Explicit symplectic multidimensional exponential fitting modified Runge-Kutta-Nyström methods

This paper is concerned with multidimensional exponential fitting modified Runge-Kutta-Nyström (MEFMRKN) methods for the system of oscillatory second-order differential equations q″(t)+Mq(t)=f(q(t)), where M is a d×d symmetric and positive semi-definite matrix and f(q) is the negative gradient of a potential scalar U(q). We formulate MEFMRKN methods and show clearly the relationship between MEFMRKN methods and multidimensional extended Runge-Kutta-Nyström (ERKN) methods proposed by Wu et al. (Comput. Phys. Comm. 181:1955–1962, 2010). Taking into account the fact that the oscillatory system is a separable Hamiltonian system with Hamiltonian \(H(p,q)=\frac{1}{2}p^{T}p+ \frac{1}{2}q^{T}Mq+U(q)\), we derive the symplecticity conditions for the MEFMRKN methods. Two explicit symplectic MEFMRKN methods are proposed. Numerical experiments accompanied demonstrate that our explicit symplectic MEFMRKN methods are more efficient than some well-known numerical methods appeared in the scientific literature.     

A facile two-step etching method to fabricate porous hollow silica particles

We report here the fabrication of hollow silica particles with mesopores larger than 10 nm on their wall via a facile two-step etching method. Different from the conventional template method, the new method uses the silica particles as starting materials, which were synthesized using the well-known Stöber method. In the hollow silica preparation, first, we gently etch the silica particles with a NaOH solution without using template molecules to make them porous. Then, we coat the porous silica particles with poly-dimethyldiallylammonium chloride (PDDA) and treat the PDDA-coated porous silica with an ammonia solution to form the hollow silica nanospheres. In this study, we found that the NaOH dosage and ammonia concentration have significant impact on the morphology of the final products. Adsorption was also studied and results show that the hollow nanospheres can effectively uptake protein-based biomolecules (hemoglobin).     

易贡滑坡堰塞湖溃坝洪水分析

滑坡堰塞坝体主要由块石、碎石土等松散材料组成,随着上游水位的不断上升,极易失稳,一旦决口将对给下游人民的生命财产安全造成极大的威胁。因此,研究堰塞坝溃坝问题具有重要的学术意义和应用价值。2000 年 4 月 9 日,西藏林芝地区波密县易贡藏布河扎木弄沟发生大规模山体滑坡堵塞易贡藏布江,形成坝高60m,长约2500m,库容可达288×108m3,体积约28×108～30×108m3的滑坡堰塞湖, 2000年6月10日堰塞坝溃决。本文以易贡堰塞湖溃坝为例,从连续性方程及Navier Stokes方程出发,结合标准型湍流模型,并采用VOF方法进行自由面处理,基于流体计算软件Fluent模拟分析了溃坝洪水在下游弯曲河道的演进过程及不同位置的流速变化。数值模拟结果与实测资料记录基本一致,表明该模型能够模拟溃坝洪水在地形复杂弯曲河道中的演进过程。     

超线性收敛的指数下降迭代法

1　引　　言文[1]中借助于常微分方程的Liapunov方法建立了与非线性方程f(x)=0(1)在区间[a,b]内的解x*相对应的Cauchy问题dx/dt=-w(x)f(x)(2)x(0)=x0,　x0∈[a,b](3)其中f(x)在[a,b]上连续可导,f′(x)≠0,而w(x)满足w(x)f′(x)>0且使得Cauachy问题(2)—(3)的饱和解x=x(t,x0)存在唯一.于是非线性方程(1)在[a,b]内的解x*为自治系统(2)的渐近稳定的奇点,从而有limt→+∞x(t,x0)=x*,　　x0∈[a,b](4)成立.这说明对任一初值x0∈[a,b]通过解Cauchy问题(2)—(3)可得非线性方程(1)在[a,b]内的解x*.在文[2]中利用Lambert的非线性方法[3],导出了一个…     

生物正交反应在我国的研究进展

生物正交反应是指能够在生物体系中进行、且不会与天然生物化学过程相互干扰的一类化学反应. 这类反应的出现为科学家对生命进程的原位研究带来了革命性的技术, 已经成为化学生物学这一新兴交叉领域的核心方向之一. 自这一概念提出的近二十年里, 生物正交化学经历了反应类型由单一的“偶联反应”向成键偶联、断键剪切反应并重, 应用场景由简单的活细胞体系向更为复杂的生物活体升级的一系列发展历程. 同时, 在生命科学研究、医药研发、临床诊疗等多个领域展示出了广阔的应用前景. 我国化学生物学领域的学者们积极参与并推动了生物正交反应的快速发展, 在反应开发、体系优化和实际应用等方面开展了一系列原创工作, 取得了瞩目的成绩; 尤其是在“生物正交剪切反应”概念的提出与开发应用等方面产生了重要的国际影响. 本综述中, 分别按照金属介导、光介导和化学小分子介导的生物正交偶联反应以及生物正交剪切反应, 对近五年来我国学者在该领域的代表性成果进行系统介绍. 最后对生物正交反应的进一步发展与应用加以展望. 我们期待更多高效、兼容的生物正交反应得以发展, 并提出“遥控生物正交化学”的未来发展目标, 期待更多的化学家能够加入生物正交反应的开发拓展与应用探索当中.     

Pd-catalyzed regioselective C-H chlorination of disubstituted 1,2,3-triazoles

This paper mainly studied Pd-catalyzed regioselective chlorination of disubstituted 1,2,3-triazoles directed by the 1,2,3-triazole ring. A series of regioselective chlorinated products were synthesized in 47–86% yields using Pd(OAc)₂ as a catalyst and CuCl₂ as a chlorinated reagent. This method provides a new mean for the synthesis of 1,2,3-triazole halides which combines the formation of C-X bond with C-H activation.     

Supramolecular self-assembly of inclusion complexes of a multiarm hyperbranched polyether with cyclodextrins

A new class of crystalline inclusion complexes of a multiarm hyperbranched polyether combined with various cyclodextrins (CDs) was successfully prepared. Using self-condensing ring-opening polymerization, a kind of multiarm polyether with a hyperbranched poly(3-ethyl-3-oxetanemethanol) core and multiple linear poly(ethylene glycol) (PEG) arms was obtained. It has been found that this kind of hyperbranched polyether can be dissolved in water. Adding alpha-CDs to the multiarm hyperbranched polyether solution, molecular recognition results in the formation of crystalline inclusion complexes based on the noncovalent interactions between the linear PEG arms of the polyether particles and the alpha-CDs. These multiarm polyether inclusion complexes have been well characterized. Interestingly, quite different from inclusion complexes of CDs and linear polymeric guests, the complexes of the multiarm hyperbranched polyether with alpha-CDs show a novel lamellar morphology. The experimental results validate that the resultant lamellar crystals have a juxtaposed structure. In addition, the formation mechanism of these inclusion complexes of a multiarm polyether with alpha-CDs has also been well described. Besides the role of displacement of associated water molecules and the presence of hydrogen bonding between CDs in channel structure CD inclusion complexes, the noncovalent intermolecular forces between CDs and polymers also play an important role in the formation of complex architectures.     

Selecting products through text reviews: An MCDM method incorporating personalized heuristic judgments in the prospect theory

Fuzzy Optimization and Decision Making - Online reviews have become an increasingly popular information source in consumer’s decision making process. To help consumers make informed...