Are there chaotic tilings?

We develop a class of examples in the form of tiling dynamical systems for use as toy models in statistical mechanics, to analyze the possible existence of disordered crystals. We give the first such models which are disordered in the sense of having no discrete spectrum.Research supported in part by a grant from the Israel Science and Technology MinistryResearch supported in part by NSF Grant No. DMS-9001475     

Wave scattering functions and their application to multiple scattering problems

Scattering functions arise naturally in standard treatments of the effects of a material object or surface embedded in a uniform field. The most commonly used scattering function describes the far-field modulation imparted at large distances to a spherical wavefront eminating from the scatterer. The purpose of this is to develop the properties of the spectrum of scattered plane waves as an exact generalized scattering function. The linearity of the wave equations guarantees that such a representation exists; moreover, it is possible to derive the generalized scattering function from the far-field scattering function by analytic continuation. Although these properties are known, recent theoretical developments have motivated us to reexplore the interrelations among the far-field scattering function, the Green's function and various forms of the generalized scattering function as well as the symmetry properties of the generalized scattering function imposed by reciprocity. For multiple-scattering objects that can be separated by parallel planes, a system of difference equations is developed that fully accommodates the mutual interaction among the scatterers. The mutual interaction equations were developed earlier, but we show here that they can be transformed into the form that would be obtained by using the Foldy-Lax-Twersky formalism. This reinforces the equivalence between wave-space and configuration space formulations of the scattering problems.     

Efficient edge domination in regular graphs

An induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p≥3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-complete.     

Comparison of time-dependent effects of (+)-methamphetamine or forced swim on monoamines,corticosterone, glucose,creatine, and creatinine in rats

Background  

Methamphetamine (MA) use is a worldwide problem. Abusers can have cognitive deficits, monoamine reductions, and altered magnetic resonance spectroscopy findings. Animal models have been used to investigate some of these effects, however many of these experiments have not examined the impact of MA on the stress response. For example, numerous studies have demonstrated (+)-MA-induced neurotoxicity and monoamine reductions, however the effects of MA on other markers that may play a role in neurotoxicity or cell energetics such as glucose, corticosterone, and/or creatine have received less attention. In this experiment, the effects of a neurotoxic regimen of (+)-MA (4 doses at 2 h intervals) on brain monoamines, neostriatal GFAP, plasma corticosterone, creatinine, and glucose, and brain and muscle creatine were evaluated 1, 7, 24, and 72 h after the first dose. In order to compare MA's effects with stress, animals were subjected to a forced swim test in a temporal pattern similar to MA administration [i.e., (30 min/session) 4 times at 2 h intervals].     

Predictive abilities of scaled quantum mechanical molecular force fields: application to 2,3-dimethylbuta-1,3-diene

In connection with the appearance of new experimental vibrational data on the high-energy rotational isomer of 2,3-dimethylbuta-1,3-diene (I) in a low-temperature matrix and in neat crystals, the ab initio-based vibrational analysis of this molecule has been re-evaluated. Calculated wavenumbers derived from a scaled quantum-mechanical force field analysis at the MP2(FC)/aug-cc-pVDZ//MP2(FC)/aug-cc-pVDZ computational level are compared with experimental data. Several reassignments of the fundamental wavenumbers for I have been suggested in the course of the current analysis, and the existence of a high-energy non-planar s-gauche conformer of 2,3-dimethylbuta-1,3-diene has been confirmed.     

Numerical Kähler-Einstein Metric on the Third del Pezzo

The third del Pezzo surface admits a unique Kähler-Einstein metric, which is not known in closed form. The manifold’s toric structure reduces the Einstein equation to a single Monge-Ampère equation in two real dimensions. We numerically solve this nonlinear PDE using three different algorithms, and describe the resulting metric. The first two algorithms involve simulation of Ricci flow, in complex and symplectic coordinates respectively. The third algorithm involves turning the PDE into an optimization problem on a certain space of metrics, which are symplectic analogues of the “algebraic” metrics used in numerical work on Calabi-Yau manifolds. Our algorithms should be applicable to general toric manifolds. Using our metric, we compute various geometric quantities of interest, including Laplacian eigenvalues and a harmonic (1,1)-form. The metric and (1,1)-form can be used to construct a Klebanov-Tseytlin-like supergravity solution.     

Coupling routes to hexafluoro-1,3-butadiene, substituted-1,3-fluorine-containing butadienes and fluorinated polyenes

Hexafluoro-1,3-butadiene was readily prepared via a variety of self-coupling processes, such as Cu(0) mediated self-coupling of iodotrifluoroethene, Pd(0) catalyzed coupling of iodotrifluoroethene with the trifluorovinylzinc reagent, and CuBr₂ mediated coupling of the trifluorovinylzinc reagent. Perfluoro-2,3-dimethyl-1,3-butadiene was readily synthesized by the reaction of pentafluoropropenyl-2-zinc reagent with either CuBr₂ or FeCl₃. Alternatively, perfluoro-2,3-dimethyl-1,3-butadiene was prepared by oxidation of the pentafluoropropenyl-2-copper reagent with dioxygen. Cu(0) mediated coupling of an (E)-substituted ,β-difluoro-β-iodostyrene provided the first useful route to a (Z)(Z)-1,4-diaryl-1,3-tetrafluorobutadiene. Extension of the Cu(0) mediated coupling methodology to a perfluorodienyl iodide demonstrated a useful stereospecific route to perfluoropolyenes.