On the existence of a solution of a second‐order singular initial value problem

In this paper, we consider a class of second‐order initial value problems. We extend the family of second‐order initial value problems for which the existence and uniqueness of a solution is known. To handle the singularity, we introduce the more general Caratheodory type of restrictions. The solvability results of the Emden–Fowler type of equations is established as a special case.Copyright © 2014 John Wiley & Sons, Ltd.     

Long‐time behavior of a nonlinear viscoelastic beam equation with past history

This paper is concerned with the existence of a global attractor for the nonlinear viscoelastic beam equation with past history memory where g(u_t) is a damping like | u_t | ^ru_t and f(u) is a source term like | u | ^αu ? | u | ^βu, by considering 0 ≤ β < α and r > 0. Copyright © 2014 John Wiley & Sons, Ltd.     

Existence results of stochastic impulsive systems with expectations‐dependent nonlinear terms

In this paper, sufficient conditions are established for the existence and uniqueness of global solutions to stochastic impulsive systems with expectations in the nonlinear terms. The maximal interval and the estimate of mild solutions are also discussed. These results are obtained by using the fixed point theorem, interval partition, and Lyapunov‐like technique. Finally, examples are given to illustrate the theory. Copyright © 2014 John Wiley & Sons, Ltd.     

非线性互补约束规划问题的一个新的QP-free算法

本文研究了非线性互补约束均衡问题.利用互补函数以及光滑近似法,把非线性互补约束均衡问题转化为一个光滑非线性规划问题,得到了超线性收敛速度,数值实验结果表明本文提出的算法是可行的.     

The READY program: Building a global potential energy surface and reactive dynamic simulations for the hydrogen combustion

READY (REActive DYnamics) is a program for studying reactive dynamic systems using a global potential energy surface (PES) built from previously existing PESs corresponding to each of the most important elementary reactions present in the system. We present an application to the combustion dynamics of a mixture of hydrogen and oxygen using accurate PESs for all the systems involving up to four oxygen and hydrogen atoms. Results at the temperature of 4000 K and pressure of 2 atm are presented and compared with model based on rate constants. Drawbacks and advantages of this approach are discussed and future directions of research are pointed out. © 2014 Wiley Periodicals, Inc.     

Linear Group 13 E≡E Triple Bonds in E2Li62+

The triply bonded heavier main-group compounds have a textbook trans-bent geometry, in contrast to a familiar linear form found for the lightest analogues. Strikingly, the unexpected linear group 13 E≡E triple bonds were herein found in the D_4h-symmetry E₂Li₆²⁺ clusters, and they possess a large barrier (>18.0 kcal/mol) towards the dissociation of Li⁺. The perfectly surrounded Li₄ motifs and two linear coordinated Li atoms strongly suppress the increasing nonbonded electron density of heavier E atoms, making two degenerate π bonds and one multi-center σ bond in linear heavier main-group triple bonds. The surrounding Li₆ motifs not only creates an effective electronic structure to form a linear E≡E triple bond, but the resulting electrostatic interactions account for the highly stable global E₂Li₆²⁺ clusters.     

A Stable All‐Thiophene‐Based Core‐Modified [38]Octaphyrin Diradicaloid: Conformation and Aromaticity Switch at Different Oxidation States

A soluble and stable core‐modified [38]octaphyrin, MC‐T8 , containing eight thiophene rings was synthesized by Yamamoto coupling followed by oxidative dehydrogenation. X‐ray crystallographic analysis revealed a nearly planar backbone, and the molecule is globally aromatic with a dominant 38π conjugation pathway. The dication MC‐T8²⁺ is antiaromatic, and the backbone is distorted, with a different orientation of the thiophene rings. The tetracation MC‐T8⁴⁺ becomes aromatic again, with a shallow‐bowl‐shaped geometry. Both the neutral compound and the dication demonstrated open‐shell diradical character with a small singlet–triplet energy gap (?2.70 kcal mol^?1 for MC‐T8 and ?3.78 kcal mol^?1 for MC‐T8²⁺ ), and they are stable owing to effective spin delocalization.     

变时滞Hopfield神经网络的全局吸引性和全局指数稳定性

对一类具时滞的Hopfeild型神经网络模型,在非线性神经元激励函数只要求满足Lipschitz连续的条件下,利用推广的Halanay时延微分析不等式、Dini导数以及泛函微分析技术,给出了这类模型的平衡点全局指数稳定性和全局吸引性的充分条件,这些条件易于检验,且改进和推广了前人的结论.此外,此文给出了研究神经网络模型的全局吸引性的微分不等式比较方法.