Copper‐catalyzed Clauson–Kass pyrroles synthesis in aqueous media

An efficient and convenient copper‐catalyzed Clauson–Kass reaction of 2,5‐dimethoxytetrahydrofuran with amines in aqueous media has been developed, providing a wide range of N‐substituted pyrroles in good yields. It is noteworthy that the Clauson–Kass reaction of 2,5‐dimethoxytetrahydrofuran with p‐phenylenediamine or m‐phenylenediamine proceeds smoothly to afford the corresponding monopyrroles and bispyrroles with high selectivity in impressive yields. A plausible mechanism for the formation of N‐substituted pyrroles has been proposed. Copyright © 2012 John Wiley & Sons, Ltd.     

QUAFITIZED HALL EFFECT IM VERY STRONG MAGEETIC FIELD

The experimentally observed quantized Hall plateau of P_xy=3h/e² in two-dimensional electron gas, when the lowest Landau level is 1/3 filled, is discussed. The consistency of the cxtremal condition for the Hartree-Fock potential in the possible charge-density-wave state with, opening an energy gap at the Fermi level is indicated. The exactness of Such 1/3 "fractional" quantization might be justified by a modified version of Laughlin's argument based on gauge invariance.     

非线性规划的法向与梯度组合方向算法及其收敛性

求解上述非线性不等式约束的规划问题并使用梯度投影时,由于非线性约束的特性,目标函数的负梯度在迭代点所在的切平面的交上的投影方向不一定是可行方向.为了利用梯度投影求得一个可行的下降方向,并使算法具有收敛性质,往往需要不止一次的作投影计算,因而算法比较复杂.文献[1]一反以往需多次求投影来求得迭代方向的办法,首先采用斜投影以求迭代方向,使得计算减少到至多求两次投影并给出他的算法的收敛性     

二阶修正的约束变尺度算法

我们知道,70年代发展起来的约束变尺度算法是求解非线性规划问题的十分有效的方法之一.它的特点是初始点可任取且有快速的收敛速度.若我们考虑如下的非线性规划问题:     

Algorithm for Optimal Triangulations in Scattered Data Representation and Implementation

Scattered data collected at sample points may be used to determine simple functions to best fit the data. An ideal choice for these simple functions is bivariate splines. Triangulation of the sample points creates partitions over which the bivariate splines may be defined. But the optimality of the approximation is dependent on the choice of triangulation. An algorithm, referred to as an Edge Swapping Algorithm, has been developed to transform an arbitrary triangulation of the sample points into an optimal triangulation for representation of the scattered data. A Matlab package has been completed that implements this algorithm for any triangulation on a given set of sample points.     

Envelop solitons in dusty plasmas for warm dust

A nonlinear Schrödinger equation is obtained for the warm dusty plasmas. The modulational instability of envelop soliton is investigated in this paper. Both the temperature of the dust grains and the charge variations of dust grains affect the instability regions of the dusty plasmas. It also affect the amplitude and the width of the envelop soliton.     

Covering vertices of a graph by k disjoint cycles

Let d, k and n be three integers with k3, d4k−1 and n3k. We show that if d(x)+d(y)d for each pair of nonadjacent vertices x and y of a graph G of order n, then G contains k vertex-disjoint cycles converting at least min{d,n} vertices of G.