Convergence of an augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints

An augmented Lagrange algorithm for nonlinear optimizations with second-order cone constraints is proposed based on a Löwner operator associated with a potential function for the optimization problems with inequality constraints. The favorable properties of both the Löwner operator and the corresponding augmented Lagrangian are discussed. And under some mild assumptions, the rate of convergence of the augmented Lagrange algorithm is studied in detail.     

Modifications of 5,12-dihydroindolo[3,2-a]carbazole scaffold via its regioselective C2,9-formylation and C2,9-acetylation

The effective approaches for regioselective double formylation and acetylation of 5,12-dialkyl-6,7-diaryl-substituted 5,12-dihydroindolo[3,2-a]carbazoles by their treatment with dichloromethyl methyl ether in the presence of SnCl₄ or with acetyl chloride in the presence of AlCl₃ to afford the 2,9-diformyl or 2,9-diacetyl derivatives, respectively, were developed. Furthermore, new 2,9-bis(2,2-dicyanovinyl) derivatives were synthesized by the Knoevenagel condensation of diformyl-containing substrates with malononitrile, when new 2,9-bis(quinoxaline-2-yl)- and 2,9-bis(benzo[g]quinoxaline-2-yl) derivatives were formed via microwave-promoted oxidation of diacetyl-containing substrates with SeO₂ to the corresponding diglyoxals, followed by the reaction of these intermediates with o-phenylendiamine or 2,3-diaminonaphthalene, respectively. The basic optical and electrochemical properties of some 5,12-dihydroindolo[3,2-a]carbazoles were investigated.     

Schnelltests zur leistungsfähigkeit von bestimmungsverfahren

Linear analytical functions covering at least a working range of one power of ten are the basis for useful determination procedures. The efficiency of the procedure is given by characteristic data such as constant magnitude of the analytical function, the standard deviation of the procedure and the determination limit. These can be evaluated by systematic standardization, Three simple tests are described to check the possibility of standardization, and a method is given for estimating values of the characteristic data, which requires only 2 sets of 4 experiments each. Thus preliminary work in the development of reliable procedures can be carried out purposefully, with only a few experiments.     

Pre-B?tzinger复合体的从簇到峰放电的同步转迁及分岔机制

Pre-Bötzinger复合体是兴奋性耦合的神经元网络,通过产生复杂的放电节律和节律模式的同步转迁参与调控呼吸节律.本文选用复杂簇和峰放电节律的单神经元数学模型构建复合体模型,仿真了与生物学实验相关的多类同步节律模式及其复杂转迁历程,并利用快慢变量分离揭示了相应的分岔机制.当初值相同时,随着兴奋性耦合强度的增加,复合体模型依次表现出完全同步的“fold/homoclinic”,“subHopf/subHopf”簇放电和周期1峰放电.当初值不同时,随耦合强度增加,表现为由“fold/homoclinic”,到“fold/fold limit cycle”、到“subHopf/subHopf”与“fold/fold limit cycle”的混合簇放电、再到“subHopf/subHopf”簇放电的相位同步转迁,最后到反相同步周期1峰放电.完全(同相)同步和反相同步的周期1节律表现出了不同分岔机制.反相峰同步行为给出了与强兴奋性耦合容易诱发同相同步这一传统观念不同的新示例.研究结果给出了preBötzinger复合体的从簇到峰放电节律的同步转迁规律及复杂分岔机制,反常同步行为丰富了非线性动力学的内涵.     

聚乙烯醇包埋龟裂链霉菌对水中Pb~(2 )吸附性能的研究

本文研究了聚乙烯醇包埋龟裂链霉菌菌丝体的包埋条件及包埋后对水中Pb2 的吸附作用。结果表明,包埋比例为3/1（W/W）,聚乙烯醇浓度为10%,海藻酸钠浓度0.2%,在含2?Cl2饱和硼酸溶液中固化24h是包埋反应的最佳条件。包埋后的饱和吸附量可达73.0mg/g,比未包埋龟裂链霉菌下降 47.1% 。pH值对吸附量的影响较包埋前下降。升高温度有利于吸附。     

Theoretical investigation on optical properties of Möbius carbon nanobelts in one- and two-photon absorption

The first successful synthesis of fully fused and fully conjugated Möbius carbon nanobelts (CNBs) has attracted considerable attention. However, theoretical calculations based on such π-conjugated Möbius CNB are still insufficient. Herein, we theoretically investigated molecular spectroscopy of Möbius CNBs without and with n-butoxy groups via visualization methods. The results show that the presence of n-butoxy groups can significantly affect Möbius CNBs’ optical performance, changing electron-hole coherence and enhancing two-photon absorption cross-sections. Our work provides a deeper understanding of photophysical mechanisms of Möbius CNBs in one- and two-photon absorption and reveals possible applications on optoelectronic devices.