Critical behaviour of the order parameters at the SmC* to SmA phase transition in a ferroelectric liquid crystal mixture

Critical behaviour of the order parameters has been investigated in the ferroelectric liquid crystal mixture ZLI‐3654 in a 7.5 µm thick planar cell. The temperature dependence of the primary (tilt angle) and secondary (spontaneous polarisation) order parameters is considered. The critical exponent (β) has been evaluated from the fitting of the temperature dependence of the experimental data for both tilt angle and spontaneous polarisation. Experimental results are compared with the predictions of the de Gennes and Landau models.     

Dynamic Release of Propranolol HCl from Cationic Ion–Exchanger–Loaded Calcium Alginate Beads

The dynamic release of drug propranolol HCl from the propranolol HCl–resin complex (PRC) loaded calcium alginate beads has been studied in the buffer media of pH 1.2 at the physiological temperature 37°C. The PRC encapsulated beads demonstrated nearly 58.04% release while naked PRC particles released 98.00% drug in 24 h in the gastric fluid. The amount of drug released was found to increase with and decrease in the amount of sodium alginate in the beads. Similarly, with the increase in the amount of entrapped PRC particles within the beads, the quantity of drug released was also observed to increase. The degree of crosslinking of beads also affected the release kinetics. Interestingly, the release from naked PRC particles followed ‘first‐order’ kinetics while PRC particles, entrapped in calcium–alginate beads, exhibited ‘diffusion controlled’ release behavior as indicated by liner nature of fractional release vs. √t plot.     

任意阶高运算恒定性分抗逼近电路--标度格型级联双口网络

标度拓展经典负半阶分抗逼近电路,可实现具有任意分数阶微积算子运算功能的分抗逼近电路,但牺牲了运算恒定性.从电路网络的角度分析具有恒定运算性能的负半阶Carlson分形格分抗逼近电路.根据标度分形格分抗逼近电路的等效无源双口网络,探讨该双口网络右侧端口的运算有效性,设计具有高运算恒定性的任意阶标度分形格分抗逼近电路.结合负实零极点对基元系统的零极点分布及其局域化特性,阐述具有任意实数阶微积算子运算功能的标度分形格分抗逼近电路运算振荡现象的物理本质,并从理论上分析有效抑制频域运算振荡现象的方法.结合对称阻容T型节电路优化理论及方法,对任意阶对称格型级联双口网络的频域逼近性能进行优化,获得具有高逼近效益的任意阶标度分形格分抗逼近电路.具有低振荡幅度的任意阶对称格型级联双口网络为高运算恒定性的分抗逼近电路设计及应用提供了一种新方法及思路.     

Intermolecular interactions of a size‐expanded guanine analogue with gold nanoclusters

The interactions between a size‐expanded Guanine analogue x‐Guanine (xG) and gold nanoclusters, Au_n (n = 2, 4, 6, and 8), were studied theoretically using density functional theory. Geometries of neutral complexes were optimized using the B3LYP functional with the 6‐31+G(d,p) basis set for xG and the LANL2DZ basis set for gold clusters. The binding modes, interaction strength, and the charge‐transfer properties of different Au_n‐xG complexes were investigated. Natural population analysis was performed for natural bond order charges. It was found that gold nanoclusters form stable complexes with xG and these binding results in a substantial amount of electronic charge being transferred from xG to the gold clusters. The vertical first ionization potential, electron affinity, Fermi Level, and the HOMO–LUMO gap of xG and its complexes with gold nanoclusters were also analyzed. © 2013 Wiley Periodicals, Inc.     

Theoretical analysis of correlation between ionization threshold fluence in IR‐MALDI and IR absorption spectrum of matrix molecules

To investigate the correlation between the wavelength dependence of ionization threshold fluence of target molecule in matrix‐assisted laser desorption/ionization by infrared (IR) laser and the IR absorption spectrum of matrix molecule, we have analyzed the IR absorption spectra of four matrix molecules using density functional theory and correlated ab initio molecular orbital method. The calculated IR absorption spectra of the isolated molecules showed more qualitative correlation with the wavelength dependence of ionization threshold fluence than those of the solid state structures. We can consider that a portion of matrix molecules lost the ordered crystal structure and that the transition to the diluted or isolated state occurred at the early process of IR laser irradiation. © 2012 Wiley Periodicals, Inc.     

PDα‐type distributed learning control for nonlinear fractional‐order multiagent systems

This paper considers the consensus tacking problem for nonlinear fractional‐order multiagent systems by presenting a PD^α‐type iterative learning control update law with initial learning mechanisms. The asymptotical convergence of the proposed distributed learning algorithm is strictly proved by using the properties of fractional calculus. A sufficient condition is derived to guarantee the whole multiagent system achieving an asymptotic output consensus. An illustrative example is given to verify the theoretical results.     

A fast iterative method to find the matrix geometric mean of two HPD matrices

The purpose of this research is to present a novel scheme based on a quick iterative scheme for calculating the matrix geometric mean of two Hermitian positive definite (HPD) matrices. To do this, an iterative scheme with global convergence is constructed for the sign function using a novel three‐step root‐solver. It is proved that the new scheme is convergent and shown to have global convergence behavior for this target, when square matrices having no pure imaginary eigenvalues. Next, the constructed scheme is used and extended through a well‐known identity for the calculation of the matrix geometric mean of two HPD matrices. Ultimately, several experiments are collected to show its usefulness.     

第二类端点奇异Fredholm积分方程的分数阶退化核方法

本文针对第二类端点奇异Fredholm积分方程构造基于分数阶Taylor展开的退化核方法，设计了两种计算格式，一是在全区间上使用分数阶Taylor展开式近似核函数，二是在包含奇点的小区间上采用分数阶插值，在剩余区间上采用分段二次多项式插值逼近核函数.讨论了两种退化核方法收敛的条件，并给出了混合插值法的收敛阶估计.数值算例表明对于非光滑核函数分数阶退化核方法有着良好的计算效果，且混合二次插值法比全区间上的分数阶退化核方法有着更广泛的适用范围.     

Maximizing the mean subtree order

This article focuses on properties and structures of trees with maximum mean subtree order in a given family; such trees are called optimal in the family. Our main goal is to describe the structure of optimal trees in and , the families of all trees and caterpillars, respectively, of order . We begin by establishing a powerful tool called the Gluing Lemma, which is used to prove several of our main results. In particular, we show that if is an optimal tree in or for , then every leaf of is adjacent to a vertex of degree at least . We also use the Gluing Lemma to answer an open question of Jamison and to provide a conceptually simple proof of Jamison's result that the path has minimum mean subtree order among all trees of order . We prove that if is optimal in , then the number of leaves in is and that if is optimal in , then the number of leaves in is . Along the way, we describe the asymptotic structure of optimal trees in several narrower families of trees.