Fundamental solutions of the acoustic and diffusion equations in nonhomogeneous medium

A fundamental solution of the acoustical equation with a variable refraction coefficient is constructed. The solution satisfies the limiting absorption and radiation conditions. The optimal high frequency estimate is proved for square means of the solution. The source function for the diffusion equation is a by-product of this construction. Partially supported by a stipend of the Mathematical Scientific Research Institute at Berkeley, 2001.     

A conjecture of M. J. Taylor concerning determinantal congruences

Let G be a finite group. The class group of the group ring of G is a quotient of the idèlic homomorphisms of R(G) by the global functions and the determinantal functions. Using Explicit Brauer Induction, we prove Adams operations, applied to determinantal functions, satisfy some congruences which were conjectured by M. J. Taylor. As an application, we construct some new maps defined on the class group.In memory of J. Frank Adams (1930–1989)Research partially supported by NSERC Grant # 0GP0042580.     

2,12‐Dichloro‐10,20‐diphenyl‐5,7,15,17‐tetrahydro‐6H,16H‐dibenzo[d,l][1,9,2,6,10,14]dioxotetraazacyclohexadecine‐6,16‐dione dioxane solvate as a potential macrocyclic hexadentate ligand

The macrocyclic title compound crystallizes as a dioxane solvate, C₃₀H₂₂Cl₂N₄O₄·C₄H₈O₂, with two independent formula units in the unit cell. The observed syn conformation is controlled by both intramolecular N—H...O hydrogen bonds and intermolecular C—H...π interactions. The relative macrocyclic inner bore is estimated to be 4.19 Å. In the crystal structure, molecules form dimers via intermolecular C—H...π interactions, and these dimers are, in turn, linked to form columns along the a axis by intermolecular C—H...O hydrogen bonds. Both X‐ray diffraction analysis and density functional theory (DFT) calculations reveal that the macrocycle possesses very high flexibility. This property, as well as the presence of six donor atoms accessible for coordination, makes the title macrocycle a very promising ligand for complexation with the majority of transition metals.     

Gradient- and Sensitivity-Enhanced TOCSY Experiments

A pulsed field gradient version of the sensitivity-enhanced 2D TOCSY experiment is proposed which yields high-quality spectra with improved sensitivity and a minimum of two scans pert₁increment. For rapid acquisition of 1D TOCSY spectra, the 1D DPFGSE–TOCSY experiment was modified to include phase-encoded multiple-selective excitation followed by a simple spectral editing. Combination of these two building blocks is used in a sensitivity-enhanced 2D analog of the 3D TOCSY–TOCSY experiment which provides an efficient tool for resolving severely overlapped signals of oligomers in short experimental time.     

Consequences of magnetic aging for iron losses in electrical steels

Electrical steels, when submitted to operation, present continuous decrease of their magnetic properties, depending on the carbon content. This effect is attributed to the increase of the size of carbides, a process also known as coarsening or Ostwald Ripening. Loss separation can offer a better understanding of this phenomenon. Experimental results show that all effect of aging is inside the hysteresis loss component, with the excess losses unaffected. The carbon content in electrical steels should be less than 25 ppm to avoid magnetic aging.     

Rigidity of codimension two indefinite spheres

We describe all isometric immersions f:S _n ^s S _s ⁿ +2/S _s ⁿ n–s4, whenever the set of totally geodesic points does not disconnect S _s ⁿ , where S _n ^s denotes the complete n-dimensional indefinite Riemannian space form of constant positive curvature 1 and signature s.     

Kac-Moody group representations and generalization of the Sugawara construction of the Virasoro algebra

We discuss the dynamical structure of the semidirect product of the Virasoro and affine Kac-Moody groups within the framework of a group quantization formalism. This formalism provides a realization of the Virasoro algebra acting on Kac-Moody Fock states which generalizes the Sugawara construction. We also give an explicit construction of the standard Kac-Moody group representations associated with strings on SU(2) and recover, in particular, the renormalization factor of L(z) Research partially supported by the Conselleria de Cultura de la Generalitat Valenciana, the Plan de Formacion del Personal Investigador, the Comision Asesora de Investigacion Cientifica y Tecnica (CAICYT), and The British Council.     

Insights into the structure of cyclohexane from femtosecond degenerate four-wave mixing spectroscopy and ab initio calculations

In this paper, we report the use of femtosecond time-resolved degenerate four-wave mixing rotationally resolved spectroscopy to obtain very accurate structural information on the symmetric top cyclohexane. Apart from highlighting the versatility of this method in determining accurate structures of large and complex molecules without dipole moment, the present study also details the comparison of the experimentally determined rotational constant B(0) with that obtained from high-level ab initio calculations. The theoretical calculations, which were carried out at both the second-order M?ller-Plesset (MP2) and coupled-cluster with single, double, and perturbative triple substitutions [CCSD(T)] levels of theory, also take into account vibrational averaging effects. A detailed investigation of the vibrational averaging effects reveals that the corrections emerge from only the six highly symmetric A(1g) modes, a justification of which is provided by an analysis of these modes.     

A convenient two-step synthesis of 6-methylenesubstituted-4-trichloromethyl-2-methylsulfanyl pyrimidines

This work reports a two-step synthetic strategy to obtain a series of 6-methylenesubstituted-4-trichloromethyl-2-methylsulfanylpyrimidines from the cyclization of 5-bromo-4-methoxy-1,1,1-trichloro-pent-3-en-2-ones with 2-methyl-2-pseudothiourea sulfate, followed by nucleophilic substitution of 6-bromomethyl-4-trichloromethyl-2-methylsulfanylpyrimidine with a series of nucleophiles. Alternative strategies to obtain 6-halomethyl-4-trichloro[fluoro]methyl-2-methylsulfanyl pyrimidines have been addressed.     

Origin of high second- and third-order nonlinear optical response in ammonio/borato diphenylpolyene zwitterions: the remarkable role of polarized aromatic groups

We present a quantum-chemical analysis of the molecular structure and second- and third-order polarizabilities in a series of promising nonlinear optical (NLO) chromophores, the zwitterionic ammonio/borato diphenylpolyenes, R3N+Ph(C=C)nPhB-R3, whose synthesis has been reported recently. The molecular geometries are obtained via MP2/6-31G optimization, while the NLO properties are calculated with the INDO Hamiltonian using the sum-over-states and finite-field real-space methods. The real-space approach allows the direct evaluation of the NLO-active segments of the molecules, while the sum-over-states results illustrate the virtual excitations and charge-transfer pathways that are essential in the NLO response. Both methods highlight the remarkable and unexpected result that it is the strongly polarized phenylene groups that play the key role in generating a high NLO response.