Jacobi Fields Along Harmonic 2-Spheres in CP2 are Integrable

The paper shows that any Jacobi field along a harmonic map fromthe 2-sphere to the complex projective plane is integrable (thatis, is tangent to a smooth variation through harmonic maps).This provides one of the few known answers to the problem ofintegrability, which was raised in different contexts of geometryand analysis. It implies that the Jacobi fields form the tangentbundle to each component of the manifold of harmonic maps fromS² to CP² thus giving the nullity of any such harmonic map;it also has a bearing on the behaviour of weakly harmonic E-minimizingmaps from a 3-manifold to CP² near a singularity and the structureof the singular set of such maps from any manifold to CP².     

Synthesis and NKT cell stimulating properties of fluorophore- and biotin-appended 6"-amino-6"-deoxy-galactosylceramides

Alpha-galactosylceramides are potent stimulators of human T cells. Stimulation occurs through binding of the glycolipids by CD1d, presentation to T cells, and formation of a CD1d-glycolipid-T cell receptor complex. To facilitate the elucidation of the structural features of glycolipids necessary for T cell stimulation, alpha-galactosylceramides have been prepared with small molecules appended at the C6 position of the sugar. The appended molecules do not significantly influence the abilities of the glycolipids to stimulate T cells. [reaction: see text]     

Use of calculated centrifugal distortion constants (Dν, Hν, Lν and Mν) in the analysis of the B ← X system of I2

Fourier spectroscopy measurements of 14 703 lines from the B-X band system of I₂ are analyzed using centrifugal distortion constants calculated from RKR curves by the perturbation theory method of Hutson [J. Phys. B14, 851–857 (1981)]. Only vibrational and rotational constants are varied in the least-squares fits, with the centrifugal distortion constants fixed at the calculated values. The fit obtained in the present work is as good as when the centrifugal distortion constants are treated as independent parameters, but the molecular constants obtained are physically more meaningful because the statistical correlation between parameters is reduced. The analysis includes B-state vibrational levels up to v′ = 72, which is bound by only 0.5% of the well depth; the method used for calculating centrifugal distortion constants remains reliable even this close to dissociation. It is found that centrifugal distortion constants up to fifth order make significant contributions to the observed line positions.     

Favorskii-type rearrangement of α-chloro ketimines

The first examples of the Favorskii-type rearrangement of α-monochloro ketimines are reported. The regiospecific opening of the intermediate cyclopropylideneamines parallels the opening of cyclopropanones under Favorskii-conditions.     

Sodium: Dibenzo-30-crown-10 aggregates in solution: Na-23 NMR study

(n + 1):n sodium:dibenzo-30-crown-10 complexes are formed in nitromethane solutions. A model based on the coexistence in solution of 1:1, 2:1 and 3:2 complexes can account for the observed Na-23 chemical shifts, transverse and longitudinal relaxation rates. Logarithms of the equilibrium constants of formation at (25±1)°C are (2.1±0.3) and (2.5±0.3) for the 2:1 and 3:2 complexes respectively. The characteristic Na-23 relaxation rates and chemical shifts of the aggregated complexes are compatible with a structure of ion pairs linked by the crown ether.     

A multi-criteria framework as a decision support system for urban growth management applications: Central city redevelopment

The paper introduces a decision support system based on a multi-criteria framework that integrates several socio-economic, physical planning and urban design processes recently used in the U.S. for growth management of central city redevelopment. It formalizes and operationalizes the concept of the ‘critical coalition’, i.e. user groups representative of the community's interests who share common perceived values, objectives and problems within an urban setting. This critical coalition provides the decision model with the socio-economic qualitative input to establish representative priorities and importance weights, and to provide the political base for the implementation of policy actions. The framework is applied to establish locational suitability of development or redevelopment actions within a central city. This application is illustrated with examples from a pilot study to establish the suitability of residential infill within the central business district of the City of Columbus, Ohio.     

Kinetic versus thermodynamic access to imidazoisoindolones, benzimidazoisoindolones, and [1,4]diazepinoisoindolones: intramolecular nitrogen and π-aromatic trapping of N-acyliminium cation

Efficient assembly of substituted imidazo[2,1-a]isoindolones I is reported from suitable α,β-diamine IV (or corresponding β-nitroamine) and phthalic anhydride (1) in a three- or four-step sequence in good yields. The key step of this methodology is based on an intramolecular α-aza-amidoalkylation of the N-acyliminium species. Furthermore, when R₂ is an aromatic moiety a competing α-amidoalkylation took place and imidazo[2,1-a]isoindolones (or benzimidazo[2,1-a]isoindolones) I and/or isoindolo[1,4]benzodiazepines III were obtained under kinetic or thermodynamic control. The chemoselectivity of these transformations is also discussed.     

Theory and experiment of Fourier-Bessel field calculation and tuning of a pulsed wave annular array

A one-dimensional (1D) Fourier-Bessel series method for computing and tuning (beamforming) the linear lossless field of flat pulsed wave annular arrays is developed and supported with both numerical simulation and experimental verification. The technique represents a new method for modeling and tuning the propagated field by linking the quantized surface pressure profile to a known set of limited diffraction Bessel beams propagating into the medium. This enables derivation of an analytic expression for the field at any point in space and time in terms of the transducer surface pressure profile. Tuning of the field then also follows by formulating a least-squares design for the transducer surface pressure with respect to a given desired field in space and time. Simulated and experimental results for both field computation and tuning are presented in the context of a 10-ring annular array operating at a central frequency of 2.5 MHz in water.     

Application of cylindrical near-field acoustical holography to the visualization of aeroacoustic sources

The purpose of this study was to develop methods for visualizing the sound radiation from aeroacoustic sources in order to identify their source strength distribution, radiation patterns, and to quantify the performance of noise control solutions. Here, cylindrical Near-field Acoustical Holography was used for that purpose. In a practical holographic measurement of sources comprising either partially correlated or uncorrelated subsources, it is necessary to use a number of reference microphones so that the sound field on the hologram surface can be decomposed into mutually incoherent partial fields before holographic projection. In this article, procedures are described for determining the number of reference microphones required when visualizing partially correlated aeroacoustic sources; performing source nonstationarity compensation; and applying regularization. The procedures have been demonstrated by application to a ducted fan. Holographic tests were performed to visualize the sound radiation from that source in its original form. The system was then altered to investigate the effect of two modifications on the fan's sound radiation pattern: first, leaks were created in the fan and duct assembly, and second, sound absorbing material was used to line the downstream duct section. Results in all three cases are shown at the blade passing frequency and for a broadband noise component. In the absence of leakage, both components were found to exhibit a dipole-like radiation pattern. Leakage was found to have a strong influence on the directivity of the blade passing tone. The increase of the flow resistance caused by adding the acoustical lining resulted in a nearly symmetric reduction of sound radiation.