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.     

Palladium-catalyzed C-N bond formation: synthesis of 1-aryl-1H-pyrazoles from β-bromovinyl aldehydes and arylhydrazines

Cyclic and acyclic β-bromovinyl aldehydes are cyclized with an array of arylhydrazines in toluene at 125 °C in the presence of a palladium catalyst and a phosphorus chelating ligand together with NaO^tBu to give 1-aryl-1H-pyrazoles in moderate to good yields.     

Conversion estimates for gas-solid reactions: Improved estimates for irreversible systems

Solid conversion has been of much interest to research workers and the Cumulative Gas Concentration Method (CGCM) has been developed to provide bounds for the reactant solid in irreversible systems having power-law type kinetics. This CGCM is used in conjunction with the Pseudo-Steady-State (PSS) assumption and these bounds appear to be good under certain conditions and for long times.

In this work, the PSS condition is not assumed when deriving the bounds on the cumulative gas concentration and the effect of the inclusion of the transient part is analysed. A technique, based on an iterative scheme incorporating the CGCM, is developed to provide improved estimates for the reactant solid.     

Estimation of eardrum acoustic pressure and of ear canal length from remote points in the canal

Sound pressure distributions in the human ear canal, whether unoccluded or occluded with ear molds, were studied using a probe tube technique. On average, for frequencies below 6 kHz, the measuring probe tube had to be placed within 8 mm of the vertical plane containing the top of the eardrum (TOD), determined optically, in order to obtain sound pressure magnitudes within 6 dB of "eardrum pressure." To obtain that accuracy in all of the eight subjects studied, the probe had to be within 6 mm of the TOD. Since probe location relative to the drum has to be known, a purely acoustic method was developed which can be conveniently used to localize the probe-tip position, utilizing the standing wave property of the sound pressure in the ear canal. The acoustically estimated "drum location" generally lay between the optically determined vertical planes containing the TOD and the umbo. On average, the "drum location" fell 1 mm medial to the TOD. Of the 32 estimates made acoustically in various occluded and unoccluded conditions in 14 subjects, 30 estimates lay within a +/- 2-mm range of this average.     

Optimal birth control of population dynamics

The authors studied optimal birth control policies for an age-structured population of McKendrick type which is a distributed parameter system involving 1st order partial differential equations with nonlocal bilinear boundary control. The functional analytic approach of Dubovitskii and Milyutin is adopted in the investigation. Maximum principles for problems with a free end condition and fixed final horizon are developed, and the time optimal control problems, the problem with target sets, and infinite planning horizon case are investigated.     

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.