An interior trust region algorithm for solving linearly constrained nonlinear optimization

In this paper, an interior point algorithm based on trust region techniques is proposed for solving nonlinear optimization problems with linear equality constraints and nonnegative variables. Unlike those existing interior-point trust region methods, this proposed method does not require that a general quadratic subproblem with a trust region bound be solved at each iteration. Instead, a system of linear equations is solved to get a search direction, and then a linesearch of Armijo type is performed in this direction to obtain a new iteration point. From a computational point of view, this approach may in general reduce a computational effort, and thus improve the computational efficiency. Under suitable conditions, it is proven that any accumulation of the sequence generated by the algorithm satisfies the first-order optimality condition.     

Ab initio studies on reaction H2C=C(OH)Li+CH3 + (CH3 -)

The possible structures and isomerizations of H₂C=C(OH)Li are studied theoretically by the gradient analytical method at RHF/6-31+G level. According to these results, reactions of H₂C=C(OH)Li with CH₃ ⁺ and CH ₃ ^- are investigated thoroughly. When H₂C=C(OH)Li reacts with CH ₃ ⁺ , H_zC=C(OH)Li firstly changes from structure1 to structure4, and then combines with CH₃ ⁺. In this reaction, the configuration of central carbon is retained. When H₂C=C(OH)Li reacts with CH ₃ ^- , structure1 firstly breaks its C-O bond to give contact ion-pair. Then through transition state16 which is similar to structure2, the attack of CH ₃ ^- from the opposite side of^-OH replaces^-OH group and inverts the configuration of carbenoid carbon atom. All the results show that the ambident reactivity of carbenoid has close relationship with the stability of special structures. Project supported by the National Natural Science Foundation of China (Grant No. 29773025).     

TBP体系活度系数的测定和微扰理论的研究

在前人工作的基础上, 改进了液上空间气相色谱测活度系数的方法, 实验测定了TBP. 稀释剂和水形成的多个二元系、三元系和四元系的活度系数和密度. 选用的稀释剂有n-C_6H_(14)、n-C_7H_(16)、n-C_8H_(18)、C_6H_6、cy-C_6H_(12)、CCl_4和CHCl_3. 在Pierotti理论的基础上, 采用新的硬球作用表达式和径向分布函数, 并计及分子间的排斥能、色散能、取向能和诱导能, 建立了简单的活度系数模型, 并用于TBP和稀释剂体系的计算. 从二元系回归得到的分子参数较好地预测了三元系的活度系数.     

A study of a nonprimitive model for electrolyte solutions based on perturbation theory

The equation for the Helmholtz free energy for systems of small anisotropic molecules and ions is deduced by substituting the complete expression for various potential energies (including repulsive, dispersive, electrostatic, and induced energies) into the perturbation expansion. The equation is applied to pure water. The relative dielectric constant is set at unity. Based on the equal chemical potentials of equilibrated vapor and liquid phases, the molecular parameters of water are regressed from the densities of saturated vapor in the temperature range of 0 to 370°C. The ARD of regression is 1.16%. These parameters are used to predict the heat of vaporization and densities of saturated vapor and liquid phases of water in the same temperature range. The ARDs of prediction are 4.5% and 9.8%, respectively. The equation is used to correlate the osmotic coefficients of twelve 1:1 electrolyte solutions. The relative dielectric constant is set at unity. The parameters (Soft-sphere diameter and dispersive constant) of seven ions (Na⁺, K⁺, Rb⁺, Cs⁺, Cl^–, Br^–, and I^–) are obtained. The total average absolute deviation between calculated and experimental values of the osmotic coefficient is 0.041. The parameters of ions can keep constant in different systems.     

A neurodynamic approach to zero-one quadratic programming

Numerical Algorithms - This paper proposes a neurodynamic approach to zero-one quadratic programming with linear constraints. Compared with one existing neurodynamic approach to such problems, the...     

A hybrid trust region algorithm for unconstrained optimization

This paper presents a hybrid trust region algorithm for unconstrained optimization problems. It can be regarded as a combination of ODE-based methods, line search and trust region techniques. A feature of the proposed method is that at each iteration, a system of linear equations is solved only once to obtain a trial step. Further, when the trial step is not accepted, the method performs an inexact line search along it instead of resolving a new linear system. Under reasonable assumptions, the algorithm is proven to be globally and superlinearly convergent. Numerical results are also reported that show the efficiency of this proposed method.     

Didepside Formation by the Nonreducing Polyketide Synthase Preu6 of Preussia isomera Requires Interaction of Starter Acyl Transferase and Thioesterase Domains

Orsellinic acid (OA) derivatives are produced by filamentous fungi using nonreducing polyketide synthases (nrPKSs). The chain-releasing thioesterase (TE) domains of such nrPKSs were proposed to also catalyze dimerization to yield didepsides, such as lecanoric acid. Here, we use combinatorial domain exchanges, domain dissections and reconstitutions to reveal that the TE domain of the lecanoric acid synthase Preu6 of Preussia isomera must collaborate with the starter acyl transferase (SAT) domain from the same nrPKS. We show that artificial SAT-TE fusion proteins are highly effective catalysts and reprogram the ketide homologation chassis to form didepsides. We also demonstrate that dissected SAT and TE domains of Preu6 physically interact, and SAT and TE domains of OA-synthesizing nrPKSs may co-evolve. Our work highlights an unexpected domain–domain interaction in nrPKSs that must be considered for the combinatorial biosynthesis of unnatural didepsides, depsidones, and diphenyl ethers.     

碱金属烯醇盐的从头算

在RHF／3－21GRHF／321G,RHF／6-31＋G,MP2／6－31＋G,RHF／lanl2dz,MP2／lanl2dz和MP2／6－31＋G水平上,对CH2＝CH（OM）（M＝Li,Na,K,Rb,C。）进行了研究．结果表明,所有化合物都有平面式和非平面桥式两种构型.结构参数、自然轨道布局分析和反应热均反映出碱金属对烯酸负离子的共振有很大程度的限制,不同的碱金属盐差别不十分明显．     

求解带界约束的非线性方程组的混合方法

基于非单调技术和L-M算法, 提出了一种新的求解带界约束的非线性方程组的混合方法. 在一定条件下, 该算法具有全局收敛性. 数值试验表明该算法是有效的.