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     

Quantum Conservative Gates for Finite-Valued Logics

We introduce some conservative gates for finite-valued logics which are able to realize all the main connectives of the many-valued logics of ?ukasiewicz, the MV-algebras of Chang and Brower–Zadeh algebras. After a brief exposition of the motivations for this work, the gates are defined and their properties are explored. Finally, a possible quantum realization of them is proposed, using three techniques: a “brute force” method--an extension of the Conditional Quantum Control argument, and a new technique which we call the Constants Method. For all these techniques, the unitary operator which describes the gate is a sum of local operators.     

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.     

Longitudinally detected electron spin resonance: Recent developments

Multiple-quantum spectroscopies are reviewed in the frame of electron paramagnetic resonance. Some properties of different nonlinear techniques are discussed for both transverse and longitudinal detection. The connections of effects recently presented with the procedure of longitudinal detection of electron paramagnetic resonance (LODESR) in presence of double transverse irradiation are stressed. Peculiarities of LODESR spectroscopy and its capabilities in facing problems related to relaxations in presence of very slow dynamic processes are evidentiated. Recent results show the vitality of the LODESR technique, that in the future could be applied to new fields, owing to experimental updating.     

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.     

Signatures of the fast dynamics in glassy polystyrene: first evidence by high-field electron paramagnetic resonance of molecular guests

The reorientation of one small paramagnetic molecule (spin probe) in glassy polystyrene (PS) is studied by high-field electron paramagnetic resonance spectroscopy at two different Larmor frequencies (190 and 285 GHz). Two different regimes separated by a crossover region are evidenced. Below 180 K the rotational times are nearly temperature independent with no apparent distribution. In the temperature range of 180-220 K a large increase of the rotational mobility is observed with the widening of the distribution of correlation times which exhibits two components: (i) a deltalike, temperature-independent component representing the fraction of spin probes w which persist in the low-temperature dynamics; (ii) a strongly temperature-dependent component, to be described by a power distribution, representing the fraction of spin probes 1-w undergoing activated motion over an exponential distribution of barrier heights g(E). Above 180 K a steep decrease of w is evidenced. The shape and the width of g(E) do not differ from the reported ones for PS within the errors. For the first time the large increase of the rotational mobility of the spin probe at 180 K is ascribed to the onset of the fast dynamics detected by neutron scattering at T(f)=175+/-25 K.     

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.