The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming

We analyze the rate of local convergence of the augmented Lagrangian method in nonlinear semidefinite optimization. The presence of the positive semidefinite cone constraint requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and variational analysis on the projection operator in the symmetric matrix space. Without requiring strict complementarity, we prove that, under the constraint nondegeneracy condition and the strong second order sufficient condition, the rate of convergence is linear and the ratio constant is proportional to 1/c, where c is the penalty parameter that exceeds a threshold . The research of Defeng Sun is partly supported by the Academic Research Fund from the National University of Singapore. The research of Jie Sun and Liwei Zhang is partly supported by Singapore–MIT Alliance and by Grants RP314000-042/057-112 of the National University of Singapore. The research of Liwei Zhang is also supported by the National Natural Science Foundation of China under project grant no. 10471015 and by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, China.     

Cyclodextrin-supported Co(OH)2 Clusters as Electrocatalysts for Efficient and Selective H2O2 Synthesis

Co-based material catalysts have shown attractive application prospects in the 2 e⁻ oxygen reduction reaction (ORR). However, for the industrial synthesis of H₂O₂, there is still lack of Co-based catalysts with high production yield rate. Here, novel cyclodextrin-supported Co(OH)₂ cluster catalysts were prepared via a mild and facile method. The catalyst exhibited remarkable H₂O₂ selectivity (94.2 % ~ 98.2 %), good stability (99 % activity retention after 35 h), and ultra-high H₂O₂ production yield rate (5.58 mol g_catalyst⁻¹ h⁻¹ in the H-type electrolytic cell), demonstrating its promising industrial application potential. Density functional theory (DFT) reveals that the cyclodextrin-mediated Co(OH)₂ electronic structure optimizes the adsorption of OOH* intermediates and significantly enhances the activation energy barrier for dissociation, leading to the high reactivity and selectivity for the 2 e⁻ ORR. This work offers a valuable and practical strategy to design Co-based electrocatalysts for H₂O₂ production.     

A note on the convergence of ADMM for linearly constrained convex optimization problems

This note serves two purposes. Firstly, we construct a counterexample to show that the statement on the convergence of the alternating direction method of multipliers (ADMM) for solving linearly constrained convex optimization problems in a highly influential paper by Boyd et al. (Found Trends Mach Learn 3(1):1–122, 2011) can be false if no prior condition on the existence of solutions to all the subproblems involved is assumed to hold. Secondly, we present fairly mild conditions to guarantee the existence of solutions to all the subproblems of the ADMM and provide a rigorous convergence analysis on the ADMM with a computationally more attractive large step-length that can even exceed the practically much preferred golden ratio of \((1+\sqrt{5})/2\).     

硫氰酸铋(Ⅲ)配合物UV光区摩尔吸光系数的研究

本研究了吐温－８０水溶液中硫氰酸铋配合物的吸收光谱,最大吸收波长λｍａｘ＝３３５ｎｍ,其摩尔吸光系数ε３３５＝２．６１×１０＾４,与ＰＡＲ、偶氮胂（Ⅲ）与铋（Ⅲ）的配合物的ε６１０＝２．７０×１０＾４相近,性 种新的三元配合物,并用解释在吐温－８０水溶液中硫氰酸铋为一种灵敏的显色反应。     

铟与4,5—二羟基—1,3—苯二磺酸配合显色反应热力学摩尔吸？…

用分光光度法测定了在２０．０±０．１℃温度下,以ＮａＣｌＯ４为支持电解质的水溶液中,Ｔｉｒｏｎ与高价铟离子形成配合物１：１显色反应的热力学摩尔吸收光系数,考察了ａ值对摩尔吸光系数与溶液离子强度效应的纯性关系的影响,测得ａ＝６．５时的势和学摩尔吸光系数,其ｌｏｇε°＝３．６９。     

N-杂环卡宾及其金属络合物的合成*

由于其强给电子能力、结构易修饰性和拓扑学特性,N-杂环卡宾成为继有机膦配体之后又一类重要的配体。其金属络合物在均相及不对称催化领域的催化性能是近期研究的热点,已有许多成功的结果。本文综述了近年来N-杂环卡宾及其金属络合物以及N-杂环卡宾的重要前体咪唑盐的合成方法。金属-N-杂环卡宾络合物的合成方法包括：(a)游离卡宾与金属化合物直接络合;(b)咪唑盐与金属化合物在强碱作用下络合;(c)利用Ag-NHC通过卡宾配体转移方法制备新的金属络合物。关于N-杂环卡宾前体的合成途径主要有：(a)乙二醛、伯胺和多聚甲醛的缩合反应;(b)卤代烷与咪唑及其取代咪唑的烷基化反应;(c)原甲酸酯与1,2-二胺的成环反应;(d)肼或酰胺与酸酐的环化反应;(e)用Na/K对环硫脲化合物的还原反应。     

电热法引爆淀粉

按中师化学第一册(82年版,人教社出版)97页的装置做淀粉(面粉)的爆炸实验,由于蜡烛不好固定、放热少等因素的影响,实验往往失败。笔者通过多次的实验证明,采用电热法引爆淀粉的实验是比较理想的。     

NO2在矿物颗粒物表面的非均相反应

NO2在矿物颗粒物表面的非均相反应会改变矿物颗粒物的化学组成、粒径、形貌、吸湿性,进而影响矿物颗粒物的散射、反射、吸收等光学性质和成云能力,改变其直接和间接辐射强迫,最终对大气氧化性和气候变化产生重要的影响.本文综述了NO:在矿物颗粒物表面的非均相反应的研究体系和研究方法,阐述N02在氧化物颗粒物表面反应产物、反应机理的实验和推测结果,总结了测定的摄取系数,提出了NO2在矿物颗粒物表面非均相反应待深入研究的科学问题.     

Allylation and alkylation of oxindoleketimines via imine umpolung strategy

When treated with an alkoxide base like t-BuOK in aprotic solvent, N-diphenylmethyl imino oxindoles, made conveniently through condensation of corresponding isatins with N-diphenylmethyl amine, are deprotonated to form azaallyl anions. Allylation and alkylation of this type of intermediates proceed smoothly with diverse C-electrophiles. Acidic work up finishes 3-amino-3-allyl/alkyl oxindoles. The overall transformation equals to an umpolung process at the C3 of isatins.     

Effects of processing additives in non-fullerene organic bulk heterojunction solar cells with efficiency >11%

The solar cell surface morphologies with different additives observed with slightly changed in roughness. It is easily to get the best PCE of 11.1% with using 0.5% DIO additives.