Unusual Corrections to Scaling in the 3-State Potts Antiferromagnet on a Square Lattice

At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2 and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as J/kT according to Ae ² (1+be ^– +···), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal.     

The propagation of ultrasound in an austenitic weld

The propagation of ultrasound through an austenitic weld is investigated experimentally as well as in a numerical simulation. The weld is insonified at normal incidence to the fusion line with a longitudinal contact transducer. In order to experimentally trace the ultrasound through the weld, slices of different thicknesses from the original weld have been fabricated. Through-transmission A-scans have then been produced for each weld slice and compared with the corresponding numerical simulation. A comparison of the direction of ultrasound propagation through the weld for the two approaches shows quite good agreement. However, attenuation due to scattering at grain boundaries in the weld is poorly modelled in the simulation. In order to improve this, a better model of the weld is needed.     

An inhomogeneous wave equation and non-linear Diophantine approximation

A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution is studied. Both the Lebesgue and Hausdorff measures of this set are obtained.     

Ring Opening of Pymisyl‐Protected Aziridines with Organocuprates

The pyrimidine‐2‐sulfonyl (pymisyl) group is introduced as a new protecting group that can be used to activate aziridines towards ring opening. It is readily introduced and removed under mild conditions. Regioselective ring opening of pymisyl‐protected 2‐methyl‐aziridine with organocuprates gives the corresponding sulfonamides in high yields, and the pymisyl group can subsequently be removed upon treatment with a thiolate. The versatility of this new nitrogen protecting group is illustrated with a new synthesis of Selegiline, a monoamine oxidase‐B inhibitor marketed for the treatment of Parkinson’s disease.     

Coordination of imidazoles by Cu(II) and Zn(II) as studied by NMR relaxometry, EPR, far-FTIR vibrational spectroscopy and ab initio calculations: effect of methyl substitution

Synthetic imidazole ligands are typically substituted at the N(1) ((1)-Im) position while natural imidazole ligands are substituted at the C(4) ((4)-Im) position. To outline the difference in coordination properties, the methyl-substituted imidazoles Me(4)-Im and Me(1)-Im were complexed with CuCl(2) and ZnCl(2) and investigated by NMR relaxometry, electron paramagnetic resonance, far-Fourier transform IR vibrational spectroscopy, and ab initio calculations. Me(4)-Im, Me(1)-Im, and Im in excess form the usual tetragonal D(4h) [CuL(4)X(2)] complexes with CuCl(2) whereas the methylated imidazoles form pseudotetrahedral C(2v) complexes instead of the usual octahedral O(h) [ZnIm(6)](2+) complex. All imidazoles display a high degree of covalence in the M-L σ- and π-bonds and the π-interaction strength affects the relative energies of complexation. Opportunities to tailor complexes by the chemical properties of the substituents are envisaged due to the role of the inductive and hyperconjugative effects, rather than position.     

Automatic convexity of rank-1 convex functions

We announce new structural properties of 1-homogeneous rank-1 convex integrands, and discuss some of their consequences.     

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.     

A column generation approach for solving the patient admission scheduling problem

This paper addresses the Patient Admission Scheduling (PAS) problem. The PAS problem entails assigning elective patients to beds, while satisfying a number of hard constraints and as many soft constraints as is possible, and arises at all planning levels for hospital management. There exist a few, different variants of this problem. In this paper we consider one such variant and propose an optimization-based heuristic building on branch-and-bound, column generation, and dynamic constraint aggregation to solve it. We achieve tighter lower bounds than previously reported in the literature and, in addition, we are able to produce new best known solutions for five out of twelve instances from a publicly available repository.