Let Rn = max0≤j≤n Sj − Sn be a random walk Sn reflected in its maximum. We give necessary and sufficient conditions for finiteness of passage times of Rn above horizontal or certain curved (power law) boundaries. Necessary and sufficient conditions are also given for the finiteness of the expected passage time of Rn above linear and square root boundaries. 2000 MSC Subject Classifications: prim...

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The paper presents a general theory of coupling of eigenvalues of complex matrices of arbitrary dimension depending on real parameters. The cases of weak and strong coupling are distinguished and their geometric interpretation in two and three-dimensional spaces is given. General asymptotic formulae for eigenvalue surfaces near diabolic and exceptional points are presented demonstrating crossin...

Spectroscopic constants for the ground and low-lying excited electronic states of the Ga2 molecule have been studied using MRSDCI and MRCPA methods with an extensive basis set of Gaussian-type functions. In this study, we are going to present spectroscopic constants and potential energy curves for the ground Pu and the excited Sg , Sg , Pu, Dg, …2†Sg and Su states, in which electron correlation...

Above a critical temperature, a supported single domain ferromagnetic particle responds to an applied magnetic field as if it were a paramagnet with a very large spin. Its average magnetization is given by the Langevin equation as expected from simple thermodynamic considerations. The average magnetization of an ensemble of unsupported ferromagnetic clusters also approximately follows the Lange...

We present a review of rigorous mathematical results about non– adiabatic transitions in molecular systems that are associated with avoided crossings of electron energy level surfaces. We then present a novel numerical technique for studying these transitions that is based on expansions in semiclassical wavepackets.

We consider asymptotic properties of curve-crossing counts of linear processes and nonlinear time series by curves. Central limit theorems are obtained for curve-crossing counts of short-range dependent processes. For the long-range dependence case, the asymptotic distributions are shown to be either multiple Wiener–Itô integrals or integrals with respect to stable Lévy processes, depending on ...

We predict a double-resonant feature in the magnetic field dependence of the phonon-mediated longitudinal conductivity σxx of a two-subband quasi-twodimensional electron system in a quantizing magnetic field. The two sharp peaks in σxx appear when the energy separation between two Landau levels belonging to different size-quantization subbands is favorable for acoustic-phonon transitions. One-p...