捕食模型正周期解存在性的一个注记

利用重合度理论中的延拓定理讨论了多滞量捕食模型(dN_1(t))/dt=N_1(t)[r_1(t)-a_(11)(t)N_1(t-τ_1(t))-a_(12)(t)N_2(t-τ_2(t))] (dN_2(t))/dt=N_2(t)[-r_2(t)+a_(21)(t)N_1(t-τ_3(t))]的正周期解的存在性,得到了保证上述系统周期解存在的一组时滞依赖的充分条件,补充和完善了已有学者的工作.     

一类点边同时变化的增长网络的度分布

本文研究一个节点和连边能同时发生变化的网络模型,把模型中的节点度的演化过程看成一族马氏链。从模型的演化机制中得到该马氏链的状态转移概率,用马氏链的方法证明了该模型的稳态度分布是存在的,并得到了度分布的精确表达式。从而说明了该网络是标度指数为3的无标度网络。     

Multifractal structure of the product measure of two independent general subordinators’ occupation measures

In this paper, we mainly investigate the multifractal spectrum of the random measure derived from two independent general subordinators. This work was supported by National Natural Science Foundation of China (Grant No. 10871200)     

非线性优化修正Frisch函数方法的乘子映射

对于同时含有等式与不等式约束的非线性优化问题的修正Frisch函数方法,给出其乘子映射和解映射的导数的估计.将得到的估计用于建立修正Frisch函数方法的线性收敛速率.在线性无关的约束规范,严格互补条件和二阶充分性条件成立的前提下,证得该收敛率与1/c成正比.本文的收敛性分析依赖于矩阵的奇异值分解,其方法可以用来分析其他的修正Lagrange方法.     

Recombination of photodissociated iodine: a time-resolved x-ray-diffraction study

A time-resolved x-ray-diffraction experiment is presented that aims to study the recombination of laser-dissociated iodine molecules dissolved in CCl4. This process is monitored over an extended time interval from pico- to microseconds. The variations of atom-atom distances are probed with a milliangstrom resolution. A recent theory of time-resolved x-ray diffraction is used to analyze the experimental data; it employs the correlation function approach of statistical mechanics. The most striking outcome of this study is the experimental determination of time-dependent I-I atom-atom distribution functions. The structure of the CCl4 solvent changes simultaneously; the solvent thus appears as a reaction partner rather than an inert medium hosting it. Thermal expansion of the system is nonuniform in time, an effect due to the presence of the acoustic horizon. One concludes that a time-resolved x-ray diffraction permits real-time visualization of solvent and solute motions during a chemical reaction.     

Palladium(II)-catalyzed asymmetric synthesis of (Z)-alpha-alkylidene-gamma-butyrolactams from (Z)-N-allylic 2-Alkynamides. Total synthesis of (-)-isocynometrine

Pd(OAc)2 combined with nitrogen-containing ligands catalyzed the cyclization of (Z)-N-allylic 2-alkynamides in acetic acid to afford the alpha-(Z)-acetoxyalkylidene-gamma-butyrolactams in high yield and high stereoselectivity. When chiral nitrogen-containing ligands were used, the catalytic asymmetric protocol was achieved with moderate enantioselectivity (up to 80 degrees C). The utility of this new methodology was exemplified by the total synthesis of (-)-isocynometrine.     

Diastereoselective, vinylogous mukaiyama aldol additions of silyloxy furans to cyclic ketones: annulation of butenolides and gamma-lactones

[reaction: see text] Vinylogous Mukaiyama aldol reactions employing silyloxyfurans and substituted cyclic ketones are described. These annulations proceed with moderate to good diastereoselectivity. The potential application of this process to the synthesis of butenolide and gamma-lactone containing natural products was demonstrated by further transformations of the addition products.     

Pressure-induced transition in magnetoresistance of single-walled carbon nanotubes

We applied hydrostatic pressure (up to 10 GPa) to single-walled carbon nanotube bundles at low temperature (down to 2 K) to measure their magnetoresistance (MR) in a field up to 12 T. We found a pressure-induced transition in MR from positive to negative in the high-field regime. The onset of the transition occurs at approximately 1.5 GPa, which correlates closely with the tube shape transitions. The characteristics of the high-pressure MR are consistent with a model of pressure-induced two-dimensional weak localization.