Self-assembly of coil-rod-coil molecules into bicontinuous cubic and oblique columnar assemblies depending on coil chain length

Coil-rod-coil molecules 1–3, consisting of four biphenyls and a p-terphenyl unit linked together with ether bonds as a rod segment and poly(propylene oxide) (PPO) with a degree of polymerization (DP) of 7, 12, 17 as coil segments were synthesized. These molecules contain lateral methyl groups at 2 and 5 positions of the middle benzene ring of p-terphenyl. The self-assembling behavior of molecules 1–3 was investigated by means of DSC, POM and SAXS in the bulk state. Molecule 1 self-organizes into a lamellar structure in the bulk state and transfers into a bicontinuous cubic structure in the liquid crystalline phase. While, molecules 2, 3 containing longer coil chains than 1 self-assemble into the hexagonal perforated lamellar (HPL) structures and the oblique columnar structures in the solid state and liquid crystalline phase, respectively. These results reveal that self-organizing behavior of such molecules is dramatically influenced by the length of the coil chains connected with the rod building block, as well as the lateral methyl groups incorporating in the middle of the rod segment.     

Finding optimal finite field strengths allowing for a maximum of precision in the calculation of polarizabilities and hyperpolarizabilities

The finite field method, widely used for the calculation of static dipole polarizabilities or the first and second hyperpolarizabilities of molecules and polymers, is thoroughly explored. The application of different field strengths and the impact on the precision of the calculations were investigated. Borders could be defined and characterized, establishing a range of feasible field strengths that guarantee reliable numerical results. The quality of different types of meshes to screen the feasible region is assessed. Extrapolation schemes are presented that reduce the truncation error and allow to increase the precision of finite field calculations by one to three orders of magnitude. © 2013 Wiley Periodicals, Inc.     

Tailoring of ionic supramolecular assemblies based on ammonium carboxylates toward liquid‐crystalline micellar cubic mesophases

Ionic liquid crystals based on ionic complexation of tris(2‐aminoethyl)amine (1) with 3,4,5‐tris(7,7,8,8,9,9,10,10,11,11,12,12,12‐tridecafluorododecyloxy)benzoic acid (2) and with 3,4,5‐tris(2‐octyldodecyloxy)benzoic acid (3) were investigated. The ionic complex with the partially fluorinated alkyl chains (1·2) exhibited a morphological transition from a hexagonal columnar mesophase to a Pm3n micellar cubic phase upon increasing the molar ratio of 2 to 1. For the complex with the branched alkyl chains (1·3) a micellar cubic mesophase was exclusively generated at appropriate composite ratios. The generation of the micellar cubic mesophases is attributed to the introduction of the laterally expanded volume of the alkyl chains compared with the corresponding normal dodecyl chains. Their thermal stabilities were most enhanced at a specific molar ratio of 1:5 for 1·2 and 1:4 for 1·3. This result corresponds to the most suitable chain volume for the stable micellar cubic mesophase.     

基于Chebyshev多项式的神经网络中长期负荷预测研究

高精度负荷预测在提高电力系统的安全性和经济性方面有着极其重要的意义,而现有的负荷预测方法因参数有限,难以完全反映其内在规律,因而导致预测结果不够准确.为此提出了一种基于Chebyshev多项式神经网络模型的预测方法.该方法使用递推最小二乘法训练神经网络权值系数,以获得高精度的参数估计,从而实现Chebyshev多项式神经网络模型对负荷量的最优拟合,再利用训练好的Chebyshev多项式神经网络模型实现中长期负荷预测.研究结果表明,该方法能较好模拟负荷变化规律,有效提高了负荷预测精度,在电力系统负荷预测中有较大的应用价值.     

A new framework for implicit restarting of the Krylov–Schur algorithm

This paper introduces a new framework for implicit restarting of the Krylov–Schur algorithm. It is shown that restarting with arbitrary polynomial filter is possible by reassigning some of the eigenvalues of the Rayleigh quotient through a rank‐one correction, implemented using only the elementary transformations (translation and similarity) of the Krylov decomposition. This framework includes the implicitly restarted Arnoldi (IRA) algorithm and the Krylov–Schur algorithm with implicit harmonic restart as special cases. Further, it reveals that the IRA algorithm can be turned into an eigenvalue assignment method. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical discretization-based kernel type estimation methods for ordinary differential equation models

We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator.     

New q‐Hermite polynomials: characterization,operators algebra and associated coherent states

This paper addresses a construction of new q‐Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three‐term recursive relation as well as the second‐order differential equation obeyed by these new polynomials are explicitly derived. Relevant operator actions, including the eigenvalue problem of the deformed oscillator and the self‐adjointness of the related position and momentum operators, are investigated and analyzed. The associated coherent states are constructed and discussed with an explicit resolution of the induced moment problem. The phase collapse in a q‐deformed boson system is studied.     

1‐Factor and Cycle Covers of Cubic Graphs

Let G be a bridgeless cubic graph. Consider a list of k 1‐factors of G. Let be the set of edges contained in precisely i members of the k 1‐factors. Let be the smallest over all lists of k 1‐factors of G. Any list of three 1‐factors induces a core of a cubic graph. We use results on the structure of cores to prove sufficient conditions for Berge‐covers and for the existence of three 1‐factors with empty intersection. Furthermore, if , then is an upper bound for the girth of G. We also prove some new upper bounds for the length of shortest cycle covers of bridgeless cubic graphs. Cubic graphs with have a 4‐cycle cover of length and a 5‐cycle double cover. These graphs also satisfy two conjectures of Zhang 18 . We also give a negative answer to a problem stated in 18 .     

A note on spectrum distribution of constraint preconditioned generalized saddle point matrices

In this note, results concerning the eigenvalue distribution and form of the eigenvectors of the constraint preconditioned generalized saddle point matrix and its minimal polynomial are given. These results extend previous ones that appeared in the literature. Copyright © 2009 John Wiley & Sons, Ltd.