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.     

Unstable minimal surfaces and Heegaard splittings

Partially supported by NSF grant DMS-8701746     

Parity violation in the 17/2−–17/2+ doublet in93Tc

The parity-violating mixing of the 17/2^– and 17/2⁺ levels in⁹³Tc nuclei, polarized by the tilted multifoil interaction, was measured by the observation of the forward-backward-ray asymmetry. The nuclear polarization, induced by the tilted multifoils, was measured directly for the neighboring^88,90Zr isomers. The forward to backward asymmetry was determined to be A=(2.5±2.1) 10^–3 which implies a parity violating matrix element ¦H _PV )¦=(4.0±3.7)meV.     

Charge reversal of three alkylamide ions: Free nitrenium ions

The methylnitrenium, ethylnitrenium and dimethylnitrenium ions are prepared by charge reversal collisional activation (CR CA) of the corresponding negative ions; their collisional activation mass spectra are shown to support the assigned structures. MINDO/3 energies are used to evaluate relative energies of [CH₄N]⁺ and [C₂H₆N]⁺ isomers, and to determine whether unstable forms rearrange spontaneously to stable ones. As in other examples, charge reversal here generates cations that do not exist in an energy well, but their transient existence is established because their fragmentation is more rapid than their rearrangement to a more stable form.     

Thermisches Verhalten von Caesiumchloroferraten(III) und Caesiumchloroferrat(III)-Hydraten. II. Die Rehydratation der Zersetzungsprodukte von Cs3[FeCl6] – Eine ramanspektroskopische Untersuchung unter definierter Wasserdampfatmosphäre [1]

The Thermal Behaviour of Caesiumchloroferrates(III) and Caesiumehloroferrate(III) Hydrates. II. The Rehydration of Decomposition Products of Cs₃[FeCl₆] — A Raman Spectroscopic Study under Definite Atmosphere of Water Vapour Cs₃[FeCl₆] formed by dehydration of Cs₃[FeCl₆] · H₂O at about 160°C does not change at normal atmosphere within 3 till 4 hours. Rehydration under the vapour pressure of the eliminated water yields the monohydrate in nearly the same time. In the same manner rehydration of the solid mixture of Cs[FeCl₄] and 2 CsCl formed by thermal decomposition of the metastable Cs₃[FeCl₆] (280°C) produces the intermediates Cs₃[Fe₂Cl₉] and Cs₂[Fe(H₂O)Cl₅] in mixtures with CsCl and, finally, Cs₃[FeCl₆] · H₂O. The formation of Cs₃[Fe₂Cl₉] from Cs[FeCl₄] and CsCl is accelerated by water. The reaction cycle has been studied using Raman and IR spectroscopy. The results will be discussed with respect to thermoanalytical data.     

Arseniodochloride

Arsenic Iodochlorides The immediate formation of the ternaric halides in equilibrium is observed if AsCl₃ and AsI₃ are mixed in an inert solvent (CCl₄, CS₂). By photometric measurements at 381 nm the concentration of AsI₃ should be determined in the mixture while c was determined by gaschromatography. A new absorption band at 345 nm is assigned to arsenic iodochlorides. As from the calculated equilibrium constants follows the preferred formation of AsICl₂, the new absorption band at 345 nm is assigned to this compound.