Insight into chain dimensions in PEO/water solutions

Small‐Angle Neutron Scattering has been performed from poly(ethylene oxide) in deuterated water at temperature ranging from 10 to 80 °C. A simple fitting model was used to obtain a correlation length and a Porod exponent. The correlation length L characterizes the average distance between entanglements in the semidilute region and is proportional to the individual coil sizes in the dilute region. L was found to increase with temperature in the semidilute region but it decreases with temperature in the dilute region. This decrease is the precursor to the single‐chain collapse which applies to very dilute polymer solutions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2196–2200, 2007     

Critical percolation exploration path and SLE 6: a proof of convergence

It was argued by Schramm and Smirnov that the critical site percolation exploration path on the triangular lattice converges in distribution to the trace of chordal SLE ₆. We provide here a detailed proof, which relies on Smirnov’s theorem that crossing probabilities have a conformally invariant scaling limit (given by Cardy’s formula). The version of convergence to SLE ₆ that we prove suffices for the Smirnov–Werner derivation of certain critical percolation crossing exponents and for our analysis of the critical percolation full scaling limit as a process of continuum nonsimple loops. Research of Charles M.Newman was partially supported by the US NSF under grants DMS-01-04278 and DMS-06-06696.     

微脉冲电子枪的初步实验研究

给出了微脉冲电子枪的模拟计算及其初步实验结果. 该电子枪采用铜铝镁合金作为冷阴极材料, 在以磁控管作为微波功率源的出束实验中得到了100mA/cm²的电流密度.实验结果与次级电子倍增解析计算和SEEG程序的模拟计算结果基本符合, 初步验证了微脉冲电子枪的基本原理, 为今后实验中得到更大的电流密度打下了基础.     

Decay Rates in Probability Metrics Towards Homogeneous Cooling States for the Inelastic Maxwell Model

We quantify the long-time behavior of solutions to the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell molecules by means of the contraction property of a suitable metric in the set of probability measures. Existence, uniqueness, and precise estimates of overpopulated high energy tails of the self-similar profile proved in ref. 9 are revisited and derived from this new Liapunov functional. For general initial conditions the solutions of the Boltzmann equation are then proved to converge with computable rate as t → ∞ to the self-similar solution in this distance, which metrizes the weak convergence of measures. Moreover, we can relate this Fourier distance to the Euclidean Wasserstein distance or Tanaka functional proving also its exponential convergence towards the homogeneous cooling states. The findings are relevant in the understanding of the conjecture formulated by Ernst and Brito in refs. 15, 16, and complement and improve recent studies on the same problem of Bobylev and Cercignani⁽⁹⁾ and Bobylev, Cercignani and one of the authors.⁽¹¹⁾     

中间层Re的加入对覆膜钡钨阴极性能的改善

研究了一种新型的覆膜钡钨阴极——双层膜(Os-W/Re膜)钡钨阴极.对这种新型阴极的发射性能进行了测试，重点对其老炼前后表面薄膜的微观形貌进行了分析，表明中间层Re膜的加入使覆膜钡钨阴极的性能得到了改善.通过对Os-W双元合金膜钡钨阴极和Os-W/Re双层膜钡钨阴极发射特性的比较，发现Os-W/Re双层膜阴极的直流发射性能好于Os-W合金膜阴极.对两种阴极激活后发射表面的X射线光电子能谱分析表明，Os-W/Re双层膜阴极激活后表面形成的三元合金膜是其发射特性优于Os-W合金膜阴极的主要原因.应用扫描电子显微镜分析比较两种阴极激活老炼后的表面状态，结果表明：Os-W合金膜阴极在老炼一段时间后，其表面薄膜出现开裂，这会导致阴极发射均匀性下降；而Os-W/Re双层膜阴极在同样老炼条件下，发射表面薄膜均匀并保持完整，从而确保覆膜钡钨阴极发射均匀性和工作可靠性. 关键词： 双层膜钡钨阴极 Os-W/Re膜 Os-W膜 薄膜开裂     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION

The boundedness of the every solution and the asymptotic behavior of all solutions of the nonlinear neutral delay differential equation [x(t) - P(t)x(t - t)]' Q1 (t)f(x{t-σ1))-Q2(t)f(x(t -σ2))=0,t≥t0 are investigated, whereτ,σ1,σ2∈(0,∞), P∈C([t0,∞),R), and Q1,Q2∈C([t0,∞),R), f∈C(R,R). The sufficient conditions obtained improve the existing results in the literatures.     

一个反应扩散方程的门槛结果

本文讨论反应扩散方程Ｃａｕｃｈｙ问题解的整体存在性，渐近性质和Ｂｌｏｗｕｐ问题．其中或者１＜ｑ＜ｐ＜＋∞，ｎ＝２．得到门槛结果．     

Novel ethero atoms containing polyesters based on 2,6‐naphthalendicarboxylic acid: A comparative study with poly(butylene naphthalate)

Poly(butylene naphthalate) (PBN), poly(diethylene naphthalate) (PDEN), and poly(thiodiethylene naphthalate) (PTDEN) were synthesized and characterized in terms of chemical structure and molecular weight. The polyesters were examined by TGA, DSC, and DMTA. All the polymers showed a good thermal stability, even though depending on chemical structure. At room temperature they appeared as semicrystalline materials; the effect of the introduction along the PBN polymer chain of ether oxygen atoms or sulfur ones was a lowering in the T_g value, a decrement of T_m, and a decrease of the crystallization rate. Changing in chemical structure also affects the main α absorption associated with the glass transition which moves to lower temperature and whose energetic requirements decrease. The results were explained as due to the presence of highly flexible C? S? C or C? O? C bonds in the polymeric chain. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1694–1703, 2007     

Asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors

We derive results on the asymptotic behavior of tails and quantiles of quadratic forms of Gaussian vectors. They appear in particular in delta–gamma models in financial risk management approximating portfolio returns. Quantile estimation corresponds to the estimation of the Value-at-Risk, which is a serious problem in high dimension.