The molecular origins of the two-dimensional Raman spectrum of an atomic liquid. II. Instantaneousnormal-mode theoryThe anharmonic features of the short-time dynamics of fluids: The time evolution and mixing of instantaneous normal modes Since the sharply varying forces that control the arrangement of molecules in liquids are themselves intrinsically anharmonic, the natural assumption would be that any picture that regarded molecular motion as harmonic would be at best a rough phenomenological guide. This expectation is, in fact, not a correct one. While the packing forces that determine liquid structure are indeed strongly anharmonic, the short-time displacements and librations that molecules execute are actually quite harmonic. It is possible to show rigorously that, for short enough (subpicosecond) time intervals, the dynamics of liquids is governed by a set of independent, collective, harmonic modes-the instantaneous normal modes of the liquid. In this paper we illustrate this fact by predicting the translational and rotational dynamics of a model diatomic liquid using the instantaneous normal modes computed by simulation. When compared to the exact molecular-dynamics results for the same autocorrelation functions, we find that perfect agreement is maintained only for very short times, but that if one removes the artificial runaway dynamics caused by the imaginaryfrequency modes, reasonable levels of agreement are maintained for much longer time intervals. We also investigate the nature of the coupled translational-rotational motion by looking at the relevant translational and rotational projections of the modes. We find that the negative (backscattering) regions of both the translational-and rotational-velocity autocorrelation functions can be understood in terms of these same instantaneous harmonic modes. 8522

The data of this pilot study suggest a better than 80% efficacy of the new 7-day levofloxacin triple therapy, which is within the range of the French triple therapy in patients with MET- and CLA-susceptible strains. The data suggest that the new levofloxacin triple therapy may also be an option in patients with MET- and CLA-resistant H. pylori strains.

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IntroductionThis paper will prove the following assertion: If M is a compact manifold of While this fact may be of some interest in its own right it seems to us that the techniques used to prove it have independent interest.In Section 1 we explain in detail the meaning of the above assertion.In Section 2 we show how to characterize the cut locus C(p, ~) in terms of the behavior of the energy function E(7) defined on the space f2 of piecewise smooth paths starting at p. Namely, we think of f2 as fibred over M and then [ [E(e) l fibre over x] has a degenerate minimum or at least two minima}. C(p, ~) = {x~MThe idea now is to analyze the behavior of E(c~) on f2 as e is varied. Unfortunately 12 itself does not have the structure of a smooth manifold, so in Section 3 we show how to construct a finite dimensional model B of f2 and functions H(c~): B~lR which correspond to E(c 0 on f2 so that B is fibred over M and the above characterization of C(p,c~) still holds using H(e) instead of E(e)