Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.     

Mössbauer spectroscopic study of ferrocene derivatives in the adsorption and liquid-crystalline states

Mössbauer spectra of ferrocene derivatives in the solid, adsorption and liquidcrystalline states were measured at temperatures ranging from 78 to 423 K. The peak intensities of the Mössbauer spectra of ferrocene derivatives adsorbed on silica gel decreased markedly with an increase in temperature. The Mössbauer absorption of [4-(4-methoxyphenoxycarbonyl)-phenoxycarbonyl]alkyl 4-ferrocenylbenzoate at 295 K during the cooling process was observed in what was assumed to be the liquid-crystalline state.     

Hybrid optical resonator type laser proposed for direct coupling into optical fiber

Combining one stable resonator with a concave mirror and a coupling-hole plane mirror, and another unstable resonator having a concave mirror and a convex mirror, a new hybrid optical resonator type laser has been proposed by overlapping the concave mirror as a common one and fitting the convex mirror exactly to the coupling-hole. Using theABCD law, the so-called g-parameters are first found for beam confinement. Then, based on the eigen-equation, the field distribution on the plano-convex mirror is obtained with the g-parameters above. Knowing this field distribution results in an effective transmittanceG _{e e}. Finally, the ratio of the inner convex to outer plane mirror radii can be determined for an optimum coupling in both the limiting cases of homogeneously and inhomogeneously broadened gain media. Some numerical examples will also be given for a CO₂ laser having the proposed hybrid resonator.     

Crystal and molecular structure of 6-0-acetylgrayanotoxin III

The crystal and molecular structure of a grayanotoxin III derivative, 6-0-acetylgrayanotoxin III is presented. The crystal is orthorhombic, space group P2₁2₁2₁, witha=15.582(3),b=21.304(3),c=6.339(3)Å,V=2104(1) ų Z=4. The structure was solved by direct methods and refined by full matrix least-squares methods to a finalR=0.047 for 1763 independent reflections withF ₀>3 (F ₀) The molecule is based on a tetracyclic structure consisting of two five-membered, one six-membered, and one seven-membered ring with various conformations.