The contribution of K.-H. Elster to generalized conjugation theory and nonconvex duality

This article surveys the main contributions of K.-H. Elster to the theory of generalized conjugate functions and its applications to duality in nonconvex optimization.     

Homoclinic orbits for first order Hamiltonian systems with some twist conditions

In this paper, we study the nonperiodic first-order Hamiltonian system ù = J L(t)u +J H(t, u), where H ∈ C1(R × R2n). With some assumptions on L, the corresponding Hamiltonian operator has only discrete spectrum. By using the index theory for self-adjoint operator equation,we establish the existence of multiple homoclinic orbits for the asymptotically quadratic nonlinearty satisfying some twist conditions between infinity and origin.     

Weak Euler Approximation for Itô Diffusion and Jump Processes

This article studies the rate of convergence of the weak Euler approximation for Itô diffusion and jump processes with Hölder-continuous generators. It covers a number of stochastic processes including the nondegenerate diffusion processes and a class of stochastic differential equations driven by stable processes. To estimate the rate of convergence, the existence of a unique solution to the corresponding backward Kolmogorov equation in Hölder space is first proved. It then shows that the Euler scheme yields positive weak order of convergence.     

Metal‐Free Aminosulfonylation of Aryldiazonium Tetrafluoroborates with DABCO⋅(SO2)2 and Hydrazines

The coupling of aryldiazonium tetrafluoroborates, DABCO?(SO₂)₂, and hydrazines under metal‐free conditions leads to the formation of aryl N‐aminosulfonamides. The reaction proceeds smoothly at room temperature and shows broad functional‐group tolerance. A radical process is proposed for this transformation.     

One-pot synthesis of various xanthene derivatives using ionic liquid 1, 3-disulfonic acid imidazolium hydrogen sulfate as an efficient and reusable catalyst under solvent-free conditions

In this study, 1,3-disulfonic acid imidazolium hydrogen sulfate （DSIMHS） is used as an efficient and reusable ionic liquid for the green, mild, and efficient synthesis of xanthenes under solvent-free conditions. Simple and easy work-up, low cost, green process, short reaction times and excellent yields of the products are the advantages of this procedure. Further, the catalyst can be recycled and reused at least for four times without a noticeably decrease in its catalytic activity.     

Photo-induced Synthesis and Characterization of Poly（methyl methacrylate） Grafted Sodium Salt of Partially Carboxymethylated Guar Gum

Photo-induced graft copolymerization of methyl methacrylate（MMA） onto sodium salt of partially carboxymethylated guar gum（Na-PCMGG, DS = 0.291） was carried out in an aqueous medium using ceric ammonium nitrate（CAN） as photoinitiator to synthesize a novel graft copolymer, Na-PCMGG-g-PMMA, which may find its potential application as a metal adsorbent. The influences of synthesis variables such as concentrations of photoinitiator（CAN）, nitric acid and monomer（MMA） as well as reaction time, temperature and amount of substrate on the grafting yields were studied and the reaction conditions for optimum photo-grafting were evaluated. At optimum concentration, the maximum values of the grafting yields achieved were G = 271.61% and GE = 63.89%. The experimental results were found to be in very good agreement with the proposed kinetic scheme. The photo-graft copolymerization of MMA onto Na-PCMGG（ DS = 0.291） was also carried out in the presence and absence of ultraviolet radiation for studying the efficiency of the photoinitiator. The influence of carboxymethyl groups introduced onto the guar gum molecules with regard to its behavior towards ultra-violet radiation induced grafting with MMA was also investigated. Photo-grafting process was confirmed and the products were characterized with the help of the spectroscopic（1H-NMR and FTIR） and SEM techniques.     

(英)硫酸氢钾高效催化一锅法合成5-未取代的3,4-二氢嘧啶-2(1H)-酮

无溶剂条件下,硫酸氢钾可有效催化芳香醛、苯乙酮衍生物和脲的三组分"一锅法"Biginelli反应来合成5-未取代的3,4-二氢嘧啶-2(1H)-酮。确定了优化反应条件。产品结构经IR、1H NMR、MS和元素分析进行表征。     

任意边界条件下双模量矩形薄板的弯曲

将双模量板等效为两个各向同性小矩形板组成的层合板,假定该层合板的中性面即为两个小矩形板的交界面。根据中性面上应力为零且薄板全厚度上应力的代数和为零,推导了双模量矩形薄板的中性面位置。本文采用严宗达提出的带补充项的双重正弦傅里叶级数通解,该通解可以适用于任意边界条件的矩形薄板且不需要叠加或者重新构造。联立边界条件和控制方程,求得通解中的待定系数并代入到通解中,即可得到任意边界条件下双模量矩形薄板的弯曲解析解。与有限元结果比较,本文结果符合工程精度要求。     

基于拟相对内部集值优化问题弱有效元的最优性条件

本文研究了基于拟相对内部的非凸集值优化问题弱有效元的最优性条件.首先,讨论了弱有效元与线性子空间之间的关系,利用涉及拟相对内部的凸集分离定理,获得了弱有效元的最优性条件.其次,给出了基于拟相对内部弱有效元的Lagrange乘子定理.     

Vorticity-streamfunction formulation of unsteady incompressible flow past a cylinder: Sensitivity of the computed flow field to the location of the outflow boundary

The influence of the location of the outflow computational boundary on the unsteady incompressible flow past a circular cylinder at Reynolds number 100 is examined. The vorticity-streamfunction formulation of the Navier-Stokes equations is used in all computations. Two types of outflow boundary conditions are subjected to a series of tests in which the domain length is gradually reduced. The traction-free condition performs well in most cases and allows the outflow boundary to be located as close as 6.5 cylinder diameters from the body. The other boundary condition type is not as forgiving, but has the advantage of being simpler to implement and can still provide reasonably accurate solutions. It is also observed that both condition types can influence the flow field strongly and globally when the boundary is brought closer than 2.5 diameters from the body. In such cases the temporal periodicity of the solution is lost.