Complex powers of classical SG-pseudodifferential operators

Abstract Under a suitable ellipticity condition, we show that classical SG-pseudodifferential operators of nonnegative order possess complex powers. We show that the powers are again classical and derive an explicit formula for all homogeneous components. Keywords: Complex power, Weighted symbols, Noncompact manifolds     

Separating the solution sets of analytical and polynomial systems

A linear inequality system with infinitely many constraints is polynomial (analytical) if its index set is a compact interval of the real line and all its coefficients are polynomial (analytical, respectively) functions of the index on this interval. This paper provides an example of analytical system whose solution set cannot be the solution set of any polynomial system. Research supported by DGES of Spain and FEDER of UE, Grant BFM2002-04114-C02-01. Research supported by CONACyT of Mexico, Grant 130036. Research partially supported by CONACyT of Mexico, Grant 44003.     

Alkane oxygenation with H2O2 catalysed by FeCl3 and 2,2′-bipyridine

The H₂O₂-FeCl₃-bipy system in acetonitrile efficiently oxidises alkanes predominantly to alkyl hydroperoxides. Turnover numbers attain 400 after 1 h at 60 °C. It has been assumed that bipy facilitates proton abstraction from a H₂O₂ molecule coordinated to the iron ion (these reactions are stages in the catalytic cycle generating hydroxyl radicals from the hydrogen peroxide). Hydroxyl radicals then attack alkane molecules finally yielding the alkyl hydroperoxide.     

Enzymatic desaturation of fatty acids: delta11 desaturase activity on cyclopropane acid probes

The formation of methylenecyclopropanes by enzymatic desaturation of 11-cyclopropylundecanoic acid (1) and its disubstituted derivatives cis- and trans-3-5 has been investigated using the Delta(11) desaturase of Spodoptera littoralis as model enzyme. Gas chromatography coupled to mass spectrometry analyses of methanolyzed lipidic extracts from tissues incubated with each probe revealed that all the cyclopropyl fatty acids were transformed into the corresponding 11-cyclopropylidene acids, except for compound trans-5 (5b), which was not desaturated at C11. The formation of methylenecyclopropane 9 as the only reaction product from 1 indicates that a potential radical intermediate is too short-lived to allow rearrangement reactions. Information on the Delta(11) desaturase substrate binding domain is provided considering the cyclopropyl probes 3-5 as conformationally restricted analogues of the straight-chain substrates.     

Oxygen equilibrium pressure above V2O5−x and thermodynamic properties of this oxide system

Measurements of oxygen equilibrium pressure above the V₂O_5?x oxide system have been performed within the temperature range 575 to 615°C. The results have been used to determine the standard enthalpy and entropy in the reaction V₆O₁₃ + O₂ = 3 V₂O₅. The thermodynamic properties of the V₂O_5?x system (at x < 1) cited in the literature have been discussed for all the equilibria postulated.     

Abnormally mild synthesis of bis(dithiolo)pyrroles from 2,5-dimethylpyrroles

[chemical reaction: see text]. Treatment of N-substituted 2,5-dimethylpyrroles 2 with an equilibrated mixture of disulfur dichloride and DABCO in chloroform at 0 degrees C gives pentathiepinopyrroles 3 in moderate yields; further reaction of 3 with the same mixture at room temperature leads, in an extensive reaction cascade, to bis(dithiolo)pyrroles 4 in high yield; 2 can be converted into 4 in a one-pot operation under unusually mild conditions.     

Kinetics of self-condensation of acetone over heterogeneous Ba(OH)2 and Sr(OH)2 catalysts

Catalytic performance of Ba(OH)₂ and Sr(OH)₂ in self-condensation of acetone was examined in the temperature range from 273 to 303 K. A kinetic model of second order with respect to acetone was used for interpretation of the results obtained for the diacetone alcohol formation.This revised version was published online in December 2005 with corrections to the Cover Date.     

Mimicking photosynthesis in a computationally designed synthetic metalloprotein

While advances in protein design have made possible the construction of protein architectures with nativelike properties and predictable structures and function, there are as of yet no examples of functional, protein-based, solar energy conversion systems. This communication describes the design and characterization of an artificial reaction center (RC) protein that closely resembles the function of the natural photosynthetic RC. The synthetic protein, designed by the protein design program CORE, participates in multiple reduction/oxidation cycles with exogenous acceptors/donors following photoexcitation. The designed metalloprotein, aRC, consists of a tetrahelical bundle functionalized with two bis-histidine bound metal cofactors: a Ru(bpy)2 moiety and a heme group. Two distinct bis-histidine binding sites were engineered for each of these metal centers. Photoexcitation of aRC results in rapid ET from the RuII complex to the heme group (kET >/= 5 x 1010 s-1) yielding a long-lived (70 ns) charge-separated state (CSS), RuIII/FeII. This long-lived CSS participates in subsequent ET reactions with exogenous donors and acceptors in multiple photocycles, thus mimicking the basic function of native photosynthetic RCs. This study illustrates the successful design and construction of a protein-based functional charge separation device using a combination of automated computational protein design and knowledge of the engineering principles of biological electron tunneling extracted from natural electron-transfer systems. To our knowledge, this represents the first example of a functional protein-based artificial reaction center.     

Oxygen equilibrium pressure as a measure of oxygen binding energy in the V2O5−x system

Using the redox mechanism of vanadia catalyst action as a starting point, oxygen binding energy and its measurement have been discussed. Experimental results on the equilibrium oxygen pressure are presented and two types of equilibrium are distinguished: chemisorbed and redox. It has been shown that univariant redox equilibrium is appropriate for characterizing vanadia catalysts.     

Phlogophites intercalated with Al2O3 pillars and modified with transition metals as catalysts of the DeNOx process

Natural phlogophite, pre-treated with acids and intercalated with alumina pillars, was used as catalytic support. Transition metals (Fe, Cu) were deposited on the surface of the modified clay materials by an ion-exchange method. The obtained samples were characterized with respect to structure (XRD), texture (BET), composition (EPMA) and chemical nature of the deposited transition metals species (UV-vis-DRS). The phlogophite based materials have been found to be active and selective catalysts of the DeNOx process. The Fe-containing samples were catalytically active at lower temperatures than the clays modified with copper. A competitive ammonia oxidation by oxygen decreased the effectiveness of the DeNOx process in the high temperature range.