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.     

Magnetic resonance imaging (MRI) and pathophysiology of the rat kidney in streptozotocin-induced diabetes.

Proton magnetic resonance imaging was performed on rats before induction of diabetes with streptozotocin (STZ) and at 2 and 12 days postinduction. Images revealed an increase in maximal longitudinal and axial dimensions of the kidneys at 2 days and a further increase at 12 days. Similarly, an increase in the size of the remaining kidney was seen in a rat which underwent uninephrectomy as a positive control. Two major differences were observed between the kidney undergoing compensatory hypertrophy and those developing diabetic nephropathy: (i) Expansion of the renal vasculature was seen only in images of the diabetic rat; (ii) A loss in conspicuity of the normal corticomedullary junction was seen in the T2-weighted images of the diabetic rat but not in the uninephrectomized rat. Histologic examination revealed that the medulla increased to a size greater than the cortex during diabetic nephropathy whereas the medullary volume was less than that of the cortex during compensatory hypertrophy. In vitro T1 relaxation times in cortex, outer medulla and inner medulla of kidneys from control rats were measured and compared with the same respective regions in diabetic rats. When these values were correlated with tissue water content, a linear increase in relaxation rate versus percent water content from cortex to inner medulla was found in the control kidneys, but this correlation was absent in diabetic nephropathy. These studies demonstrate that MRI is an effective noninvasive tool for studying the course of renal hypertrophy and hydration changes in the development of renal disease in STZ-induced diabetes in the rat.     

Synthesis of an isomer of the germacranolide isoaristolactone

Photocycloadditlon of (+)-isoplperltenone and cyclobutene-1-carboxylic acid gives an adduct which upon reduction with NaCNBH₃ followed by thermolysis yields an isomer of isoaristolactone in an overall yield of 26%.     

Ab initio characterization of several states of nitroxylium (NO). Comparison of fragmentation energies of nitroxylium,nitroxyl (NO3), and nitrate

Ab initio calculations have been performed at the self-consistent field (HF) level, and its perturbative extensions up to fourth-order (MPn), for several electronic states of nitroxylium (NO) as well as for a large number of reference species. Geometries are optimized at the HF/DZ and HF/DZP levels (double zeta and double zeta plus polarization bases). The ground state is found to be the D_3h ¹A₁′ state, with the C_2v ¹A₁ (closed Y) state higher by 0.94 eV. The relationship between adding electrons or oxygen atoms to NO⁺ and NO is explored, especially in relation to fragmentation energies of NO (q = 0 or 1). A comparison is drawn between NO and two isoelectronic species, CO₃ and C(CH₂)₃, where no surprises are found.