THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Automated separation and measurement of radioxenon for the Comprehensive Test Ban Treaty

A fully automatic radioxenon sampler/analyzer (ARSA) has been developed and demonstrated for the collection and quantitative measurement of the four xenon radionuclides,^131mXe(11.9 d),^133mXe(2.2 d),¹³³Xe(5.2 d), and¹³⁵Xe(9.1 hr), in the atmosphere. These radionuclides are important signatures in monitoring for compliance to a Comprehensive Test Ban Treaty (CTBT). Activity ratios of these radionuclides permit source attribution. Xenon, continuously and automatically separated from the atmosphere, is automatically analyzed by electron-photon coincidence spectrometry providing a lower limit of detection of about 100 μBq/m³. The demonstrated detection limit is about 100 times better than achievable with reported laboratory-based procedures for the short-time collection intervals of interest.     

Synthesis and structures of heterocyclic azidogallanes [(CH3)ClGaN3]4 and [(CH3)BrGaN3]3 en route to [(CH3)HGaN3]x: an inorganic precursor to GaN

The synthesis of [(CH3)ClGaN3]4 (1) with a heterocyclic cyclooctane-like structure and [(CH3)BrGaN3]3 (2) with a trimeric structure has been demonstrated. X-ray structural determinations reveal that 1 and 2 consist of Ga4N4 eight-membered rings and Ga3N3 six-membered rings, respectively, in which the Ga atoms are bridged by the alpha nitrogens of the azide groups. [(CH3)ClGaN3]4 crystallizes in the tetragonal space group P42(1)c with a = 11.017(4) A, c = 8.699(7) A, and Z = 8. [(CH3)BrGaN3]3 crystallizes in the triclinic space group P1 with a = 8.1080(10) A, b = 9.9390(13) A, c = 10.4439(13) A, alpha = 86.069(3) degrees, beta = 86.771(3) degrees, gamma = 80.829(2) degrees, and Z = 6. The reaction of 1 and 2 with LiGaH4 yields [(CH3)HGaN3]x, which is a new low-temperature source of GaN.     

Host-guest interactions template: the synthesis of a [3]catenane

Formation of a [3]catenane containing dibenzo-24-crown ether wheels and a large dipyridiniumethane ring is templated by formation of a host-guest adduct between the [3]catenane and the external crown ether.     

Total synthesis of (-)-laulimalide

(-)-Laulimalide (1), a structurally novel macrolide isolated in trace amounts from marine sponges, promotes abnormal tubulin polymerization and apoptosis in vitro, with a similar mode of action to that of Taxol(R), but with potentially less susceptibility to multidrug resistance. Herein, a flexible and convergent asymmetric synthesis of (-)-laulimalide is described. This synthesis featured a highly diastereoselective Sakurai reaction of 2 with 3 and a regioselective macrolactonization of an unprotected vicinal diol. Laulimalide was synthesized in 25 steps (longest linear; 36 overall) in 3.5% overall yield, providing a uniquely short and efficient route to 1 and its analogues.