General theory of domain decomposition: Beyond Schwarz methods

Recently, Herrera presented a general theory of domain decomposition methods (DDM). This article is part of a line of research devoted to its further development and applications. According to it, DDM are classified into direct and indirect, which in turn can be subdivided into overlapping and nonoverlapping. Some articles dealing with general aspects of the theory and with indirect (Trefftz–Herrera) methods have been published. In the present article, a very general direct‐overlapping method, which subsumes Schwarz methods, is introduced. Also, this direct‐overlapping method is quite suitable for parallel implementation. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 495–517, 2001     

Globally convergent DC trust-region methods

In this paper, we investigate the use of DC (Difference of Convex functions) models and algorithms in the application of trust-region methods to the solution of a class of nonlinear optimization problems where the constrained set is closed and convex (and, from a practical point of view, where projecting onto the feasible region is computationally affordable). We consider DC local models for the quadratic model of the objective function used to compute the trust-region step, and apply a primal-dual subgradient method to the solution of the corresponding trust-region subproblems. One is able to prove that the resulting scheme is globally convergent to first-order stationary points. The theory requires the use of exact second-order derivatives but, in turn, the computation of the trust-region step asks only for one projection onto the feasible region (in comparison to the calculation of the generalized Cauchy point which may require more). The numerical efficiency and robustness of the proposed new scheme when applied to bound-constrained problems is measured by comparing its performance against some of the current state-of-the-art nonlinear programming solvers on a vast collection of test problems.     

NH vs. CH hydrogen bond formation in metal-organic anion receptors containing pyrrolylpyridine ligands

Anion complexation studies on a series of platinum(II) tetrakis(pyrrolylpyridine) salts demonstrate the importance of CH-anion hydrogen bonds in coordinating anionic guests in solution and the solid-state.     

A new numerical approach for the advective-diffusive transport equation

A new numerical solution procedure is presented for the one-dimensional, transient advective-diffusive transport equation. The new method applies Herrera's algebraic theory of numerical methods to the spatial derivatives to produce a semi-discrete approximation. The semi-discrete system is then solved by standard time marching algorithms. The algebraic theory, which involves careful choice of test functions in a weak form statement of the problem, leads to a numerical approximation that inherently accommodates different degrees of advection domination. Algorithms are presented that provide either nodal values of the unknown function or nodal values of both the function and its spatial derivative. Numerical solution of several test problems demonstrates the behavior of the method.     

Anion binding properties of 5,5'-dicarboxamido-dipyrrolylmethanes

A series of 5,5'-dicarboxamido-dipyrrolylmethanes have been synthesized and in some cases crystallographically characterized. Proton NMR titrations have revealed that these compounds, that contain only four neutral hydrogen bond donors and are acyclic, selectively bind anions in very competitive solvent media such as DMSO-d6/water mixtures.     

The algebraic theory approach for ordinary differential equations: Highly accurate finite differences

This article reports further developments of Herrera's algebraic theory approach to the numerical treatment of differential equations. A new solution procedure for ordinary differential equations is presented. Finite difference algorithms of 0(h^r), for arbitrary “r” are developed. The method consists in constructing local approximate solutions and using them to extract information about the sought solution. Only nodal information is derived. The local approximate solutions are constructed by collocation, using polynomials of degree G. When “n” collocation points are used at each subinterval, G = n + 1and the order of accuracy is 0(h^2n?1). The procedure here presented is very easy to implement. A program in which n can be chosen arbitrarily, was constructed and applied to selected examples.     

Unified formulation of numerical methods. I. Green's formulas for operators in discontinuous fields

Applying the method of weighted residuals and then interpreting the resulting equations by means of Green's formulas for discontinuous functions, a direct method of analysis is developed. The scheme includes finite differences, finite elements, and boundary methods. This is the first of a sequence of articles in which the methodology is presented. A fundamental ingredient of the procedure are general Green's formulas for operators defined in discontinuous fields. They are developed in this first article.     

Identification of peptides that neutralize bacterial endotoxins using β-hairpin conformationally restricted libraries

Bacterial endotoxins are the major mediator of septic shock; therefore, endotoxin-neutralizing molecules could have biomedical applications. The septic shock cascade relies in a series of molecular recognition processes. The large contact-surface described for the interacting macromolecules, in most cases, prevents the identification of small molecules that could modulate such recognition events. Here we report on a beta-hairpin conformationally restricted combinatorial library that has been generated and screened towards the identification of new peptides that neutralize bacterial endotoxins. Starting with a de novo designed linear peptide that shows a beta-hairpin structure population of around 30%, (Ramirez-Alvarado, M., Blanco, F. J. and Serrano, L. Nat. Struc. Biol., 7, 604-612 (1996)), we selected four positions to build up a combinatorial library of 20(4) sequences. Deconvolution of the library reduced such a sequence complexity to 8 defined sequences. The newly identified peptides have a biological activity equivalent to that reported for peptides derived from natural endotoxin-binding proteins.     

Synthesis of new vinylpyridinium salts

This article reports the reactions of salts of 4‐ureylmethylpyridinium and 4‐ethoxycarbonylaminomethylpyridinium with carbonylic compounds, performed with the aim of obtaining new vinylpyridinium salts. These reactions can lead to the formation of both condensation and dimerization products. The type of products formed is conditioned by the nature of the salts and carbonyl groups involved. The interest generated by the condensation products formed lies in their potential cholinergic activity. J. Heterocyclic Chem., 2011.