A θ-stable approximations of abstract Cauchy problems

Summary We study the approximation of linear parabolic Cauchy problems by means of Galerkin methods in space andA -stable multistep schemes of arbitrary order in time. The error is evaluated in the norm ofL _t ² (H _x ¹ ) L _t (L _x ² ).     

Breaking of permutation symmetry and diagonal group action: Nielsen model and the standard model as low-energy limit

We point out that, on the basis of a theorem by L. Michel, every model based on the symmetryG ... G has a generic low-energy limit the breaking to diagonal action, i.e., toG. This applies in particular to the proposal by Nielsen to consider such a model withG the standard model group.     

Properties of Integers and Finiteness Conditions for Semigroups

Let h and k be integers greater than 1; we prove that the following statements are equivalent: 1) the direct product of h copies of the additive semigroup of non-negative integers is not k-repetitive; 2) if the direct product of h finitely generated semigroups is k-repetitive, then one of them is finite. Using this and some results of Dekking and Pleasants on infinite words, we prove that certain repetitivity properties are finiteness conditions for finitely generated semigroups.     

Solid-state supramolecular organization, established directly from powder diffraction data, and photoluminescence efficiency of rigid-core oligothiophene-S,S-dioxides

The "rigid-core" material 3,5-dimethyl-2,3'-bis(3-methylthiophene)-dithieno[3,2-b:',3'-d]thiophene-4,4-dioxide (DTTOMe4) has the highest photoluminescence ever reported for thiophene-based molecules in the solid state. We report the structure of this material, determined directly from powder X-ray diffraction data using the Genetic Algorithm method for structure solution, followed by Rietveld refinement, and the structural properties are discussed in relation to the structures of the corresponding subsystems DTTO and DTTOMe. While the crystal structures of the latter compounds contain cofacial dimers, the crystal structure of DTTOMe4 comprises layers of molecules aligned in an antiparallel fashion. Intermediate neglect of differential overlap with single configuration interaction (INDO/SCI) calculations on the intermolecular interactions in the three crystal structures show that the different solid-state photoluminescence efficiencies of DTTOMe4, DTTOMe, and DTTO cannot be correlated with the different types of dipole-dipole alignment in the solid state. Instead, photoluminescence efficiencies correlate well with the rate of formation of nonradiatively decaying charge-transfer pairs upon photoexcitation. Because of larger intermolecular distances in DTTOMe4, the photoluminescence is less effectively quenched by charge-transfer processes than in DTTOMe and DTTO.     

PHOTOCHEMISTRY and PHOTOBIOLOGY WITHOUT LIGHT

Abstract— This review covers the literature since 1980 on chemically and enzymatically generated electronically excited species. The emphasis lies on triplet states of carbonyl products that are derived from dioxetanes and dioxetanones as precursors or from suitable enzymatic oxygenations. Singlet oxygen, an important excited state species in biological processes, is not explicitly treated. The utilization of triplet excited carbonyl products to promote photochemical and photobiological transformations by energy transfer are of primordial interest and not the photomechanistic behavior, photophysical properties and inherent photochemical reactions of such excited state species. Thus, the coverage concentrates on photodamage of DNA and RNA, the photochemistry of flavins, vitamin D, tryptophan, arachidonic acid, chlorophyll, lipid peroxidation, urocanase activation, excitation of chlorophlasts, and the aerobic oxidation of Schiff bases derived from amino acids and proteins. The potential perspectives of employing authentic dioxetanes and enzymatically generated dioxetane intermediates as effective photon equivalents in photochemotherapy, phototoxicity, photoaffinity labeling and photogenotoxicity are pointed out, in the hope of stimulating more intensive activity in this emerging and novel bioorganic and photobiological field.     

On the supposed equilibrium Ph6Pb2Ph4Pb+Ph2Pb in solution

The reaction between pentadeuteriophenyllithium and hexaphenyldilead combined with new measurements of isotopic exchange between Ph₆Pb₂ (labelled with RaD) and Ph₄Pb, have shown that the dilead compound is undissociated in solution. These results cast doubt upon the previously reported equilibrium: Ph₆Pb₂Ph₄Pb+Ph₂Pb.     

Xenicane Diterpenes Revisited: Thermal (E)→(Z) isomerization and conformational motions. A unifying picture

Kinetic and equilibrium studies show that typical xenicanes such as dictyolactone ( 1 ) and 4-hydroxydictyolactone ( 3 ) undergo slow conformation medium-ring flipping between the predominant trans-( 1a or 3a ; Me(20) trans to H–C(3)) and the minor cis-conformers ( 1b or 3b ; Me(20) cis to H–C(3); see Scheme 1). The formation of the latter is inhibited in heterocyclic-ring-opened congeners such as 18-acetoxy-4-hydroxydictyo-19-al ( 7 ). Molecular-mechanics calculations suggest that typical-xenicane cis-conformers are disfavoured by mainly C(4)–C(5) torsional strain. This is confirmed by the observation of two sizably populated cis-and trans-conformers for the unnatural 4-oxoxenicanes 10–12 . Unusually facile thermal (E)→(Z) isomerization of xenicanes 1,3,10–12 , and 7 is also observed (→ 13–17 and 9 , resp.; Scheme 3), reflecting great strain relief in the transition state. Conflicting results in the literature now fit into this scheme which provides a basis for unravelling recognition phenomena with these biologically active systems.     

(η3‐Allyl‐2κ3C)(chloro‐1κCl)(μ‐N,N′‐diethyldithioxamidato‐1:2κ4S,S′:N,N′)[diphenyl(2‐pyridyl)phosphine‐1κP]palladium(II)platinum(II) chloroform solvate

The title compound, [PdPtCl(C₃H₅)(C₆H₁₀N₂S₂)(C₁₇H₁₄NP)]·CHCl₃, was obtained by deprotonation of the initial platinum(II) complex of the di­thio­xamide and subsequent reaction with [Pd(η³‐C₃H₅)(μ‐Cl)]₂. Both metal atoms exhibit a square‐planar coordination geometry, with the two planes forming a dihedral angle of 21.7 (2)°. The di­thio­xamide bis‐chelating bridge is flat.