Synthesis of masked haloareneboronic acids via iridium-catalyzed aromatic C-H borylation with 1,8-naphthalenediaminatoborane (danBH)

“Masked” areneboronic acids have been prepared by Ir-catalyzed C-H borylation of arenes. A [Ir(OMe)(cod)]₂ complex with a DPPE ligand showed the highest catalytic activity in the C-H borylation of benzene at 80 °C. The reaction system can be applied to substituted arenes, including halogen-substituted arenes. 1,3-Dihalobenzenes undergo the C-H borylation at their 5-positions in a regioselective fashion, affording 3,5-dihaloareneboronic acid derivatives, which serve as useful coupling modules for the convergent dendrimer synthesis.     

An effective solution for a real cutting stock problem in manufacturing plastic rolls

We confront a practical cutting stock problem from a production plant of plastic rolls. The problem is a variant of the well-known one dimensional cutting stock, with particular constraints and optimization criteria defined by the experts of the company. We start by giving a problem formulation in which optimization criteria have been considered in linear hierarchy according to expert preferences, and then propose a heuristic solution based on a GRASP algorithm. The generation phase of this algorithm solves a simplified version which is rather similar to the conventional one dimensional cutting stock. To do that, we propose a Sequential Heuristic Randomized Procedure (SHRP). Then in the repairing phase, the solution of the simplified problem is transformed into a solution to the real problem. For experimental study we have chosen a set of problem instances of com-mon use to compare SHRP with another recent approach. Also, we show by means of examples, how our approach works over instances taken from the real production process. All authors are supported by MEC-FEDER Grant TIN2007-67466-C02-01 and by contract CN-05-127 of the University of Oviedo and the company ERVISA, and by FICYT under grant BP04-021.     

An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings

In this paper, we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a strict pseudo-contraction mapping in the setting of real Hilbert spaces. We establish some weak and strong convergence theorems of the sequences generated by our proposed scheme. Our results combine the ideas of Marino and Xu’s result [G. Marino, H.K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl. 329 (2007) 336–346], and Takahashi and Takahashi’s result [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–515]. In particular, necessary and sufficient conditions for strong convergence of our iterative scheme are obtained.     

General local convergence theory for a class of iterative processes and its applications to Newton’s method

General local convergence theorems with order of convergence r≥1$r\ge 1$ are provided for iterative processes of the type _xn+1=T_xn$x_{n+1}=T{x}_n$, where T:D⊂X→X$T:D\subset X\to X$ is an iteration function in a metric space X$X$. The new local convergence theory is applied to Newton iteration for simple zeros of nonlinear operators in Banach spaces as well as to Schröder iteration for multiple zeros of polynomials and analytic functions. The theory is also applied to establish a general theorem for the uniqueness ball of nonlinear equations in Banach spaces. The new results extend and improve some results of [K. Do?ev, Über Newtonsche Iterationen, C. R. Acad. Bulg. Sci. 36 (1962) 695–701; J.F. Traub, H. Wo?niakowski, Convergence and complexity of Newton iteration for operator equations, J. Assoc. Comput. Mach. 26 (1979) 250–258; S. Smale, Newton’s method estimates from data at one point, in: R.E. Ewing, K.E. Gross, C.F. Martin (Eds.), The Merging of Disciplines: New Direction in Pure, Applied, and Computational Mathematics, Springer, New York, 1986, pp. 185–196; P. Tilli, Convergence conditions of some methods for the simultaneous computation of polynomial zeros, Calcolo 35 (1998) 3–15; X.H. Wang, Convergence of Newton’s method and uniqueness of the solution of equations in Banach space, IMA J. Numer. Anal. 20 (2000) 123–134; I.K. Argyros, J.M. Gutiérrez, A unified approach for enlarging the radius of convergence for Newton’s method and applications, Nonlinear Funct. Anal. Appl. 10 (2005) 555–563; M. Giusti, G. Lecerf, B. Salvy, J.-C. Yakoubsohn, Location and approximation of clusters of zeros of analytic functions, Found. Comput. Math. 5 (3) (2005) 257–311], and others.     

Auxiliary Principle and Iterative Algorithms for Lions-Stampacchia Variational Inequalities

In this paper, we extend the auxiliary principle (Cohen in J. Optim. Theory Appl. 49:325–333, 1988) to study a class of Lions-Stampacchia variational inequalities in Hilbert spaces. Our method consists in approximating, in the subproblems, the nonsmooth convex function by a sequence of piecewise linear and convex functions, as in the bundle method for nonsmooth optimization. This makes the subproblems more tractable. We show the existence of a solution for this Lions-Stampacchia variational inequality and explain how to build a new iterative scheme and a new stopping criterion. This iterative scheme and criterion are different from those commonly used in the special case of nonsmooth optimization. We study also the convergence of iterative sequences generated by the algorithm. This work was supported by the National Natural Science Foundation of China (10671135), the Specialized Research Fund for the Doctoral Program of Higher Education (20060610005), the National Natural Science Foundation of Sichuan Education Department of China (07ZB068) and the Open Fund (PLN0703) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University).     

Convergence of SSOR methods for linear complementarity problems

In this paper, by applying the SSOR splitting, we propose two new iterative methods for solving the linear complementarity problem LCP (M,q). Convergence results for these two methods are presented when M is an H-matrix (and also an M-matrix). Finally, two numerical examples are given to show the efficiency of the presented methods.     

Projected iterative algorithms for complex symmetric systems arising in magnetized multicomponent transport

We investigate iterative algorithms for solving complex symmetric constrained singular systems arising in magnetized multicomponent transport. The matrices of the corresponding linear systems are symmetric with a positive semi-definite real part and an imaginary part with a compatible nullspace. We discuss well posedness, the symmetry of generalized inverses and Cholesky methods. We investigate projected stationary iterative methods as well as projected orthogonal residuals algorithms generalizing previous results on real systems. As an application, we consider the linear systems arising from the kinetic theory of gases and providing transport coefficients of partially ionized gas mixtures subjected to a magnetic field.     

New third-order method for solving systems of nonlinear equations

In this paper, we present a new iterative method to solve systems of nonlinear equations. The main advantages of the method are: it has order three, it does not require the evaluation of any second or higher order Fréchet derivative and it permits that the Jacobian be singular at some points. Thus, the problem due to the fact that the Jacobian is numerically singular is solved. The third order convergence in both one dimension and for the multivariate case are given. The numerical results illustrate the efficiency of the method for systems of nonlinear equations.      

On the characterization of strong convergence of an iterative algorithm for a class of multi-valued variational inclusions

This paper introduces an Ishikawa type iterative algorithm for finding approximating solutions of a class of multi-valued variational inclusion problems. Characterization of strong convergence of this iterative method is established. L. C. Ceng’s research partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, China and the Dawn Program Foundation in Shanghai. S. Schaible’s research partially supported by the National Science Council of Taiwan. This research was partially supported by the grant NSC 96-2628-E-110-014-MY3.