On duality for square root convex programs

Conjugate function theory is used to develop dual programs for nonseparable convex programs involving the square root function. This function arises naturally in finance when one measures the risk of a portfolio by its variance–covariance matrix, in stochastic programming under chance constraints and in location theory.     

Synthesis of 4,6-dimethyl-tetrahydro- and hexahydro-dibenzothiophene

2-Bromo-3-methylcyclohexanone was synthesized by conjugate addition of trimethylaluminium to 2-bromo-2-cyclohexen-1-one with copper bromide as catalyst, coupled with 2-methylthiophenol and annulated with the aid of polyphosphoric acid to 4,6-dimethyl-1,2,3,4-tetrahydrodibenzothiophene. The latter was hydrogenated to 4,6-dimethyl-1,2,3,4,4a,9b-hexahydrodibenzothiophene, another intermediate in the hydrodesulfurization of 4,6-dimethyldibenzothiophene, by zinc and trifluoroacetic acid, and dehydrogenated to 4,6-dimethyldibenzothiophene.     

A modified PRP conjugate gradient method

This paper gives a modified PRP method which possesses the global convergence of nonconvex function and the R-linear convergence rate of uniformly convex function. Furthermore, the presented method has sufficiently descent property and characteristic of automatically being in a trust region without carrying out any line search technique. Numerical results indicate that the new method is interesting for the given test problems. This work is supported by Guangxi University SF grands X061041 and China NSF grands 10761001.     

AN AFFINE SCALING INTERIOR ALGORITHM VIA CONJUGATE GRADIENT PATH FOR SOLVING BOUND-CONSTRAINED NONLINEAR SYSTEMS

In this paper we propose an affine scaling interior algorithm via conjugate gradient path for solving nonlinear equality systems subject to bounds on variables. By employing the affine scaling conjugate gradient path search strategy, we obtain an iterative direction by solving the linearize model. By using the line search technique, we will find an acceptable trial step length along this direction which is strictly feasible and makes the objective func- tion nonmonotonically decreasing. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Furthermore, the numerical results of the proposed algorithm indicate to be effective.     

Convergence of CG and GMRES on a tridiagonal Toeplitz linear system

The Conjugate Gradient method (CG), the Minimal Residual method (MINRES), or more generally, the Generalized Minimal Residual method (GMRES) are widely used to solve a linear system Ax=b. The choice of a method depends on A’s symmetry property and/or definiteness), and MINRES is really just a special case of GMRES. This paper establishes error bounds on and sometimes exact expressions for residuals of CG, MINRES, and GMRES on solving a tridiagonal Toeplitz linear system, where A is Hermitian or just normal. These expressions and bounds are in terms of the three parameters that define A and Chebyshev polynomials of the first or second kind. AMS subject classification (2000)  65F10, 65N22     

Transferring Boundedness from Conjugate Operators Associated with Jacobi, Laguerre, and Fourier–Bessel Expansions to Conjugate Operators in the Hankel Setting

In this paper we establish transference results showing that the boundedness of the conjugate operator associated with Hankel transforms on Lorentz spaces can be deduced from the corresponding boundedness of the conjugate operators defined on Laguerre, Jacobi, and Fourier–Bessel settings. Our result also allows us to characterize the power weights in order that conjugation associated with Laguerre, Jacobi, and Fourier–Bessel expansions define bounded operators between the corresponding weighted L ^p spaces. This paper is partially supported by MTM2004/05878. Third and fourth authors are also partially supported by grant PI042004/067.     

一种改进的共轭梯度法及全局收敛性

本文在DY共轭梯度法的基础上对解决无约束最优化问题提出一种改进的共轭梯度法.该方法在Wolfe线搜索下能够保证充分下降性,并在目标函数可微的条件下,证明了算法的全局收敛性.大量数值试验表明,该方法是很有效的.     

1,8-Diazabicyclo[5.4.0]undec-7-ene (DBU)-promoted efficient and versatile aza-Michael addition

A convenient and versatile method was developed for aza-Michael addition using a substoichiometric amount of 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU). Various nitrogen nucleophiles were efficiently introduced to α,β-unsaturated carbonyl compounds employing 0.5 equiv of DBU. Furthermore, other heteroatomic nucleophiles could also be introduced successfully under the same reaction conditions.     

EXPANSION OF STEP-TRANSITION OPERATOR OF MULTI-STEP METHOD AND ITS APPLICATIONS (Ⅱ)

We give some formulae for calculation of the expansions for (1) composition of step-transition operators (STO) of any two difference schemes (DS) for ODE's, (2) inverse operator of STO of any DS, and (3) conjugate operator of STO of any DS.     

共轭效应的本质及其在有机反应中的特殊性

共轭效应是有机化学中特别重要的电子效应之一,存在于共轭体系之中;大学有机化学教学目标要求学生掌握并能熟练应用共轭效应理论解决有机化学中的实际问题。由于共轭效应涉及微观认知,学生普遍感觉不易理解。但作为教学重点与难点,又必须掌握;同时也是学生大学毕业后继续深造学习所必须的基础理论知识,理解、掌握并能熟练应用该理论知识解决有机化学中的学习问题显得尤为重要。本文采用密度泛函理论方法计算并给出了3个二烯烃分子轨道中最高占据分子轨道(HOMO)、最低空分子轨道(LUMO)结构图,揭示了共轭体系内部因存在电荷转移现象而产生电子云的平均化本质,表现在键参数中的键长平均化变化。