Normal families and fixed points of iterates

Let F be a family of holomorphic functions and suppose that there exists ε 0 such that if f ∈ F, then |(f 2 ) (ξ)|≤4-ε for all fixed points ξ of the second iterate f 2 . We show that then F is normal. This is deduced from a result which says that if p is a polynomial of degree at least 2, then p 2 has a fixed point ξ such that |(p 2 ) (ξ)|≥4. The results are motivated by a problem posed by Yang Lo.     

The Allen–Cahn equation with dynamic boundary conditions and mass constraints

The Allen–Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint, which may involve either the solution inside the domain or its trace on the boundary. The system of nonlinear partial differential equations can be formulated as a variational inequality. The presence of the constraint in the evolution process leads to additional terms in the equation and the boundary condition containing a suitable Lagrange multiplier. A well‐posedness result is proved for the related initial value problem. Copyright © 2014 John Wiley & Sons, Ltd.     

END样本最近邻密度估计的强相合速度

本文研究了扩展负相依(END)样本最近邻密度估计的强相合性问题.利用END序列的Bernstein型不等式和截尾的方法,获得了END样本最近邻密度估计的强相合速度,推广了NA样本和ND样本最近邻密度估计的相应结果.     

Simple power supply for power load controlled isoelectric focusing

The power supply for IEF based on features of the Cockcroft‐Walton voltage multiplier (CW VM) is described in this work. The article describes a design of the IEF power supply, its electric characteristics, and testing by IEF analysis. A circuit diagram of the power supply included two opposite charged branches (each consisting of four voltage doublers). The designed CW VM was powered by 230 V/50 Hz alternate current and it generated up to 5 kV and 90 mW at the output. Voltage and current characteristics of the power supply were measured by known load resistances in the range from 10 kΩ to 1 GΩ, which is a common resistance range for IEF strip geometry. Further, the power supply was tested by a separation of a model mixture of colored pI markers using a 175 × 3 × 0.5 mm focusing bed. Automatically limited power load enabled analysis of samples without previous optimization of the focusing voltage or electric current time courses according to sample composition. Moreover, the developed power supply did not produce any intrinsic heat and was easy to set up with cheap and commonly available parts.     

Oligo-Quinolylene–Vinylene Foldamers

Quinoline based aromatic amide foldamers are known to adopt stable folded conformations. We have developed a synthetic approach to produce similar oligomers where all amide bonds, or part of them, have been replaced by an isosteric vinylene group. The results of solution and solid state structural studies show that oligomers exclusively containing vinylene linkages are not well folded, and adopt predominantly flat conformations. In contrast, a vinylene segment flanked by helical oligoamides also folds in a helix, albeit with a slightly lower curvature. The presence of vinylene functions also result in an extension of π-conjugation across the oligomer that may change charge transport properties. Altogether, these results pave the way to foldamers in which both structural control and specific electronic properties may be engineered.     

Adaptive RAKE receiver in chaos based pilot-added DS-CDMA system

This paper presents the theoretical analysis of adaptive multiuser RAKE receiver scheme in frequency selective fading channel for direct-sequence code division multiple access (DS-CDMA) system. Least mean square (LMS) algorithm is used to estimate the channel coefficients. Chaotic sequences are used as spreading sequence and corresponding bit error rate (BER) in closed form is derived for imperfect channel estimation conditions. Performances of chaotic sequences are compared with pseudorandom noise (PN) sequences. Under perfect synchronization assumption, various simulation results are shown to investigate the performance of the proposed system.     

Determination of the gas chromatographic elution sequences of the (+)- and (−)-enantiomers of stable atropisomeric PCBs on Chirasil-dex

Pure enantiomers of chiral (atropisomeric) polychlorinated biphenyls (PCBs) obtained by high-performance liquid chromatography were used to establish the gas chromatographic elution sequences of the (+)- and (−)-enantiomers of six PCB atropisomers on Chirasil-Dex. The elution order was found to be (−/+) for PCBs 84, 132, 136, and 176 and (+/−) for PCBs 135 and 174. The retention characteristics of all 19 tri- and tetra-ortho atropisomeric PCBs were also investigated. Nine of the atropisomers could be separated using this chiral selector. PCBs 95, 132, and 149 were completely resovled and PCBs 84, 91, 135, 136, 174, and 176 were partially separated (R = 0.7–0.9). All of the separated congeners are 2,3,6-substituted in at least one ring, and conversely – none of the congeners that lacks 2,3,6-substitution could be separated. Thus, chiral recognition and enantiomer separation seems to be strongly governed by 2,3,6-substitution.     

解单障碍问题的Lagrangian乘子非匹配网格区域分解法

针对二阶椭圆型单障碍问题提出了一类基于非匹配网格的Lagrang ian乘子非重叠型区域分解方法.并在适当条件下给出了该方法的收敛性分析和收敛速度估计.     

基于拟相对内部集值优化问题弱有效元的最优性条件

本文研究了基于拟相对内部的非凸集值优化问题弱有效元的最优性条件.首先,讨论了弱有效元与线性子空间之间的关系,利用涉及拟相对内部的凸集分离定理,获得了弱有效元的最优性条件.其次,给出了基于拟相对内部弱有效元的Lagrange乘子定理.     

NSD序列加权和的中心极限定理及其在EV回归模型中的应用

基于负超可加相依(简称为NSD)随机序列的性质及其一些不等式,利用随机变量的截断方法建立了NSD随机序列加权和的中心极限定理,从而推广了负相协NA随机序列的相应结论.并将其应用到变系数EV回归模型,得到了未知参数LS估计的渐近正态性.