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.     

An accurate method to predict the stress concentration in composite laminates with a circular hole under tensile loading

The paper presents a theoretical-numerical hybrid method for determining the stresses distribution in composite laminates containing a circular hole and subjected to uniaxial tensile loading. The method is based upon an appropriate corrective function allowing a simple and rapid evaluation of stress distributions in a generic plate of finite width with a hole based on the theoretical stresses distribution in an infinite plate with the same hole geometry and material. In order to verify the accuracy of the method proposed, various numerical and experimental tests have been performed by considering different laminate lay-ups; in particular, the experimental results have shown that a combined use of the method proposed and the well-know point-stress criterion leads to reliable strength predictions for GFRP or CFRP laminates with a circular hole. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 531–570, July–August, 2007.     

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.     

Conformational energies of cyclenes

An universal function for non-bonded interactions, which takes into account the relative orientation of the bonds is considered in calculating the conformational energies of cycloalkenes and cycloalkadienes. A comparison is made with previous results obtained by using usual 6-exp functions for non-bonded interactions.     

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.     

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.     

Hydrolysis of new phthalimide-derived esters catalyzed by immobilized lipase

The last step of the production of four phthalimide-derived acids, designed to act as antiasthma drugs, was performed by enzymatic hydrolysis of the respective methyl or ethyl esters. The esters 4-ethyl-[2-(1,3-dioxo-1,3-dihydro-2-isoindoylyl)]-phenoxyacetic methyl ester (PHT-MET), 4-ethyl-[2-(1,3-dioxo-1,3-dihydro-2-isoindoylyl)]-phenoxyacetic ethyl ester, 4-(1,3-dioxo-1,3-dihydro-2-isoindoylyl)-phenoxyacetic ethyl ester, and 2-(1,3-dioxo-1, 3-dihydro-2-isoindoylyl)-phenoxyacetic ethyl ester were hydrolyzed by immobilized lipase. The enzymatic reaction could be used only to produce the desired 4-substituted compounds. The best result that was found to hydrolysis of PHT-MET, and, therefore, that ester was selected for optimization experiments in a three-phase system. Reactions were performed with solid biocatalyst (Lipozyme® RM IM), organic solvent phase (ethyl acetate), and aqueous phase (saturated Na₂CO₃ solution). To optimize the reaction conditions, an experimental design optimization procedure was used. The variables studied were the amount of enzyme, the temperature, and the volume of the aqueous solution. Time course experiments were then performed for different initial enzyme concentrations (0.5, 0.9, and 1.4 U_H/mL of solvent). The optimized reaction conditions found were 20 mg of Lipozyme (0.9 U_H/mL_solvent) and 5.0 mL of Na₂CO_3(sat) at 40°C for 6 h.     

Thermal and dynamic mechanical analysis of cross-linked poly(esterurethanes)

New cross-linked poly(esterurethanes) (PEU) based on unsaturated olygo(alkyleneester)diol (OAE), 4,4’-diphenylmethane diisocyanate (MDI) and styrene or methyl methacrylate as curing monomers were prepared. The synthesis of PEU was performed in two steps. In the first step OAE was obtained from adipic acid, maleic anhydride and ethylene glycol. In the second step a prepolymer was obtained in a reaction of OAE with different amounts of 4,4’-diphenylmethane diisocyanate followed by crosslinking using previously mentioned curing monomers. The influence of structure of the poly(esterurethanes) on thermal and dynamic mechanical properties is studied. Thermogravimetric analysis shows that cross-linked poly(esterurethanes) demonstrate high thermal stability. Moreover the dynamic mechanical thermal analysis shows that the presence of styrene cross-linking chains in polymers lead to the phase separation in cross-linked poly(esterurethanes).