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.     

Continuous approximation schemes for stochastic programs

One of the main methods for solving stochastic programs is approximation by discretizing the probability distribution. However, discretization may lose differentiability of expectational functionals. The complexity of discrete approximation schemes also increases exponentially as the dimension of the random vector increases. On the other hand, stochastic methods can solve stochastic programs with larger dimensions but their convergence is in the sense of probability one. In this paper, we study the differentiability property of stochastic two-stage programs and discuss continuous approximation methods for stochastic programs. We present several ways to calculate and estimate this derivative. We then design several continuous approximation schemes and study their convergence behavior and implementation. The methods include several types of truncation approximation, lower dimensional approximation and limited basis approximation.His work is supported by Office of Naval Research Grant N0014-86-K-0628 and the National Science Foundation under Grant ECS-8815101 and DDM-9215921.His work is supported by the Australian Research Council.     

Tuning the optical properties of fluorinated indolylfulgimides

Photochromic fluorinated indolylfulgides have been identified as potential candidates for a wide range of applications including optical switches, photoregulators of biological processes, and optical memory media. In humid environments or biological systems, hydrolytic stability is essential. In an effort to improve hydrolytic stability, a series of indolylfulgimides has been synthesized from a parent trifluoromethyl-substituted indolylfulgide. The nitrogen of the succinimide moiety is linked to either a dimethyl amino or one of seven substituted phenyl groups. The phenyl groups feature substituents with increasing electron-withdrawing ability. The spectral characteristics of each compound have been examined, revealing that the wavelength absorption maxima of each form increases with increasing electron-withdrawing ability of the substituted N-phenyl ring. The quantum yields of the photoreactions have been determined with the N-(phenyl)fulgimide showing a ring closure value of nearly 0.30 in toluene. In addition, the hydrolytic, thermal, and photochemical stabilities of each compound have been measured. The fulgimides exhibit at least a 200-fold enhancement of hydrolytic stability for the Z-form and over a 1000-fold enhancement for the C-form in comparison to the same form of the parent fulgide. The N-(2,3,5,6-tetrafluoro-4-trifluoromethylphenyl)fulgimide can undergo up to 3000 photochemical cycles (coloration followed by bleaching) before losing 20% of its initial absorbance at photostationary state.     

Electronic spectra of 12-S-CIS conformationally locked retinals

The electronic absorption spectra of the four new 12-$\text{s}$-$\text{cis}$-locked retinals (1a–1d) bearing 7-$\text{trans}$, 11-$\text{trans}$ double bond geometries are described and compared with those of analogous 7-$\text{trans}$, 11-$\text{cis}$-geometries (1e–1h) and parent retinals (2a-h).