Weyl formula for hypoelliptic operators of Schrödinger type

In this work we consider a general class of hypoelliptic operators, for which we give an estimate of the remainder of the so-called Weyl asymptotic formula for the eigenvalues.

     

Gas-phase reactions of 1,4-benzodioxan, 2,3-dihydrobenzofuran,and 2,3-benzofuran with OH radicals and O3

The kinetics of the gas-phase reactions of 1,4-benzodioxan, 2,3-dihydrobenzofuran, and 2,3-benzofuran with OH radicals and O₃ have been studied at 298 ± 2 K and atmospheric pressure of air and the products have also been investigated. 1,4-Benzodioxan and 2,3-dihydrobenzofuran were chosen as volatile model compounds for dibenzo-p-dioxin and dibenzofuran, respectively. The rate constants, or upper limits thereof, for the O₃ reactions were (in cm³ molecule^?1 s^?1 units): 1,4-benzodioxan, <1.2 × 10^?20; 2,3-dihydrobenzofuran, <1 × 10^?19; and 2,3-benzofuran, (1.83 ± 0.21) × 10^?18. Using a relative rate method, the rate constants for the OH radical reactions (in cm³ molecule^?1 s^?1 units) were: 1,4-dibenzodioxan, (2.52 ± 0.38) × 10^?11; 2,3-dihydrobenzofuran, (3.66 ± 0.56) × 10^?11; and 2,3-benzofuran, (3.73 ± 0.74) × 10^?11. Salicylaldehyde was observed as a product of the OH radical-initiated and O₃ reactions of 2,3-benzofuran, with measured formation yields of 0.26 ± 0.05 and 0.13 ± 0.07, respectively.     

Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients

A new active-set method for smooth box-constrained minimization is introduced. The algorithm combines an unconstrained method, including a new line-search which aims to add many constraints to the working set at a single iteration, with a recently introduced technique (spectral projected gradient) for dropping constraints from the working set. Global convergence is proved. A computer implementation is fully described and a numerical comparison assesses the reliability of the new algorithm.     

Rate constants for the gas-phase reactions of Cl atoms with a series of hydrofluorocarbons and hydrochlorofluorocarbons at 298 ± 2 K

A relative rate method has been used to determine rate constants for the gas-phase reactions of a series of hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs) at 298 ± 2 K and atmospheric pressure of air. Based on a rate constant for the reaction of the Cl atom with CH₄ of (1.0 ± 0.2) ? 10^?13 cm³ molecule^?1 s^?1 at 298 K, the following Cl atom reaction rate constants (in units of 10^?15 cm³ molecule^?1 s^?1) were obtained: CH₃F, 340 ± 70; CH₃CHF₂, 240 ± 50; CH₂FCl, 110 ± 25; CHFCl₂, 21 ± 4; CHCl₂CF₃, 14 ± 3; CHFClCF₃, 2.7 ± 0.6; CH₃CFCl₂, 2.4 ± 0.5; CHF₂Cl, 2.0 ± 0.4; CH₂FCF₃, 1.6 ± 0.3; CH₃CF₂Cl, 0.37 ± 0.08; and CHF₂CF₃, 0.24 ± 0.05. These Cl atom reaction rate constants are compared with literature data and with the corresponding OH radical reaction rate constants. © John Wiley & Sons, Inc.     

Genus two extremal surfaces: Extremal discs, isometries and Weierstrass points

It is known that the largest disc that a compact hyperbolic surface of genusg may contain has radiusR=cosh⁻¹(1/2sin(π/(12g−6))). It is also known that the number of such (extremal) surfaces, although finite, grows exponentially withg. Elsewhere the authors have shown that for genusg>3 extremal surfaces contain only one extremal disc. Here we describe in full detail the situation in genus 2. Following results that go back to Fricke and Klein we first show that there are exactly nine different extremal surfaces. Then we proceed to locate the various extremal discs that each of these surfaces possesses as well as their set of Weierstrass points and group of isometries. Both authors partially supported by Grant BFM2000-0031 of the SGPI.MCYT.     

Determination of volatile organic compounds in recycled polyethylene terephthalate and high-density polyethylene by headspace solid phase microextraction gas chromatography mass spectrometry to evaluate the efficiency of recycling processes

A method for the determination of volatile organic compounds (VOCs) in recycled polyethylene terephthalate and high-density polyethylene using headspace sampling by solid-phase microextraction and gas chromatography coupled to mass spectrometry detection is presented. This method was used to evaluate the efficiency of cleaning processes for VOC removal from recycled PET. In addition, the method was also employed to evaluate the level of VOC contamination in multilayer packaging material containing recycled HDPE material. The optimisation of the extraction procedure for volatile compounds was performed and the best extraction conditions were found using a 75 μm carboxen-polydimethylsiloxane (CAR-PDMS) fibre for 20 min at 60 °C. The validation parameters for the established method were linear range, linearity, sensitivity, precision (repeatability), accuracy (recovery) and detection and quantification limits. The results indicated that the method could easily be used in quality control for the production of recycled PET and HDPE.     

Tedarenes A and B: structural and stereochemical analysis of two new strained cyclic diarylheptanoids from the marine sponge Tedania ignis

Ring strain causes planar chirality in tedarenes A and B, two cyclic diarylheptanoids isolated from the marine sponge Tedania ignis. In both molecules, the chiral plane is an olefinic system, which is very rare among natural products. In tedarene A (1), interconversion is too fast to allow isolation of the enantiomeric atropisomers but still slow enough to cause coalescence of some (1)H and (13)C NMR signals at room temperature. In tedarene B (2), which also shows stable central and axial chirality, the two planar diastereomers are in slow equilibrium. Tedarene B is the smallest natural product with central, axial, and planar chirality in the same simple molecule. The identification of planar chirality as the difference between its conformational isomers allowed the use of theoretical prediction of the CD spectrum to determine the absolute configuration of the stereogenic carbon C-9 as well as of the biphenyl chiral axis.