Forced, weakly nonlinear oscillations of a two degree-of-freedom autoparametric vibration absorber system are studied for resonant excitations. The method of averaging is used to obtain first-order approximations to the response of the system. A complete bifurcation analysis of the averaged equations is undertaken in the subharmonic case of internal and external resonance. The "locked pendulum" mode of response is found to bifurcate to coupled-mode motion for some excitation frequencies and forcing amplitudes. The coupled-mode response can undergo Hopf bifurcation to limit cycle motions, when the two linear modes are mistuned away from the exact internal resonance condition. The software packages AUTO and KAOS are used and a numerically assisted study of the Hopf bifurcation sets, and dynamic steady solutions of the amplitude or averaged equations is presented. It is shown that both super-and sub-critical Hopf bifurcations arise and the limit cycles quickly undergo period-doubling bifurcations to chaos. These imply chaotic amplitude modulated motions for the system.

The interaction of iron atoms with oxygen molecules and atoms in an argon matrix over the temperature range from 15 to 40 K has been examined. The iron atoms are produced by a hollow-cathode sputtering device. Iron-oxygen complexes are identified by oxygen-18 isotope shifts in the infrared spectra, annealing behavior, and comparison to known compounds. A band at 956 cm-' is assigned to the 0-0 stretching frequency of a side-bonded FeOt structure, an assignment at variance with current literature. A band at 872 cm-l is assigned to FeO while a band at 969 cm-' is assigned to an Fe-O stretching mode of linear 0-Fe-O. A band at 946 cm-l is tentatively assigned to metastable bent 0-Fe-O species which disappears upon annealing the matrix at 25 K. Oxygen atoms are formed on the surface of the matrix during its formation by the reaction of O2 molecules with excited argon atoms from the hollow-cathode discharge. The verification of the existence of a stable Fe02 complex which still contains an 0-0 bond lends credence to the proposal of a molecularly adsorbed O2 precursor state in iron oxidation. IntroductionThe interaction of oxygen with Fe atoms is of interest because of its bearing on such diverse processes as corrosion of structural metals and oxygen transport in biological systems.

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Nonlinear flexural vibrations of a rectangular plate with uniform stretching are studied for the case when it is harmonically excited with forces acting normal to the midplane of the plate. The physical phenomena of interest here arise when the plate has two distinct linear modes of vibration with nearly the same natural frequency. It is shown that, depending on the spatial distribution of the external forces, the plate can undergo harmonic motions either in one of the two individual modes or in a mixed-mode. Stable single-mode and mixed-mode solutions can also coexist over a wide range in the amplitudes and frequency of excitation. For low damping levels, the presence of Hopf bifurcations in the mixed-mode response leads to complicated amplitude-modulated dynamics including period doubling bifurcations, chaos, coexistence of multiple chaotic motions, and crisis, whereby the chaotic attractors suddenly disappear and the plate resumes small amplitude harmonic motions in a single-mode. Numerical results are presented specifically for 1:1 resonance in the (1, 2) and (3, 1) plate modes.

Dietary fat enhances prostate cancer progression, possibly by suppressing GPx3 expression and increasing proliferation of prostate intraepithelial neoplasia (PIN) epithelial cells.