Trichothiazole A,a dichlorinated polyketide containing an embedded thiazole isolated from Trichodesmium blooms

Mass spectrometry-guided isolation of the lipophilic extract of Trichodesmium bloom material led to the isolation and structure characterization of a new thiazole-containing di-chlorinated polyketide (1). The structure of 1 was deduced using 1D and 2D NMR analysis, high-resolution mass spectrometry analysis and complementary spectroscopic procedures. Trichothiazole A possesses interesting structural features, such as a terminal alkyne, two vinyl chlorides and a 2,4-disubstituted thiazole. Trichothiazole A showed moderate cytotoxicity to Neuro-2 A cells (EC₅₀: 13.3 ± 1.1 μM).     

Five-membered ring chelate complexes of Ni(II), Pd(II) and Pt(II) derived of di-(2-pyridyl)-N-ethylimine

Cis-diaquobis{di-(2-pyridyl)-N-ethylimine}nickel(II) chloride (2) was obtained from the reaction of di-(2-pyridyl)-N-ethylimine (1) and [NiCl₂dppe] [dppe = cis-1,2-bis(diphenylphosphino)ethylene] in a 2:1 ratio in hot acetonitrile. Cis-dichloro{di-(2-pyridyl)-N-ethylimine}palladium(II) (3) and cis-dichloro{di-(2-pyridyl)-N-ethylimine}platinum(II) (4) complexes were obtained from the reaction of MCl₂ (M = Pd, Pt) and (1) in equimolar ratio in hot acetonitrile. Compounds 1–4 were characterized by IR spectroscopy, elemental analysis, and mass spectrometry; the complexes 3 and 4 were characterized in solution by NMR. In addition, solid state structures of compounds 1–4 were determined using single crystal X-ray diffraction analyses. X-ray diffraction data of the complexes 3 and 4 showed a distorted square planar local geometry at palladium and platinum atoms with the chlorine atoms in a cis-coordination; in 2 a local octahedral geometry at nickel atom was observed. Complexes 3 and 4 are arranged as dimers with a M?M distance of 3.4567(4) Å (M = Pd) and 3.4221(4) Å (M = Pt), respectively; 2 consists of units linked by intermolecular hydrogen bonding.     

Structural relationship between negative thermal expansion and quartic anharmonicity of cubic ScF3

Cubic scandium trifluoride (ScF3) has a large negative thermal expansion over a wide range of temperatures. Inelastic neutron scattering experiments were performed to study the temperature dependence of the lattice dynamics of ScF3 from 7 to 750 K. The measured phonon densities of states show a large anharmonic contribution with a thermal stiffening of modes around 25 meV. Phonon calculations with first-principles methods identified the individual modes in the densities of states, and frozen phonon calculations showed that some of the modes with motions of F atoms transverse to their bond direction behave as quantum quartic oscillators. The quartic potential originates from harmonic interatomic forces in the DO9 structure of ScF3, and accounts for phonon stiffening with the temperature and a significant part of the negative thermal expansion.     

Formulas and Asymptotics for the Asymmetric Simple Exclusion Process

This is an expanded version of a series of lectures delivered by the second author in June, 2009. It describes the results of three of the authors’ papers on the asymmetric simple exclusion process, from the derivation of exact formulas for configuration probabilities, through Fredholm determinant representation, to asymptotics with step initial condition establishing KPZ universality. Although complete proofs are in general not given, at least the main elements of them are.     

Ruthenium-catalysed transfer hydrogenation reactions with dimethylamine borane

Dimethylamine-borane adduct has been used as the hydrogen source for the reduction of carbonyl compounds, imines, oximes, nitriles, nitroarenes and alkenes using [Ru(p-cymene)Cl₂]₂ as the catalyst.     

Tau functions for the Dirac operator on the Poincaré disk

In this paper we define tau functions for holonomic fields associated with the Dirac operator on the Poincaré disk. The deformation analysis of the tau functions is worked out and in the case of the two point function, the tau function is expressed in terms of a Painlevé function of type VI.     

The notion of motion: covariational reasoning and the limit concept

This paper investigates outcomes of building students’ intuitive understanding of a limit as a function's predicted value by examining introductory calculus students’ conceptions of limit both before and after instruction. Students’ responses suggest that while this approach is successful at reducing the common limit equals function value misconception of a limit, new misconceptions emerged in students’ responses. Analysis of students’ reasoning indicates a lack of covariational reasoning that coordinates changes in both x and y may be at the root of the emerging limit reached near x = c misconception. These results suggest that although dynamic interpretations of limit may be intuitive for many students, care must be taken to foster a dynamic conception that is both useful at the introductory calculus level and is in line with the formal notion of limit learned in advanced mathematics. In light of the findings, suggestions for adapting the pedagogical approach used in this study are provided.