Finite-temperature phase transition in a class of four-state Potts antiferromagnets

We argue that the four-state Potts antiferromagnet has a finite-temperature phase transition on any Eulerian plane triangulation in which one sublattice consists of vertices of degree 4. We furthermore predict the universality class of this transition. We then present transfer-matrix and Monte?Carlo data confirming these predictions for the cases of the Union Jack and bisected hexagonal lattices.     

GRASP with path relinking for the orienteering problem

In this paper, we address an optimization problem resulting from the combination of the well-known travelling salesman and knapsack problems. In particular, we target the orienteering problem, originated in the context of sport, which consists of maximizing the total score associated with the vertices visited in a path within the available time. The problem, also known as the selective travelling salesman problem, is NP-hard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in routing and tourism. We propose a heuristic method—based on the Greedy Randomized Adaptive Search Procedure (GRASP) and the Path Relinking methodologies—for finding approximate solutions to this optimization problem. We explore different constructive methods and combine two neighbourhoods in the local search of GRASP. Our experimentation with 196 previously reported instances shows that the proposed procedure obtains high-quality solutions employing short computing times.     

On evolutoids of planar convex curves

There are many interesting curves which we can associate with a given convex curve, however, in this work we are especially interested in studying the relations between the given curve and its evolutoids: that is, the curve obtained as the envelope of lines making a fixed angle with the normal line at every point of the curve. The first result is an inequality between the area enclosed by the given curve and the area enclosed by its evolutoid. Also, we proved that a convex curve is of constant width (centrally symmetric) if and only if its evolutoid for a fixed angle is of constant width (centrally symmetric).     

Interpretation of vicinal proton–proton coupling constants of heteroaromatic molecules in terms of topological electron density descriptors

The indirect vicinal proton–proton coupling constants for pyrrole, furan, thiophene and 15 related heteroaromatic compounds were calculated using the Khon–Sham approximation. An analysis of the four Ramsey contributions to the coupling constants was carried out showing that the Fermi contact term is always positive and dominant, although the remaining contributions have a nonnegligible net negative contribution. The trends observed for the proton–proton coupling constants were rationalized in terms of the properties of the electron density. It was found that electron delocalization between the corresponding hydrogen atoms plays a major role on the observed behavior with the charges of the carbon atoms bonded to them and the accompanying geometric variations being also of importance in the coupling mechanism. Copyright © 2010 John Wiley & Sons, Ltd.     

The Solution Conformation of Lactal and ITS Hexa-O-Acetyl Derivative

Abstract

The conformation of lactal (1) in D₂O and DMSO-d₆ has been investigated by employing NMR techniques and molecular mechanics calculations. The glucal ring shows a ⁴ H₅ conformation in deuterium oxide and DMSO-d₆. In contrast, the glucal ring of the hexa-O-acetyl derivative (2) in CDCl₃ can be described as an equilibrium between the ⁴ H₅ and ⁴ H₅ forms. The disaccharide 1 has a restricted flexibility with the Φ angle oscillating about -105 ± 30° and the Ψ angle varying about -145 ± 30°. Compound 2 shows a similar conformational behaviour.     

Hiv-1 Specific Reverse Transcriptase Inhibitors: why are Tsao-Nucleosides so Unique?

1. INTRODUCTION

AIDS will still be one of the most important challenges for the Scientific Community in the approaching new century. Since the identification, in 1983-84,^1,2 of human immunodeficiency virus (HIV) as the etiological agent of AIDS, significant progress has been made in the treatment of HIV-infected patients. This has been in part due to the discovery and clinical use of an increasing number of anti-HIV drugs. However, while highly active antiretroviral therapy (HAART)³ approaches have reduced the morbidity and mortality, the intertwined problems of drug induced viral resistance, poor compliance with complex regimens and therapy failure continue. Therefore, there remains a pressing need for the development of new antiviral agents that can be used not only as first line therapeutic candidates, but also in the antiretroviral-experienced patient population.