Ultrathin gradient films using thiol‐ene polymerizations

The application of surface‐attached, thiol‐ene polymer films for controlling material properties in a gradient fashion across a surface was investigated. Thiol‐ene films were attached to the surface by first depositing a thiol‐terminated self‐assembled monolayer and performing a thiol‐ene photopolymerization reaction on the surface. Property gradients were created either by creating and modifying a gradient in the surface thiol density in the SAM or by changing the polymerization conditions or both. Film thickness was modified across the substrate by changing either the density of the anchoring thiol functional groups or by changing the reaction conditions such as exposure time. Thicker films (1–11 nm) were obtained by polymerizing acrylate polymer brushes from the surface with varying exposure time (0–60 s). The two factors, that is, the surface thiol density and the exposure time, were combined in orthogonal directions to obtain thiol‐ene films with a two‐dimensional thickness gradient with the maximum thickness being 4 nm. Finally, a thiol‐acrylate Michael type addition reaction was used to modify the surface thiol density gradient with the cell‐adhesive ligand, Arg‐Gly‐Asp‐Ser (RGDS), which subsequently yielded a gradient in osteoblast density on the surface. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 7027–7039, 2006     

在Armijo型线搜索下共轭梯度法簇的全局收敛性

本文我们讨论了一簇共轭梯度法，它可被看作是FR法和DY法的凸组合．我们提出了两种Armijo型线搜索，并在这两种线搜索下，讨论了共轭梯度法簇的全局收敛性．     

A nonmonotone truncated Newton–Krylov method exploiting negative curvature directions, for large scale unconstrained optimization

We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative curvature direction. A test based on the quadratic model of the objective function is used to select the most promising between the two search directions. Both the latter selection rule and the CG stopping criterion for approximately solving Newton’s equation, strongly rely on conjugacy conditions. An appropriate linesearch technique is adopted for each search direction: a nonmonotone stabilization is used with the approximate Newton step, while an Armijo type linesearch is used for the negative curvature direction. The proposed algorithm is both globally and superlinearly convergent to stationary points satisfying second order necessary conditions. We carry out a significant numerical experience in order to test our proposal.     

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.     

On Lagrange multipliers of trust-region subproblems

Trust-region methods are globally convergent techniques widely used, for example, in connection with the Newton’s method for unconstrained optimization. One of the most commonly-used iterative approaches for solving trust-region subproblems is the Steihaug–Toint method which is based on conjugate gradient iterations and seeks a solution on Krylov subspaces. This paper contains new theoretical results concerning properties of Lagrange multipliers obtained on these subspaces. AMS subject classification (2000)  65F20     

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.