Gevrey properties of real planar singularly perturbed systems

By applying geometric techniques to real analytic singularly perturbed vector fields on the plane, we develop a way to give a bound on the Gevrey type of the Taylor development of canard manifolds at degenerate planar turning points. By blowing up the phase space at the turning point, we find asymptotic estimates even when such expansions w.r.t. traditional phase space variables do not exist. The asymptotic estimates are then used to give a sufficient and necessary condition on the existence of (local) canard solutions.     

On the number of full levels in tries

We study the asymptotic distribution of the fill‐up level in a binary trie built over n independent strings generated by a biased memoryless source. The fill‐up level is the number of full levels in a tree. A level is full if it contains the maximum allowable number of nodes (e.g., in a binary tree level k can have up to 2^k nodes). The fill‐up level finds many interesting applications, e.g., in the internet IP lookup problem and in the analysis of level compressed tries (LC tries). In this paper, we present a complete asymptotic characterization of the fill‐up distribution. In particular, we prove that this distribution concentrates on one or two points around the most probably value k = ?log_1/qn ? log log log n + 1 + log log(p/q)?, where p > q = 1 ? p is the probability of generating the more likely symbol (while q = 1 ? p is the probability of the less likely symbol). We derive our results by analytic methods such as generating functions, Mellin transform, the saddle point method, and analytic depoissonization. We also present some numerical verification of our results. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

关于半线性热方程的死角性质

本文考虑下述问题：这里，．本文证明了在发生死角时只有有限个死角点．     

一类非牛顿渗流方程爆破界的估计

本文利用拟线性常微分方程解的非存在性定理得到了一类拟线性反应扩散方程(非牛顿渗流方程)爆破界的估计,从而推广了半线性反应扩散方程(牛顿渗流方程)相应结果.     

Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions

In this paper, the author considers the Cauchy problem for semilinear wave equations with critical exponent in n≥4 space dimensions. Under some positivity conditions on the initial data, it is proved that there can be no global solutions no matter how small the initial data are.     

Asymptotic analysis and estimates of blow‐up time for the radial symmetric semilinear heat equation in the open‐spectrum case

We estimate the blow‐up time for the reaction diffusion equation u_t=Δu+ λf(u), for the radial symmetric case, where f is a positive, increasing and convex function growing fast enough at infinity. Here λ>λ^*, where λ^* is the ‘extremal’ (critical) value for λ, such that there exists an ‘extremal’ weak but not a classical steady‐state solution at λ=λ^* with ∥w(?, λ)∥_∞→∞ as 0<λ→λ^*?. Estimates of the blow‐up time are obtained by using comparison methods. Also an asymptotic analysis is applied when f(s)=e^s, for λ?λ^*?1, regarding the form of the solution during blow‐up and an asymptotic estimate of blow‐up time is obtained. Finally, some numerical results are also presented. Copyright © 2007 John Wiley & Sons, Ltd.     

密胺-脲甲醛树脂合成工艺放大研究

以密胺－脲甲醛树脂合成的小试工艺条件为依据，完成了放大试验过程的工艺研究。研究结果与小试研究的工艺条件相吻合。     

High temperature corrosion behaviour of M(Co,Ni)CrAIY-coatings on high temperature materials-microanalytical investigations

In our former investigations, the phenomenon high temperature corrosion (HTC) was described exemplarily on selected materialcoating combinations for blades of stationary gas turbines, mainly in the temperature region of up to 750° C. To answer the question, in which manner higher gas inlet and/or higher material surface temperature would influence the HTC behaviour, a special analytical technique—the integral layer profile analysis—was introduced to ameliorate concentration profile methods. By examining IN 738 LC specimens with CoCrAlY plasma spray coating, stressed by hot gas at 900° C, the limits of this system are shown by explaining the corrosion mechanism; the method is also used for other systems, e.g. U 520 with NiCrAlY coating at 750° C.     

Superoxes,high temperature universal phases in (GC)2

Most of the common classes of organic compounds chromatograph normally on Superoxes. There is no tailing or adverse effect from excessively different activity different activity coefficients. Superoxes are therefore universal phases for gas chromatography. This is also expressed by a wide useful temperature range from ～50° to ～300°. High MW Superox-4 has a MAOT about 20° higher than the lower MW Superox-0.1. Several applications illustrating the versatility of Superox phases in (GC)² are presented.