Maximizing a Linear Fractional Function on a Pareto Efficient Frontier

We consider the problem of maximizing a linear fractional function on the Pareto efficient frontier of two other linear fractional functions. We present a finite pivoting-type algorithm that solves the maximization problem while computing simultaneously the efficient frontier. Application to multistage efficiency analysis is discussed. An example demonstrating the computational procedure is included.     

Portfolio optimization in stochastic markets

We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.     

新型含氧亚甲基和亚胺桥键液晶化合物分子结构与光谱的密度泛函理论研究

采用密度泛函理论方法在B3LYP/6-31G*水平上对6个新型含氧亚甲基和亚胺桥键液晶化合物分子的几何结构进行优化计算,讨论了取代基H,CH3,CH3O,C2H5O,NO2,Cl对分子电荷、前线轨道能量和电子吸收光谱等性质的影响.在此基础上使用含时密度泛函理论方法计算了分子第一激发态的电子垂直跃迁能,得到最大吸收波长λmax.计算表明,取代基的引入导致最大吸收波长红移.     

Contractibility of Efficient Frontier of Simply Shaded Sets

In finite dimensional Euclidean space, we prove the contractibility of the efficient frontier of simply shaded sets. This work extends the result of Peleg [7], which confirms the contractibility of the efficient frontier in the convex case.     

Transformations of 3,4-bisindolylmaleimides with differently bonded indole and maleimide moieties under the action of protic acids: A quantum chemical study

Intramolecular cyclization reactions of 3,4-bis(indol-3-yl)maleimides 1, 3-(indol-1-yl)-4-(indol-3-yl)maleimides 2, and 3,4-bis(indol-1-yl)maleimides 3 under the action of protic acids were studied in order to estimate the parameters of the interaction between protonated and unprotonated indole moieties. Geometric parameters, charge distributions, energy characteristics, and information concerning the frontier orbitals of bisindolylmaleimides 1–3 were obtained from density functional B3LYP/6-31G(d) quantum chemical calculations. Alternative pathways of protonation of bisindolylmaleimides with differently bonded indole and maleimide moieties were studied and pathways of cyclization of corresponding conjugated acids leading to polyannelated compounds were analyzed. All the key intermediates of the cyclization reactions correspond to stationary points on the potential energy surfaces (minima and transition states). Analysis of the potential energy surfaces revealed almost linear dependences of the activation energies of the cyclization reactions under study on the distances between the reaction centers, on the angle of approach of intramolecular electrophile, and on the energy gap (energy difference between frontier orbitals). The key role in the cyclization reactions is played by structural similarity between the starting indoleninium cations and the activated complexes of the reactions under study. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 754–760, May, 2006.     

双核金属酞菁类化合物催化脱硫机理研究Ⅳ──中心金属离子对MPc－PcM催化活性的影响

实验研究结果表明双核金属酞菁类化合物ＭＰｃ－ＰｃＭ（Ｍ＝Ｖ、Ｃｒ、Ｍｎ、Ｆｅ、Ｃｏ、Ｎｉ、Ｃｕ）是催化Ｈ＿２Ｓ液相氧化反应的良好催化剂，且其催化活性顺序为Ｃｏ＞Ｎｉ＞Ｖ＞Ｆｅ＞Ｃｕ＞Ｃｒ＞Ｍｎ．采用量子化学理论计算方法（ＩＮＤＯ／Ｓ）分析了其前线分子轨道的构成特征，结果表明这几种ＭＰｃ－ＰｃＭ的ＬＵＭＯ轨道皆为有金属离子参与形成的π轨道，但ＨＯＭＯ轨道间的差异却很大．Ｍ＝Ｃｏ、Ｎｉ、Ｃｕ、Ｃｒ时，其ＨＯＭＯ为π轨道；而Ｍ＝Ｆｅ、Ｍｎ时，其ＨＯＭＯ却为σ轨道．正是在前线分子轨道的轨道类型、共轭程度及金属轨道贡献三方面因素的协同作用下，才导致ＭＰｃ－ＰｃＭ的催化活性顺序并非按中心金属离子价电子层ｄ电子数的递变而呈现出规律性的变化．     

Instructions for Authors

Chinese Physics B （Chin. Phys. B）, formerly titled Chinese Physics, is an international comprehensive academic journal, aiming to publish original papers and rapid communications reflecting creative and innovative achievements in physics, as well as review papers about important accomplishments in frontier of physics. The journal is published monthly in English by the Chinese Physical Society （CPS） and the IOP Publishing. Chin. Phys. B has already been included in six world famous international index systems including SCI and INSPEC.     

Instructions for Authors

<正>Chinese Physics B(Chin.Phys.B),formerly titled Chinese Physics,is an international comprehensive academic journal,aiming to publish original papers and rapid communications reflecting creative and innovative achievements in physics,as well as review papers about important accomplishments in frontier of physics.The journal is published monthly in English by the Chinese Physical Society(CPS)and the IOP Publishing.Chin.     

Instructions for Authors

Chinese Physics B(Chin.Plivs.B).formerly titled Chinese Physics,is an international compreliensive academic journal,aiming to publish original papers and rapid communications reflecting creative and innovative achievements in physics,as well review papers about important accomplishments in frontier of physics.The journal is published monthly in English by the Chinese Physical Society(CPS)and the IOP Publishing.Chin.