independent policies, and each policy is allowed to claim more than once before it expires. As each kind of policy is issued according to a non‐homogeneous Poisson process, the long run behaviour of the new risk process is investigated. When the tail of the claim size distribution is regularly varying, the standardized risk process is proved to converge to a stable law. When each kind of policy is issued according to a homogeneous Poisson process, we also give a diffusion approximation of the new risk process. Copyright © 2007 John Wiley & Sons, Ltd.     

On the structure of certain natural cones over moduli spaces of genus-one holomorphic maps

We show that certain naturally arising cones over the main component of a moduli space of J₀-holomorphic maps into Pn have a well-defined Euler class. We also prove that this is the case if the standard complex structure J₀ on Pn is replaced by a nearby almost complex structure J. The genus-zero analogue of the cone considered in this paper is a vector bundle. The genus-zero Gromov-Witten invariant of a projective complete intersection can be viewed as the Euler class of such a vector bundle. As shown in a separate paper, this is also the case for the “genus-one part” of the genus-one GW-invariant. The remaining part is a multiple of the genus-zero GW-invariant.     

一类浮游生物植化相克时滞抛物方程的稳态解

本文研究了水生生态系统中种群间能产生抑制毒素的Volterra竞争模型,用上下解的方法讨论了稳态解的渐近行为,得到了系统存在唯一全局稳定正稳态解的充分条件.     

On comparability of integral forms

We prove comparability of certain homogeneous anisotropic integral forms. As a consequence we obtain a Hardy type inequality generalising that for the fractional Laplacian. We give an application to anisotropic censored stable processes in Lipschitz domains.