随机Richlet级数的增长性

本文构造了全平面上的无限级Dirirchlet级数,使得它对型函数的增长性与一个已知的不同分布随机Dirichlet的增长性相同,从而通过前者增长性与指数,系数的关系可研究后者的增长性.     

有限元插值误差的下界估计

基于一维区域上的拟一致剖分,证明了线性元插值误差的最优下界估计.基于此并利用超收敛理论,我们得到了有限元离散误差的上、下界.     

上下解方法在四阶非局部边值问题中的应用

考虑具有p-Laplacian算子的四阶微分方程非局部边值问题.通过构造Green函数,利用上下解方法,结合单调迭代技巧得到了四阶非局部边值问题迭代解的存在性.最后给出实例验证主要结论.     

(D)族负象限相依随机变量和的精致大偏差

在负象限相依结构下,得到了支撵在(-∞,∞)上的(D)族随机变量非中心化以及中心化部分和的精致大偏差.同时,还在较弱的条件下,得到了相应的中心化随机和的精致大偏差.     

Lower bounds in communication complexity based on factorization norms

We introduce a new method to derive lower bounds on randomized and quantum communication complexity. Our method is based on factorization norms, a notion from Banach Space theory. This approach gives us access to several powerful tools from this area such as normed spaces duality and Grothendiek's inequality. This extends the arsenal of methods for deriving lower bounds in communication complexity. As we show, our method subsumes most of the previously known general approaches to lower bounds on communication complexity. Moreover, we extend all (but one) of these lower bounds to the realm of quantum communication complexity with entanglement. Our results also shed some light on the question how much communication can be saved by using entanglement. It is known that entanglement can save one of every two qubits, and examples for which this is tight are also known. It follows from our results that this bound on the saving in communication is tight almost always. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

光催化活性二氧化钛溶胶的低温制备与表征

以钛酸丁酯为原料,在70 ℃制备了具有光催化活性的TiO2溶胶.用X射线衍射仪(XRD)和透射电子显微镜(TEM)表征了溶胶结构;用紫外-可见分光光度计研究了TiO2溶胶对甲基橙的吸附和光催化降解性能.XRD图谱表明TiO2溶胶粒子的一次粒径约4 nm,晶型主要为锐钛矿型,并含有少量结晶不完善的板钛矿型;TEM图像表明溶胶中TiO2粒子分散良好,二次粒径约10 nm.吸附实验表明TiO2溶胶使甲基橙溶液褪色约17%;光催化实验表明TiO2溶胶光催化性能优异,自然光催化降解甲基橙溶液(10 mg/L),16min后甲基橙浓度几乎降为0.     

Continuity at the extreme points

We prove that a bounded convex lower semicontinuous function defined on a convex compact set K is continuous at a dense subset of extreme points. If there is a bounded strictly convex lower semicontinuous function on K, then the set of extreme points contains a dense completely metrizable subset.     

Traveling wave solutions in delayed higher dimensional lattice differential systems with partial monotonicity

In this paper, we consider the existence of traveling wave solutions in delayed higher dimensional lattice differential systems with partial monotonicity. By relaxing the monotonicity of the upper solutions and allowing it greater than positive equilibrium point, we establish the existence of traveling wave solutions by means of Schauder's fixed point theorem. And then, we apply our results to delayed competition‐cooperation systems on higher dimensional lattices.     

环中关于理想同余的粗糙集的性质

讨论了环中由理想同余关系所决定的下、上近似的一些特殊性质．     

Observation of Unusual Molecular Diffusion Behaviour below the Lower Critical Solution Temperature of Water/2‐Butoxyethanol Mixtures by using Fluorescence Correlation Spectroscopy

The effect of solute affinity on solute diffusion in binary liquids well below the lower critical solution temperature (LCST) was studied by using fluorescence correlation spectroscopy. We measured the hydrodynamic radii of a hydrophobic and an amphiphilic fluorescent dye under systematic variation of the relative molar fractions of water/2‐butoxyethanol and, for comparison, of water/methanol mixtures, which do not show phase separation. We found that the apparent hydrodynamic radius of the hydrophobic dye almost doubled in water/2‐butoxyethanol, whereas it remained largely unchanged for the amphiphilic dye and in water/methanol mixtures. Our results indicate that the translational diffusion of solutes is influenced by transient local solution structures, even at temperatures well below the LCST. We conclude that, even far below LCST, different solutes can experience different environments in binary liquid mixtures depending on both the solute and solvent properties, all of which impact their reactivity.