Algorithms for optimal area triangulations of a convex polygon

Given a convex polygon with n vertices in the plane, we are interested in triangulations of its interior, i.e., maximal sets of non-intersecting diagonals that subdivide the interior of the polygon into triangles. The MaxMin area triangulation is the triangulation of the polygon that maximizes the area of the smallest triangle in the triangulation. Similarly, the MinMax area triangulation is the triangulation that minimizes the area of the largest area triangle in the triangulation. We present algorithms that construct MaxMin and MinMax area triangulations of a convex polygon in O(n²logn) time and O(n²) space. The algorithms use dynamic programming and a number of geometric properties that are established within the paper.     

Hydroxyl radical and hydroxide ion in liquid water: a comparative electron density functional theory study

Ab initio density functional theory molecular dynamics simulations of the solvated states of the hydroxyl radical and hydroxide ion are performed using the Becke-Lee-Yang-Parr (BLYP) exchange-correlation functional (Becke, A. D. Phys. Rev. A 1988, 38, 3098. Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785). The structures of the solvation shells of the two species are examined. It is found that the OH radical forms a relatively well-defined solvation complex with four neighboring water molecules. Three of these molecules are hydrogen bonded to the OH, while the fourth is hemibonded via a three-electron two-centered bond between the oxygen atoms of the OH and water. The activity and the diffusion mechanism of the OH radical in water is discussed in comparison with the OH- ion. Although the results are partially influenced by the tendency of the BLYP density functional to overestimate hemibonded structure, the present simulations suggest that the widely accepted picture of rapid diffusion of OH radical in water through hydrogen exchange reaction may need to be reconsidered.     

Acid catalyzed intramolecular attack of β‐phenylthioureido group on amide function. Parallel formation of thiodihydrouracil and 4‐iminothiodihydrouracil. Different pathways in the Edman degradation reaction in the formation of six‐ versus five‐membered cyclic intermediates

Contrary to the cleavage of α‐phenylthioureido peptides 1 proceeding through intermediate 2‐anilinothiazolinone 2 , the b‐analog cis‐2‐(3‐phenylthioureido)cyclopentane‐carboxamide 5 forms transiently 4‐imino‐2‐thioxopyrimidine 6 . Monitoring amide cyclization and hydrolysis of iminopyrimidine 6 in acid by UV showed that an equilibrium between 5 and 6 was reached followed by slower conversion of both compounds into 2‐oxo‐4‐thioxopyrimidine 7 . Both processes were characterized by isosbestic points, the first due to parallel conversion of 5 into 6 and 7 (or 6 into 5 and 7 ) at a constant ratio while the second identical for both reactants – to conversion of equilibrated 5 and 6 into 7 . The special isosbestic points allowed the determination of the individual constants of Scheme 2. Further confirmation was obtained from NMR product analysis and following the cyclization of amide 5 in DMSO:DCl. Product 2‐oxo‐4‐ thioxopyrimidine 7 hydrolyzed reversibly to thioureido acid 8 . The cyclization rate of 8 allowed the participation of 6‐oxothiazine 10 formed by sulfur attack to be excluded. The absence of sulfur attack in the six‐membered case is explained by the longer C? S bond bringing about greater bond angle strain at the tetrahedral ring atoms due to the geometrical characteristics of five‐ and six‐membered rings with planar segments. The cyclizations of amide 5 to iminopyrimidine 6 and to thiodihydrouracil 7 are first order in [H⁺], while the reactions of protonated imine 6 H⁺ are zero order to amide and ?1 to thiodihydrouracil. The reaction orders can be reconciled by assuming a rate determining proton transfer from the tetrahedral intermediate in amide cyclization. Copyright © 2007 John Wiley & Sons, Ltd.     

Local cohomology modules with infinite dimensional socles

In this paper we prove the following generalization of a result of Hartshorne: Let be a commutative Noetherian local ring of dimension at least two, , and . Let be a homogeneous element of such that the coefficients of form a system of parameters for . Then the socle of is infinite dimensional.

     

Ribozymomimetic Chemical Synthesis of Peptide Bond Using Phosphorous Acid/Oxirane Mediators

Abstract

A model system is created that mimics natural ribosome as well as the way of ribozyme action. It uses oxirane analogue as condensation reagent and H₃PO₃ as activator for the carboxyl group and as protecting reagent for the NH₂ function. In order to demonstrate the ability of the H₃PO₃/oxirane system to mimic natural peptide bond synthesis on the ribosome as well as to mimic the ribozyme synthesis and hydrolysis of an inter biomonomeric bond, four model compounds containing an amide bond were synthesized using phosphorous acid/oxirane mediators.

GRAPHICAL ABSTRACT     

Microwave-assisted and conventional sol-gel preparation of photocatalytically active ZnO/TiO2/glass multilayers

For the first time a combination of microwaves and/or the conventional treatment method was used to dry and heat multilayered sol-gel ZnO/TiO₂/glass structures. Compact or porous TiO₂ films were deposited as a bottom layer, covered with a ZnO film. The structures were characterized by X-ray Diffraction (XRD), Energy Dispersive X-ray Spectroscopy (EDX) and Scanning Electron Microscopy (SEM). Only peaks of wurtzite ZnO crystalline phase were registered on the X-Ray diffractograms. The microwave irradiation leads to a formation of poorly crystallized multilayers with very small crystallites and enhanced surface roughness. This results in a better photocatalytic activity of these structures than the structures of the samples treated conventionally. It was established that the morphology of the bottom titania layer affects the reaction of photocatalytic degradation of Malachite Green dye (MG). The structures with the compact bottom TiO₂ films showed higher activities than those on porous TiO₂ films. This study offers an energy saving method of producing ZnO/TiO₂/glass multilayered structures of various morphologies and pronounced photocatalytic properties. The method does not involve any calcination step, normally applied to achieve a good degree of crystallization. This makes the method suitable for protecting substrates of low thermal stability.      

Investigation of the dynamic stereochemistry of dimesityl-2,4,6-trimethoxyphenylmethane by complete lineshape analysis and 2D EXSY NMR spectroscopy

The static and dynamic stereochemistry of dimesityl-2,4,6-trimethoxyphenylmethane in solution was investigated by lineshape analysis of 1D NMR spectra and cross-peak amplitude processing in 2D EXSY spectra, recorded at variable temperatures. Previous studies on this propeller-shaped chiral compound show that the stereomer threshold interconversion is associated with helicity reversal and occurs through [1,2]- and [1,3]-two ring flips of one mesityl and the 2,4,6-trimethoxyphenyl rings. In the present study, the experimental rate constants of the [1,2]- and [1,3]-two ring flips, which are identical, were determined at various temperatures by combining quantitative 2D EXSY spectra processing and complete lineshape analysis (CLSA) of 1D NMR spectra. The latter were subjected to reference deconvolution and linear prediction in order to eliminate the lineshape distortions due to magnetic field inhomogeneity. The activation parameters of these ring flips were determined by an Eyring equation analysis of the temperature dependence of the rate constant. The experimentally determined activation enthalpy and entropy for the two-ring flips, and those obtained from theoretical ab initio calculations at different levels of theory and basis sets, were found to be in good agreement.