Mimicking dihydroxy acetone phosphate-utilizing aldolases through organocatalysis: a facile route to carbohydrates and aminosugars

[reaction: see text] A practical and environmentally friendly organocatalytic strategy designed to mimic the DHAP aldolases has been developed and shown to be effective in the preparation of carbohydrates and aminosugars. (S)-Proline and (S)-2-pyrrolidine-tetrazole catalyzed the aldol reaction between dihydroxy acetone variants such as 1,3-dioxan-5-one and 2,2-dimethyl-1,3-dioxan-5-one with aldehydes to give the corresponding polyols in good yields with very high ees.     

Ultrasonic wave propagation across a thin nonlinear anisotropic layer between two half-spaces

Boundary conditions and perturbation theory are combined to create a set of equations which, when solved, yield the reflected and transmitted wave forms in the case of a thin layer of material that is perfectly bonded between two isotropic half-spaces. The set of perturbed boundary conditions is created by first using the fully bonded boundary conditions at each of the two interfaces between the thin layer and the half-spaces. Then, by restricting the layer's thickness to be much smaller than an acoustic wavelength, perturbation theory can be used on these two sets of boundary equations, producing a set of equations which effectively treat the thin layer as a single interface via a perturbation term. With this set of equations, the full range of incident and polar angles can be considered, with results general enough to use with a layer that is anisotropic, nonlinear, or both anisotropic and nonlinear. Finally the validity of these equations is discussed, comparing the computer simulation results of this theory to results from standard methods, and looking at cases where the results (or various properties of the results) are known or can be predicted.     

Monte Carlo simulations on the effect of substrate geometry on adsorption and compression

Canonical Monte Carlo simulations were used to study the adsorption and compression of fluid layers on model substrates with cubic, (111) fcc, and graphite geometries. The effect of the relative size of the fluid and substrate molecules on adsorption was considered for strong molecule-surface interactions. In the case of monolayer formation, it was found that the surface geometry and the size of the adsorbate molecules had a significant effect on the structure of the adsorbed layer. These structures varied from well-ordered, commensurate layers to liquid-like structures. Lateral compression was observed for certain fluid to substrate molecule sizes. For the interactions studied in this work, it was found that maximum lateral compression occurred on the cubic surface when adsorbate molecules had a diameter approximately 15% larger than the substrate diameter. In the case of multilayer formation, it was found that second and higher adsorbed layers could compress into the adsorbed layers below them. For cubic substrates, the interlayer compression was predicted analytically with reasonable accuracy, with maximum interlayer compression found for fluid diameters approximately 90% the size of substrate molecule diameters.     

Novel porphyrin-fullerene assemblies: from rotaxanes to catenanes

[reaction: see text] Titration of porphyrin-fullerene rotaxanes with DABCO or 4,4'-bipyridine led to photo- and redoxactive catenanic architectures, which upon photoexcitation undergo a sequence of short-range energy and electron transfer events to give a long-lived charge-separated radical-pair state.     

Optimally Cutting a Surface into a Disk

We consider the problem of cutting a subset of the edges of a polyhedral manifold surface, possibly with boundary, to obtain a single topological disk, minimizing either the total number of cut edges or their total length. We show that this problem is NP-hard in general, even for manifolds without boundary and for punctured spheres. We also describe an algorithm with running time n ^O(g+k), where n is the combinatorial complexity, g is the genus, and k is the number of boundary components of the input surface. Finally, we describe a greedy algorithm that outputs a O(log² g)-approximation of the minimum cut graph in O(g ² n log n) time.     

Trends in exchange coupling for trimethylenemethane-type Bis(semiquinone) biradicals and correlation of magnetic exchange with mixed valency for cross-conjugated systems

A magnetostructural correlation (conformational electron spin exchange modulation) within an isostructural series of biradical complexes is presented. X-ray crystal structures, variable-temperature electron paramagnetic resonance spectroscopy, zero-field splitting parameters, and variable-temperature magnetic susceptibility measurements were used to evaluate molecular conformation and electron spin exchange coupling in this series of molecules. Our combined results indicate that the ferromagnetic portion of the exchange couplings occurs via the cross-conjugated pi-systems, while the antiferromagnetic portion occurs through space and is equivalent to incipient bond formation. Thus, molecular conformation controls the relative amounts of ferro- and antiferromagnetic contributions to exchange coupling. In fact, the exchange parameter correlates with average semiquinone ring torsion angles via a Karplus-Conroy-type relation. Because of the natural connection between electron spin exchange coupling and electronic coupling related to electron transfer, we also correlate the exchange parameters in the biradical complexes to mixed valency in the corresponding quinone-semiquinone radical anions. Our results suggest that delocalization in the cross-conjugated, mixed-valent radical anions is proportional to the ferromagnetic contribution to the exchange coupling in the biradical oxidation states.     

Conformally invariant Monge-Ampère equations: Global solutions

In this paper we will examine a class of fully nonlinear partial differential equations which are invariant under the conformal group . These equations are elliptic and variational. Using this structure and the conformal invariance, we will prove a global uniqueness theorem for solutions in with a quadratic growth condition at infinity.

     

Simultaneous effects on vowel duration in American English: a covariance structure modeling approach

The powerful techniques of covariance structure modeling (CSM) long have been used to study complex behavioral phenomenon in the social and behavioral sciences. This study employed these same techniques to examine simultaneous effects on vowel duration in American English. Additionally, this study investigated whether a single population model of vowel duration fits observed data better than a dual population model where separate parameters are generated for syllables that carry large information loads and for syllables that specify linguistic relationships. For the single population model, intrinsic duration, phrase final position, lexical stress, post-vocalic consonant voicing, and position in word all were significant predictors of vowel duration. However, the dual population model, in which separate model parameters were generated for (1) monosyllabic content words and lexically stressed syllables and (2) monosyllabic function words and lexically unstressed syllables, fit the data better than the single population model. Intrinsic duration and phrase final position affected duration similarly for both the populations. On the other hand, the effects of post-vocalic consonant voicing and position in word, while significant predictors of vowel duration in content words and stressed syllables, were not significant predictors of vowel duration in function words or unstressed syllables. These results are not unexpected, based on previous research, and suggest that covariance structure analysis can be used as a complementary technique in linguistic and phonetic research.