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.     

Copolymerization reactivities and conductivities of some living polymers of p-substituted styrenes

A kinetic study in tetrahydrofuran of the addition of 1,1-diphenylethylene on para-substituted styrylcarbanions (with Cs⁺ as counterion) has given the reactivities of free ions and ion-pairs. For both species, the addition rate constant increased in the following sequence for the substituent of the phenyl ring: pH < p-CH₃ <p-CH₃O. It was also shown that in the same solvent, the dissociation constants of the polystyryl ion-pairs decreased with the electron-donating power of the substituent.     

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.     

Properties of block and graft copolymers of polybutadiene with small complexed poly(4-vinylpyridine) segments

Various diblocks, triblocks and a graft copolymer of butadiene with 4-vinylpyridine short blocks have been prepared. They were complexed with ZnCl₂ to give ionomer-like materials. For all copolymers, the T_g of the elastomeric block (?84°C to ?91°C) was unchanged by complexation. For all diblocks and triblocks with short blocks (DP _n ～ 3) the storage modulus was only slightly increased by comparison with uncomplexed materials. For the graft copolymer even with short blocks the material is less sensitive to temperature after complexation. For triblocks, when the DP _n of the vinylpyridine blocks was high enough (15 units), complexes were associated in multiplets of large size and the elastomeric properties were retained up to 200°C.     

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.     

Nanocomposite materials from latex and cellulose whiskers

Composite materials were processed by casting a mixture of aqueous suspensions of latex and microfibrils. These microfibrils, or whiskers, are extracted from a sea animal and are monocrystals of cellulose, with an aspect ratio around 100 and an average diameter of 20 nm. It has been found that the mechanical properties (shear modulus) are increased by more than two orders of magnitude in the rubbery state of the polymeric matrix, when the whisker content was 6% (w/w). This very large effect is discussed on the basis of different types of mechanical models and it is concluded that these whiskers form a rigid network, probably linked by hydrogen bonds. The formation of this network is assumed to be governed by a percolation mechanism.     

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.