An improved approximate Newton method for implicit Runge-Kutta formulas

Implicit Runge-Kutta (IRK) methods (such as the s-stage Radau IIA method with s=3,5, or 7) for solving stiff ordinary differential equation systems have excellent stability properties and high solution accuracy orders, but their high computing costs in solving their nonlinear stage equations have seriously limited their applications to large scale problems. To reduce such a cost, several approximate Newton algorithms were developed, including a commonly used one called the simplified Newton method. In this paper, a new approximate Jacobian matrix and two new test rules for controlling the updating of approximate Jacobian matrices are proposed, yielding an improved approximate Newton method. Theoretical and numerical analysis show that the improved approximate Newton method can significantly improve the convergence and performance of the simplified Newton method.     

A facile and efficient synthesis of polyfunctionalized pyridin-2(1H)-ones from beta-oxo amides under Vilsmeier conditions

A facile and efficient one-pot synthesis of polysubstituted pyridin-2(1H)-ones from a variety of beta-oxo amides under Vilsmeier conditions is described, and a mechanism involving sequential halogenation, formylation and intramolecular nucleophilic cyclization is proposed.     

An improved algorithm and its parallel implementation for solving a general blood-tissue transport and metabolism model

Fast algorithms for simulating mathematical models of coupled blood-tissue transport and metabolism are critical for the analysis of data on transport and reaction in tissues. Here, by combining the method of characteristics with the standard grid discretization technique, a novel algorithm is introduced for solving a general blood-tissue transport and metabolism model governed by a large system of one-dimensional semilinear first order partial differential equations. The key part of the algorithm is to approximate the model as a group of independent ordinary differential equation (ODE) systems such that each ODE system has the same size as the model and can be integrated independently. Thus the method can be easily implemented in parallel on a large-scale multiprocessor computer. The accuracy of the algorithm is demonstrated for solving a simple blood-tissue exchange model introduced by Sangren and Sheppard [W.C. Sangren, C.W. Sheppard, A mathematical derivation of the exchange of a labeled substance between a liquid flowing in a vessel and an external compartment, Bull. Math. Biophys. 15 (1953) 387–394], which has an analytical solution. Numerical experiments made on a distributed-memory parallel computer (an HP Linux cluster) and a shared-memory parallel computer (a SGI Origin 2000) demonstrate the parallel efficiency of the algorithm.     

Efficient and divergent synthesis of fully substituted 1H-pyrazoles and isoxazoles from cyclopropyl oximes

Efficient and divergent one-pot synthesis of fully substituted 1H-pyrazoles and isoxazoles from cyclopropyl oximes based on reaction conditions selection is reported. Under Vilsmeier conditions (POCl3/DMF), substituted 1 H-pyrazoles were synthesized from 1-carbamoyl, 1-oximyl cyclopropanes via sequential ring-opening, chlorovinylation, and intramolecular aza-cyclization. In the presence of POCl3/CH2Cl2, substituted isoxazoles were obtained from the cyclopropyl oximes via ring-opening and intramolecular nucleophilic vinylic substitution (SNV) reactions.     

Vilsmeier-Haack reactions of 2-arylamino-3-acetyl-5,6-dihydro-4H-pyrans toward the synthesis of highly substituted pyridin-2(1H)-ones

A facile and efficient one-pot synthesis of highly substituted pyridin-2(1H)-ones was developed via Vilsmeier-Haack reactions of readily available enaminones, 2-arylamino-3-acetyl-5,6-dihydro-4H-pyrans, and a mechanism involving sequential ring-opening, haloformylation, and intramolecular nucleophilic cyclization reactions is proposed.     

Facile and efficient synthesis of quinolin-2(1H)-ones via cyclization of penta-2,4-dienamides mediated by H2SO4

A facile and efficient synthesis of substituted quinolin-2(1H)-ones is developed via intramolecular cyclization of penta-2,4-dienamides mediated by concentrated H(2)SO(4) (98%), and a mechanism involving the formation of a dicationic superelectrophile, and subsequent intramolecular nucleophilic cyclization reactions is proposed.     

原子吸收法测定人精子中锌和铜含量的研究

本文采用石墨炉原子吸收法，以ＮＨ４ＮＯ３和Ｍｇ（ＮＯ３）２混合剂作基体改进剂，测定了人精子中微量元素铜和锌。基方法的特征质量分别为１０．００ｐｇＣｕ／０．００４４Ａ．Ｓ．，９．８０ＰｇＺ／０．００４Ａ．Ｓ；平均加收率为９７．４２％，锌为１０１．９１％，铜和锌的精密度分别是４．１％和４．０３％。     

趋旋性微生物在幂律流体饱和水平多孔层中的热-生物对流稳定性分析

基于趋旋性微生物和幂律流体模型,研究了在含有非Newton流体饱和多孔介质中生物对流的线性稳定性问题.利用Galerkin数值方法求解了该系统的控制方程,得到生物Rayleigh数的数值解,讨论了非Newton流体的幂律指数对生物对流稳定性在假塑性流体和膨胀性流体间的变化规律.研究结果表明,随着幂律流体的速度增大,幂律指数对生物对流稳定性的影响会发生变化,并且这种变化会受到热Rayleigh数和生物Lewis数的影响.另外,微生物趋旋性特征越明显,生物对流系统就越不稳定,而适当增大非Newton流体的幂律指数则有利于系统的稳定性.     

Convergence analysis of truncated incomplete Hessian Newton minimization method and application in biomolecular potential energy minimization

This paper gives a general convergence analysis to the truncated incomplete Hessian Newton method (T-IHN). It shows that T-IHN is globally convergent even with an indefinite incomplete Hessian matrix or an indefinite preconditioner, which may happen in practice. It also proves that when the T-IHN iterates are close enough to a minimum point, T-IHN has a Q-linear rate of convergence, and an admissible line search steplength of one. Moreover, a particular T-IHN algorithm is constructed for minimizing a biomolecular potential energy function, and numerically tested for a protein model problem based on a widely used molecular simulation package, CHARMM. Numerical results confirm the theoretical results, and demonstrate that T-IHN can have a better performance (in terms of computer CPU time) than most CHARMM minimizers.     

An incomplete Hessian Newton minimization method and its application in a chemical database problem

To efficiently solve a large scale unconstrained minimization problem with a dense Hessian matrix, this paper proposes to use an incomplete Hessian matrix to define a new modified Newton method, called the incomplete Hessian Newton method (IHN). A theoretical analysis shows that IHN is convergent globally, and has a linear rate of convergence with a properly selected symmetric, positive definite incomplete Hessian matrix. It also shows that the Wolfe conditions hold in IHN with a line search step length of one. As an important application, an effective IHN and a modified IHN, called the truncated-IHN method (T-IHN), are constructed for solving a large scale chemical database optimal projection mapping problem. T-IHN is shown to work well even with indefinite incomplete Hessian matrices. Numerical results confirm the theoretical results of IHN, and demonstrate the promising potential of T-IHN as an efficient minimization algorithm.