Synchronization of fractional‐order delayed neural networks with hybrid coupling

This article presents new theoretical results on the synchronization for a class of fractional‐order delayed neural networks with hybrid coupling that contains constant coupling and discrete‐delay coupling. This is the first attempt to investigate the synchronization problem of fractional‐order coupled delayed neural networks. Based on the fractional‐order Lyapunov stability theorem and Kronecker product properties, sufficient criteria are established to ensure the fractional‐order coupled neural network to achieve synchronization. Numerical simulations are given to illustrate the correctness of the theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 106–112, 2016     

Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime

We present several numerical methods and establish their error estimates for the discretization of the nonlinear Dirac equation(NLDE) in the nonrelativistic limit regime, involving a small dimensionless parameter 0 ε≤ 1 which is inversely proportional to the speed of light. In this limit regime, the solution is highly oscillatory in time, i.e., there are propagating waves with wavelength O(ε~2) and O(1) in time and space,respectively. We begin with the conservative Crank-Nicolson finite difference(CNFD) method and establish rigorously its error estimate which depends explicitly on the mesh size h and time step τ as well as the small parameter 0 ε≤ 1. Based on the error bound, in order to obtain ‘correct' numerical solutions in the nonrelativistic limit regime, i.e., 0 ε■ 1, the CNFD method requests the ε-scalability: τ = O(ε~3) and h= O(ε~(1/2)). Then we propose and analyze two numerical methods for the discretization of NLDE by using the Fourier spectral discretization for spatial derivatives combined with the exponential wave integrator and timesplitting technique for temporal derivatives, respectively. Rigorous error bounds for the two numerical methods show that their ε-scalability is improved to τ = O(ε~2) and h = O(1) when 0 ε■1. Extensive numerical results are reported to confirm our error estimates.     

催化的端炔C-H键与α,β-不饱和-γ-内酰胺的亲核加成反应

吡咯啉酮是一类重要的五元杂环,广泛存在于许多天然产物、生物活性分子和高聚物中.在众多吡咯啉酮衍生物中,5-炔基-2-吡咯啉酮引起了化学家们广泛的关注.因为这种分子结构不仅存在于具有潜在治疗作用的药物分子(如眼部降压药、α7乙酰胆碱受体激动剂、抗惊厥和消炎药物)中,也存在于许多天然产物中,例如刺桐类生物碱和多环类生物碱.鉴于此,人们发展了许多合成这类化合物的方法.目前文献报道最多的方法是炔基负离子对5-位具有离去基团的吡咯啉酮化合物的亲核取代反应.离去基团主要有苯硫基、1-苯并咪唑基和烷氧基等.但是这些方法操作步骤繁琐,产生大量的副产物,原子经济性不高.
　　本课题组发展了一例新型的端炔C–H键与α,β-不饱和-γ-内酰胺的亲核加成反应,合成了一系列5-炔基-2-吡咯啉酮衍生物.该反应以环状N-酰亚胺正离子为反应活性中间体,反应条件温和,操作简便.据我们所知,这是一例原子经济地合成5-炔基-2-吡咯啉酮衍生物的新方法.环状N-酰亚胺正离子是一类高活性的亲电试剂,广泛应用于构建含氮杂环体系.本课题组利用这一策略实现了一系列C–C和C–N成键反应.基于此,本文原位形成环状N-酰亚胺正离子,以端炔作为亲核试剂,与其发生亲核加成反应,合成了一系列5-炔基-2-吡咯啉酮衍生物,原子经济性为100%.
　　首先,我们以5 mol%TsOH为Br?nsted酸,考察了Lewis酸效应对反应收率的影响.结果表明, Al(OTf)3给出最好的反应收率,不加Lewis酸没有亲核加成产物生成.然后,我们以5 mol%Al(OTf)3为Lewis酸,考察了Br?nsted酸效应对反应收率的影响.结果表明, HAuCl4·4H2O给出最佳的反应收率54%,不加Br?nsted酸也没有亲核加成产物生成.值得一提的是,当HAuCl4·4H2O为单一催化剂,不加Al(OTf)3时,反应收率也达到55%.然后,我们以HAuCl4·4H2O为催化剂,考察了溶剂效应和反应温度对反应收率的影响.结果表明,四氯乙烷(TTCE)为反应最佳的溶剂,50 oC反应最佳.为了进一步提高反应收率,我们又考察了催化剂用量对反应收率的影响.结果表明,10 mol%的催化剂给出最佳的反应收率60%.进一步优化反应条件,我们没有得到更好的结果.因此最佳的反应条件： N-苄基-α,β-不饱和-γ-内酰胺1(0.4 mmol),苯乙炔2a (1.2 mmol), HAuCl4·4H2O (10 mol%), TTCE (2.0 mL),50 oC下反应15 h.
　　在确定了最佳的反应条件后,我们对端炔类底物的适用性进行了考察.结果表明,给电子的苯乙炔表现出较高的反应活性;弱吸电子的苯乙炔也表现出较高的反应活性;强吸电子的苯乙炔则抑制反应的发生;位阻效应对该反应没有明显影响;杂环端炔也给出中等以上的收率;然而,简单脂肪端炔不能给出相应的亲核加成产物.
　　本文发展了一例催化的端炔C–H键与α,β-不饱和-γ-内酰胺的亲核加成反应.该反应以环状N-酰亚胺正离子为关键中间体.反应条件温和,操作简便.构建了一种以中等的收率(45%–76%)合成一系列5-炔基-2-吡咯啉酮衍生物的方法.     

Approximation of Invariant Measures for Regime-switching Diffusions

In this paper, we are concerned with long-time behavior of Euler-Maruyama schemes associated with regime-switching diffusion processes. The key contributions of this paper lie in that existence and uniqueness of numerical invariant measures are addressed (i) for regime-switching diffusion processes with finite state spaces by the Perron-Frobenius theorem if the “averaging condition” holds, and, for the case of reversible Markov chain, via the principal eigenvalue approach provided that the principal eigenvalue is positive; (ii) for regime-switching diffusion processes with countable state spaces by means of a finite partition method and an M-Matrix theory. We also reveal that numerical invariant measures converge in the Wasserstein metric to the underlying ones. Several examples are constructed to demonstrate our theory.     

图的k部划分的一个注记

设k≥2是一个整数。本文证明了任意有m条边的图都存在一个顶点的划分V_1,V_2…,V_k,使得e(V_1,V_2…,V_k)≥k-1/k m+k-1/2k((2m+1/4)~1/2-1/2)-(k-2)~2/8k,且max{e(V_i):1≤i≤k}≤m/k~2+(k-1)/2k~2((2m+1/4)~1/2-1/2+3/8-7k-4/8k~2.我们的结果改进了[Fan G.,Hou J.,Zeng Q.,A bound for judicious k-partitions of graphs,Discrete Appl.Math.,2014,179:86—99]的主要结论.     

Isolation and Crystallographic Characterization of the Labile Isomer of Y@C82 Cocrystallized with Ni(OEP): Unprecedented Dimerization of Pristine Metallofullerenes

Although the major isomers of M@C₈₂ (namely M@C_2v(9)‐C₈₂, where M is a trivalent rare‐earth metal) have been intensively investigated, the lability of the minor isomers has meant that they have been little studied. Herein, the first isolation and crystallographic characterization of the minor Y@C₈₂ isomer, unambiguously assigned as Y@C_s(6)‐C₈₂ by cocrystallization with Ni(octaethylporphyrin), is reported. Unexpectedly, a regioselective dimerization is observed in the crystalline state of Y@C_s(6)‐C₈₂. In sharp contrast, no dimerization occurs for the major isomer Y@C_2v(9)‐C₈₂ under the same conditions, indicating a cage‐symmetry‐induced dimerization process. Further experimental and theoretical results disclose that the regioselective dimer formation is a consequence of the localization of high spin density on a special cage‐carbon atom of Y@C_s(6)‐C₈₂ which is caused by the steady displacement of the Y atom inside the C_s(6)‐C₈₂ cage.     

Structure elucidation and NMR assignments of a new 6,9-cyclotetrahydrofuranlignan from Syringa pinnatifolia

A new 6,9-cyclotetrahydrofuranlignan, 3,3′-dimethoxy-4,4′-dihydroxy-8β,9β,8′α-6,9-cyclotetrahydrofuranlignan, was isolated from the stem of Syringa pinnatifolia Hems1.var. alashanensis MA. et S. Q. ZHOU. Its structures were elucidated on the basis of spectroscopic methods including UV, IR, ESI-MS, 1D NMR and 2D NMR.     

Rhodium‐Catalyzed Oxidative Benzannulation of N‐Pivaloylanilines with Internal Alkynes through Dual C−H Bond Activation: Synthesis of Highly Substituted Naphthalenes

An efficient method was developed for the synthesis of highly substituted naphthalenes through rhodium‐catalyzed oxidative benzannulation of N‐pivaloylanilines with internal alkynes. The benzannulation reaction proceeded smoothly through dual C?H bond activation to produce the corresponding highly substituted naphthalene products in satisfactory to good yields.     

Blow-up for Stochastic Reaction-Diffusion Equations with Jumps

In this paper, we focus on stochastic reaction-diffusion equations with jumps. By a new auxiliary function, we investigate non-negative property of the local strong (variational) solutions, which applies to stochastic reaction-diffusion equations with highly nonlinear noise terms. As a byproduct, we study the problem of non-existence of global strong solutions by imposing appropriate conditions on the drift terms, which can cover many more models than the existing literature. Moreover, we also investigate the subject of Lévy-type noise-induced explosion by bringing some plausible assumptions to bear on the noise terms, which, however, need not guarantee local strong (variational) solutions to enjoy the non-negative property. Meanwhile, several examples are presented to illustrate the theory established.     

Mn助剂对K-Co-Mo催化剂结构及CO加氢合成低碳醇性能的影响

通过溶胶-凝胶法合成了一系列Mn掺杂K-Co-Mo催化剂,并利用X射线衍射、N₂吸脱附、NH₃程序升温脱附、原位漫反射红外光谱以及X射线吸收谱等技术对催化剂的结构进行了表征.活性测试结果显示Mn掺杂催化剂比未掺杂催化剂表现更高的合成低碳醇的催化活性,尤其是C₂₊醇的选择性得到了明显的提高.醇产物分布偏离了ASF分布规律,甲醇的含量显著减少,乙醇成为主要醇产物.表征结果表明Mn助剂的加入增强了Co和Mo之间的相互作用,促进了醇生成活性中心Co-Mo-O物种的生成.显著减少了催化剂强酸性位的数量,促进了弱酸性位的产生,有利于醇产物的生成.助剂的加入有利于催化剂对CO的线性和桥式吸附,促进了醇产物的生成和碳链的增长,提高了催化剂对C₂₊醇的选择性.