Selective double Suzuki cross-coupling reactions. Synthesis of unsymmetrical diaryl (or heteroaryl) methanes

Using a double Suzuki cross-coupling reaction ortho- or para-bromobenzyl bromides are easily transformed into unsymmetrical diaryl (or heteroaryl) methanes     

A numerical experimental study of inverse preconditioning for the parallel iterative solution to 3D finite element flow equations

Integration of the subsurface flow equation by finite elements (FE) in space and finite differences (FD) in time requires the repeated solution to sparse symmetric positive definite systems of linear equations. Iterative techniques based on preconditioned conjugate gradients (PCG) are one of the most attractive tool to solve the problem on sequential computers. A present challenge is to make PCG attractive in a parallel computing environment as well. To this aim a key factor is the development of an efficient parallel preconditioner. FSAI (factorized sparse approximate inverse) and enlarged FSAI relying on the approximate inverse of the coefficient matrix appears to be a most promising parallel preconditioner. In the present paper PCG using FSAI, diagonal and pARMS (parallel algebraic recursive multilevel solvers) preconditioners is implemented on the IBM SP4/512 and CLX/768 supercomputers with up to 32 processors to solve underground flow problems of a large size. The results show that FSAI may allow for a parallel relative efficiency larger than 50% on the largest problems with p=32 processors. Moreover, FSAI turns out to be significantly less expensive and more robust than pARMS. Finally, it is shown that for p in the upper range may be much improved if PCG–FSAI is implemented on CLX.     

AN ITERATIVE EQUATION ON THE UNIT CIRCLE

A functional equation of nonlinear iterates is discussed on the circle S1 for its continuous solutions and differentiable solutions. By lifting to R, the existence, uniqueness and stability of those solutions are obtained. Techniques of continuation are used to guarantee the preservation of continuity and differentiability in lifting.     

Decentralized iterative learning control for a class of large scale interconnected dynamical systems

The problem of decentralized iterative learning control for a class of large scale interconnected dynamical systems is considered. In this paper, it is assumed that the considered large scale dynamical systems are linear time-varying, and the interconnections between each subsystem are unknown. For such a class of uncertain large scale interconnected dynamical systems, a method is presented whereby a class of decentralized local iterative learning control schemes is constructed. It is also shown that under some given conditions, the constructed decentralized local iterative learning controllers can guarantee the asymptotic convergence of the local output error between the given desired local output and the actual local output of each subsystem through the iterative learning process. Finally, as a numerical example, the system coupled by two inverted pendulums is given to illustrate the application of the proposed decentralized iterative learning control schemes.     

Modified Householder iterative method free from second derivatives for nonlinear equations

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative method free from second derivatives for solving nonlinear equations of the type f(x)=0. This new method includes the two-step Newton method as a special case. We prove that the new iterative method is of fourth-order. Several examples are given to illustrate the efficiency of this new method and its comparison with other iterative methods. This method can be considered as a significant improvement of the Newton method and its variant forms.     

A parallel version of the preconditioned conjugate gradient method for boundary element equations

The parallel version of precondition techniques is developed for matrices arising from the Galerkin boundary element method for two-dimensional domains with Dirichlet boundary conditions. Results were obtained for implementations on a transputer network as well as on an nCUBE-2 parallel computer showing that iterative solution methods are very well suited for a MIMD computer. A comparison of numerical results for iterative and direct solution methods is presented and underlines the superiority of iterative methods for large systems.     

关于离散HJB方程的下解与上解

本文讨论HJB方程上、下解的几个性质,并讨论了从上解出发的一个迭代法的收敛性.     

Microwave-promoted Suzuki-Miyaura coupling reactions in a cycloalkane-based thermomorphic biphasic system

Microwave-promoted Suzuki-Miyaura coupling reaction of aryl halides attached to a cycloalkane-soluble platform was accomplished in a cycloalkane-based thermomorphic biphasic system. Following irradiation and subsequent cooling, the monophasic reaction mixture immediately formed a biphasic solution to allow facile workup and separation of the product.     

HUA’S THEOREM WITH FIVE ALMOSTE QUAL PRIME VARIABLES

§1. IntroductionIn the additive theory of prime numbers, one studies the representation of positive in-tegers by powers of primes. For the quadratic case, Hua [1] proved that each large integercongruent to 5 modulo 24 can be written as the sum of ?ve squ…