Symmetry classes of tensors via semigroup operands

The symmetry of tensors, such as the symmetric or antisymmetric ones (built on a finite-dimensional complex vector space) may be described by a complex-valued homomorphism of the symmetric group with the specification that its action equal scalar multiplication by the value, e.g. by 1 or sign. This condition may be construed as a universalizing operand (over the symmetric group with 0) homomorphism from the unsymmetrized tensors—a restructuring which permits a clearer and more effective treatment of these symmetries; freed from the multilinear setting in which they arose, it also points the way to a development of semigroup symmetries on more general universal algebras.     

Two-loop two-point functions with masses: asymptotic expansions and Taylor series,in any dimension

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and smallq ², ind dimensions, using identities derived from integration by parts. Expansions are given, in terms of hypergeometric series, for all gluon diagrams and for all but one of the quark diagrams; expansions of the latter are obtained from differential equations. Padé approximants to truncations of the expansions are shown to be of great utility. As an application, we obtain the two-loop photon self-energy, for alld, and achieve highly accelerated convergence of its expansions in powers ofq ²/m ² orm ²/q ², ford=4.     

Spectroscopic signatures of halogens in clathrate hydrate cages. 2. Iodine

UV-vis and Raman spectroscopy were used to study iodine molecules trapped in sII clathrate hydrate structures stabilized by THF, CH(2)Cl(2), or CHCl(3). The spectra show that the environment for iodine inside the water cage is significantly less perturbed than either in aqueous solution or in amorphous water-ice. The resonance Raman progression of I(2) in THF clathrate hydrate can be observed up to v = 6 when excited at 532 nm. The extracted vibrational frequency omega e = 214 +/- 1 cm(-1) is the same as that of the free molecule to within experimental error. At the same time, the UV-vis absorption spectrum of I(2) in the sII hydrate exhibits a relatively large, 1440 cm(-1), blue-shift. This is mainly ascribed to the differential solvation of the I(2) electronic states. We conclude that iodine in sII hydrate resides in a 5(12)6(4) cavity, in which the ground-state I(2) potential is not significantly perturbed by the hydrate lattice. In contrast, in water and in ice, the valence absorption band of I(2) is dramatically broadened and blue-shifted by 3000 cm(-1), and the resonance Raman scattering is effectively quenched. These observations are shown to be consistent with a strong interaction between water molecule and iodine through the lone pair of electrons on water as in the case of bromine in the same media. The results presented here, and the stability of other halogen hydrates, were used to test the predictions of simple models and force-field calculations of the host cage-guest association energy.     

An alkoxide-directed alkyne-allene cross-coupling for stereoselective synthesis of 1,4-dienes

A titanium alkoxide-mediated convergent coupling between internal alkynes and allenes is described for the regio- and stereocontrolled synthesis of substituted acyclic 1,4-dienes.     

Mechanism of titanocene-mediated epoxide opening through homolytic substitution

The mechanism of titanocene-mediated epoxide opening was studied by a combination of voltammetric, kinetic, computational, and synthetic methods. With the aid of electrochemical investigations the nature of a number of Ti(III) complexes in solution was established. In particular, the distribution of monomeric and dimeric Ti(III) species was found to be strongly affected by the exact steric conditions. The overall rate constants of the reductive epoxide opening were determined for the first time. These data were employed as the basis for computational studies of the structure and energies of the epoxide-titanocene complexes, the transition states of epoxide opening, and the beta-titanoxy radicals formed. The results obtained provide a structural basis for the understanding of the factors determining the regioselectivity of ring opening and match the experimentally determined values. By employing substituted titanocenes even more selective epoxide openings could be realized. Moreover, by properly adjusting the steric demands of the catalysts and the substrates the first examples of reversible epoxide openings were designed.