A sufficient condition for stability using slopes of isoclines in planar mappings

Coupled planar maps are often parameter dependent, with the stability of their fixed points depending on the values of the parameters chosen. As the magnitude of the eigenvalues is difficult to determine when the number of parameters is large, one commonly uses instead the Jury conditions for the Jacobian, but even this can present difficulties. In this paper, we will show a simpler sufficient criteria for local asymptotic stability that follows by comparing slopes of isoclines.     

Extinction time and the total mass of the continuous-state branching processes with competition

Consider a general continuous-state branching process with additional interaction, which destroys the branching property. We give precise conditions on the interaction term, in order to decide whether the extinction time of the process remains or not bounded as the initial value tends to infinity, and similarly for the total mass of the process.     

第32届江苏省化学竞赛选拔赛有机化学试题解析*

利用有机化学基础知识和理论对第32届江苏省化学竞赛选拔赛试题有机化学部分进行详细解析,为指导老师和参赛学生提供参考。     

以联席会和竞赛为载体构建实验教学改革交流的新平台——浙江省高校化学化工实验教学中心主任联席会暨化学学科(实验)竞赛10周年回顾

介绍成立浙江省高校化学化工实验教学中心联席会(以下简称:联席会)、举办化学学科(实验)竞赛的背景及发展情况。以联席会和竞赛为载体,建立了全省实验教学研究与改革的交流平台,扩大了实验教学示范中心的影响力和辐射面,推动了实验室建设、课程建设以及人才培养等各项工作,取得了丰硕的教学成果。     

Competition between halogen bond and hydrogen bond in complexes of superalkali Li3S and halogenated acetylene XCCH (X = F,Cl, Br,and I)

Complexes of superalkali Li₃S and XCCH (X = F, Cl, Br, and I) have been studied with theoretical calculations at the MP2/aug‐cc‐pVTZ level. Three types of structures are found: (A) the X atom combines with the S atom through a halogen bond; (B) the X atom interacts with the π electron of Li₃S by a π halogen bond; (C) the H atom combines with the S atom through a hydrogen bond. For A and B, a heavier halogen atom makes the interaction stronger, while for C, the change of interaction energy is not obvious, showing a small dependence on the nature of the X atom in HCCX. A is more stable than B and their difference in stability decreases as X varies from Cl to I. For the F and Cl complexes, A is weaker than C, however, the former is stronger than the latter in the Br and I complexes. The above three types of interactions have been analyzed by means of electron localization function, electron density difference, and energy decomposition, and the results show that they have similar nature and features with conventional interactions. © 2014 Wiley Periodicals, Inc.     

高中化学竞赛中电子效应和空间效应考点分析——以近年全国化学奥林匹克竞赛试题为例

电子效应和空间效应是有机化学的基础,近年来,这部分知识在全国化学奥林匹克竞赛中的考查比例处于上升趋势。因此,以近年全国化学奥林匹克竞赛试题为例,详细说明电子效应和空间效应在竞赛中的考点,帮助辅导化学竞赛的教师和参加化学竞赛的考生了解该部分知识需要达到的教学标准和掌握层次。     

大学生化学竞赛对实验教学改革与创新人才培养的促进作用*

大学生的化学竞赛是课内实验教学的有效延伸,也是从学生视角对实验教学效果的有效检验。通过分析和比较学生参加化学实验竞赛的过程和效果,能有效促进化学实验教学改革、课程建设及创新人才的培养。近年来吉林大学化学学院学生实验竞赛的成绩显著提高,一方面通过化学竞赛激发本科生喜爱化学和开展化学研究的热情,增加学习的主观能动性;另一方面通过竞赛发现问题,在解决问题的过程中促进实验教学改革和课程建设,学院“三阶段”模式的竞赛活动开展,更加有利于培养学生的创新意识和创新能力,促进了化学创新人才的培养。     

On the construction of non-affine jump-diffusion models

We describe a method for construction of jump analogues of certain one-dimensional diffusion processes satisfying solvable stochastic differential equations. The method is based on the reduction of the original stochastic differential equations to the ones with linear diffusion coefficients, which are reducible to the associated ordinary differential equations, by using the appropriate integrating factor processes. The analogues are constructed by means of adding the jump components linearly into the reduced stochastic differential equations. We illustrate the method by constructing jump analogues of several diffusion processes and expand the notion of market price of risk to the resulting non-affine jump-diffusion models.     

股票市场的长记忆及其动态结构

本文提出了结合平均小波系数法和自回归原始自助法的稳健长记忆检验,蒙特卡罗模拟显示该方法对于短期记忆过程具有稳定性。基于该方法对2005年4月8日至2015年6月30日的中国、美国、香港和德国股市进行了实证分析。全局检验结果表明仅中国的股票市场存在显著的长记忆,并且风险因素无法对长记忆解释,而美国、德国和香港的股市不存在长记忆。基于递增窗口的动态Hurst指数分析显示,金融危机时期4个股市都存在显著的长记忆。2010年后,除中国股市外,其余三个股市几乎不存在长记忆现象。     

Optimal portfolio execution under time-varying liquidity constraints

In this article, we take an algorithmic approach to solve the problem of optimal execution under time-varying constraints on the depth of a limit order book (LOB). Our algorithms are within the resilience model proposed by Obizhaeva and Wang (2013) with a more realistic assumption on the order book depth; the amount of liquidity provided by an LOB market is finite at all times. For the simplest case where the order book depth stays at a fixed level for the entire trading horizon, we reduce the optimal execution problem into a one-dimensional root-finding problem which can be readily solved by standard numerical algorithms. When the depth of the order book is monotone in time, we apply the Karush-Kuhn-Tucker conditions to narrow down the set of candidate strategies. Then, we use a dichotomy-based search algorithm to pin down the optimal one. For the general case, we start from the optimal strategy subject to no liquidity constraints and iterate over execution strategy by sequentially adding more constraints to the problem in a specific fashion until primal feasibility is achieved. Numerical experiments indicate that our algorithms give comparable results to those of current existing convex optimization toolbox CVXOPT with significantly lower time complexity.