A truncated Newton method in an augmented Lagrangian framework for nonlinear programming

In this paper we propose a primal-dual algorithm for the solution of general nonlinear programming problems. The core of the method is a local algorithm which relies on a truncated procedure for the computation of a search direction, and is thus suitable for large scale problems. The truncated direction produces a sequence of points which locally converges to a KKT pair with superlinear convergence rate.     

Long Time Behavior of the Cahn-Hilliard Equation with Irregular Potentials and Dynamic Boundary Conditions

The Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions is considered.The existence of the global attractor is proved and the long time behavior of the trajectories,namely,the convergence to steady states,is studied.     

An RQP algorithm using a differentiable exact penalty function for inequality constrained problems

In this paper we propose a recursive quadratic programming algorithm for nonlinear programming problems with inequality constraints that uses as merit function a differentiable exact penalty function. The algorithm incorporates an automatic adjustment rule for the selection of the penalty parameter and makes use of an Armijo-type line search procedure that avoids the need to evaluate second order derivatives of the problem functions. We prove that the algorithm possesses global and superlinear convergence properties. Numerical results are reported.     

Gauge invariance,charge conservation,and variational principles

We present new results on the correspondence between symmetries, conservation laws and variational principles for field equations in general non-abelian gauge theories. Our main result states that second order field equations possessing translational and gauge symmetries and the corresponding conservation laws are always derivable from a variational principle. We also show by the way of examples that the above result fails in general for third order field equations.     

Finding the maximum suffix with fewer comparisons

It is shown how to compute the lexicographically maximum suffix of a string of n?2 characters over a totally ordered alphabet using at most (4/3)n−5/3 three-way character comparisons. The best previous bound, which has stood unchallenged for more than 25 years, is (3/2)n−O(1) comparisons. We also prove an interesting property of an algorithm for computing the maximum suffix both with respect to a total order < and with respect to its inverse order >.     

Wavy graphene sheets from electrochemical sewing of corannulene

The presence of non-hexagonal rings in the honeycomb carbon arrangement of graphene produces rippled graphene layers with valuable chemical and physical properties. In principle, a bottom-up approach to introducing distortion from planarity of a graphene sheet can be achieved by careful insertion of curved polyaromatic hydrocarbons during the growth of the lattice. Corannulene, the archetype of such non-planar polyaromatic hydrocarbons, can act as an ideal wrinkling motif in 2D carbon nanostructures. Herein we report an electrochemical bottom-up method to obtain egg-box shaped nanographene structures through a polycondensation of corannulene that produces a new conducting layered material. Characterization of this new polymeric material by electrochemistry, spectroscopy, electron microscopy (SEM and TEM), scanning probe microscopy, and laser desorption-ionization time of flight mass spectrometry provides strong evidence that the anodic polymerization of corannulene, combined with electrochemically induced oxidative cyclodehydrogenations (Scholl reactions), leads to polycorannulene with a wavy graphene-like structure.

A bottom-up synthesis of wavy graphene structures obtained through an anodic polymerization process, combined with an electrochemically triggered oxidative cyclodehydrogenation, of the bowl-shaped polyaromatic hydrocarbon corannulene.     

The dimeric and tetrameric octarepeat fragments of prion protein behave differently to its monomeric unit

Potentiometric and spectroscopic data have shown that octarepeat dimer and tetramer are much more effective ligands for Cu(II) ions than simple octapeptide. Thus, the whole N-terminal segment of prion protein due to cooperative effects, could be more effective in binding of Cu(II) than simple peptides containing a His residue. The gain of the Cu(II) binding by longer octarepeat peptides derives from the involvement of up to four imidazoles in the coordination of the first Cu(II) ion. This type of binding increases the order of the peptide structure, which allows successive metal ions for easier coordination.     

New antidepressant drug candidate: Hypericum montbretti extract

This study was designed to investigate possible antidepressant-like effects of the extract prepared from the flowers of Hypericum montbretti Spach. (Guttiferae, Clusiaceae). Phytochemical constituents of the methanolic extract were analysed by HPLC method. The main flavonoid component was detected as rutin, and another highly concentrated phenolic compound was quercitrin. Antidepressant activity of the extract was examined by tail suspension and modified forced swimming tests, whereas the motor coordination of the animals was tested by the Rota-Rod apparatus. Reboxetine at a dose of 20 mg?kg?1 was used as a reference drug. Dose-dependent antidepressant activity was observed in both tests following the administration of extract at 100 and 250 mg?kg?1 doses. To the best of our knowledge, this is the first study reporting the antidepressant activity of H. montbretti extract. Additionally, the results of this work support previous papers reporting the antidepressant activity of rutin.     

Resin dynamics contributes to the NMR line broadening of organic molecules grafted onto a polystyrene resin

Despite the use of high resolution magic angle spinning NMR, the NMR linewidth of anchored molecules on the commonly used Merrifield solid phase resins remains larger than that of the corresponding molecules in solution. We investigate the different mechanisms that might be at the origin of this line broadening. Experimentally, we use the CPMG method to determine the (15)N relaxation times of a tethered tripeptide and show that the slow resin dynamics significantly contributes to the transverse relaxation.     

A Shifted-Barrier Primal-Dual Algorithm Model for Linearly Constrained Optimization Problems

In this paper we describe a Newton-type algorithm model for solving smooth constrained optimization problems with nonlinear objective function, general linear constraints and bounded variables. The algorithm model is based on the definition of a continuously differentiable exact merit function that follows an exact penalty approach for the box constraints and an exact augmented Lagrangian approach for the general linear constraints. Under very mild assumptions and without requiring the strict complementarity assumption, the algorithm model produces a sequence of pairs converging quadratically to a pair where satisfies the first order necessary conditions and is a KKT multipliers vector associated to the linear constraints. As regards the behaviour of the sequence x ^k alone, it is guaranteed that it converges at least superlinearly. At each iteration, the algorithm requires only the solution of a linear system that can be performed by means of conjugate gradient methods. Numerical experiments and comparison are reported.