A descent hybrid conjugate gradient method based on the memoryless BFGS update

In this work, we present a new hybrid conjugate gradient method based on the approach of the convex hybridization of the conjugate gradient update parameters of DY and HS+, adapting a quasi-Newton philosophy. The computation of the hybrization parameter is obtained by minimizing the distance between the hybrid conjugate gradient direction and the self-scaling memoryless BFGS direction. Furthermore, a significant property of our proposed method is that it ensures sufficient descent independent of the accuracy of the line search. The global convergence of the proposed method is established provided that the line search satisfies the Wolfe conditions. Our numerical experiments on a set of unconstrained optimization test problems from the CUTEr collection indicate that our proposed method is preferable and in general superior to classic conjugate gradient methods in terms of efficiency and robustness.     

Scalar conservation laws: Initial and boundary value problems revisited and saturated solutions

We revisit the classical theory of multidimensional scalar conservation laws. We reformulate the notion of the classical Kruzkov entropy solutions and study some new properties as well as the well-posedness of the initial value problem with inhomogeneous fluxes and general initial data. We also consider Dirichlet boundary value problems. We put forward a new and transparent definition for solutions and give a simple proof for their well-posedness in domains with smooth boundaries. Finally, we introduce the notion of saturated solutions and show that it is well-posed.     

Equity portfolio construction and selection using multiobjective mathematical programming

A multi-objective mixed integer programming model for equity portfolio construction and selection is developed in this study, in order to generate the Pareto optimal portfolios, using a novel version of the well known ε-constraint method. Subsequently, an interactive filtering process is also proposed to assist the decision maker in making his/her final choice among the Pareto solutions. The proposed methodology is tested through an application in the Athens Stock Exchange.     

Corresponding-states laws for protein solutions

The solvent around protein molecules in solutions is structured and this structuring introduces a repulsion in the intermolecular interaction potential at intermediate separations. We use Monte Carlo simulations with isotropic, pair-additive systems interacting with such potentials. We test if the liquid-liquid and liquid-solid phase lines in model protein solutions can be predicted from universal curves and a pair of experimentally determined parameters, as done for atomic and colloid materials using several laws of corresponding states. As predictors, we test three properties at the critical point for liquid-liquid separation: temperature, as in the original van der Waals law, the second virial coefficient, and a modified second virial coefficient, all paired with the critical volume fraction. We find that the van der Waals law is best obeyed and appears more general than its original formulation: A single universal curve describes all tested nonconformal isotropic pair-additive systems. Published experimental data for the liquid-liquid equilibrium for several proteins at various conditions follow a single van der Waals curve. For the solid-liquid equilibrium, we find that no single system property serves as its predictor. We go beyond corresponding-states correlations and put forth semiempirical laws, which allow prediction of the critical temperature and volume fraction solely based on the range of attraction of the intermolecular interaction potential.     

Antioxidant behaviour of 2′‐hydroxy‐chalcones: a study of their electrochemical properties

The electrochemical behaviour of 13 chalcone analogues was systematically studied by means of cyclic voltammetry and chronoamperometry at a glassy carbon (GC), gold and platinum working electrodes using two different supporting electrolyte/solvent combinations. It was found that chalcone analogues can be easily oxidized at both GC and gold working electrodes, but not at a platinum electrode. Principal component analysis was further employed to reveal similarities/dissimilarities between oxidation potentials, chronoamperometric signals and ability of the compounds to scavenge the reactive oxygen species H₂O₂. The study reveals the inverse proportional relationship between the scavenging ability of H₂O₂, expressed as IC₅₀, and chronoamperometric signal at 800 mV using gold as working electrode. Copyright © 2012 John Wiley & Sons, Ltd.     

A study of properties of adaptive quadratic grids for three-dimensional near-surface field computations

Curved geometries and the corresponding near-surface fields typically require a large number of linear computational elements. High-order numerical solvers have been primarily used with low-order meshes. There is a need for curved, high-order computational elements. Typical near-surface meshes consist of hexahedral and/or prismatic elements. The present work studies the employment of quadratic meshes that are relatively coarse for field simulations. Directionally quadratic high-order elements are proposed for the near-surface field regions. The quadratic meshes are compared with the conventional low-order ones in terms of accuracy and efficiency. The cases considered include closed surface volume calculations, as well as computation of gradients of several analytic fields. A special method of adaptive local quadratic meshes is proposed and evaluated. Truncation error analysis for quadratic grids yields comparison with the conventional linear hexahedral/prismatic meshes, which are subject to typical distortions such as stretching, skewness, and torsion.     

NMR study of 5-substituted pyrazolo[3,4-c]pyridine derivatives

Substituted pyrazolopyridines are potent inhibitors of phosphodiesterases and cyclin-dependent kinases. In this study, NMR was used to investigate the potential N1-H and N2-H tautomerism of 5-substituted pyrazolo[3,4-c]pyridine derivatives. Six compounds were fully characterized by using (1)H, (13)C, and (15)N chemical shifts and indirect (1)H--(13)C and (1)H--(15)N coupling constants. The (1)H NMR spectra were measured over a broad range of temperatures. All of the compounds were shown to exist predominantly in the N1-H tautomeric form. Complementary quantum-chemical calculations of the chemical shieldings and indirect spin-spin couplings support the structural conclusions drawn.     

Metastable liquid clusters in super- and undersaturated protein solutions

Dense liquid phases, metastable with respect to a solid phase, but stable with respect to the solution, have been known to form in solutions of proteins and small-molecule substances. Here, with the protein lumazine synthase as a test system, using dynamic and static light scattering and atomic force microscopy, we demonstrate submicron size clusters of dense liquid. In contrast to the macroscopic dense liquid, these clusters are metastable not only with respect to the crystals, but also with respect to the low-concentration solution: the characteristic cluster lifetime is limited to approximately 10 s, after which they decay. The cluster population is detectable only if they occupy >10(-6) of the solution volume and have a number density >105 cm-3 for 3 to 11% of the monitored time. The cluster volume fraction varies within wide limits and reaches up to 10(-3). Increasing protein concentration increases the frequency of cluster detection but does not affect the ranges of the cluster sizes, suggesting that a preferred cluster size exists. A simple Monte Carlo model with protein-like potentials reproduces the metastable clusters of dense liquid with limited lifetimes and variable sizes and suggests that the mean cluster size is determined by the kinetics of growth and decay and not by thermodynamics.