Consecutive k-out-of-n systems with maintenance

A consective k-out-of-n system consists of n linearly or cycliccally ordered components such that the system fails if and only if at least k consecutive components fail. In this paper we consider a maintained system where each component is repaired independently of the others according to an exponential distribution. Assuming general lifetime distributions for system's components we prove a limit theorem for the time to first failure of both linear and circular systems.     

Decay of the transient Cu(B)-CO complex is accompanied by formation of the heme Fe-CO complex of cytochrome cbb(3)-CO at ambient temperature: evidence from time-resolved Fourier transform infrared spectroscopy

Time-resolved step-scan Fourier infrared spectroscopy has been used to study the CO-bound cbb(3)-type cytochrome c oxidase from Pseudomonas stutzeri at room temperature. We observe a single band in the FTIR spectrum at 1956 cm(-1) (beta-form). The time-resolved data indicate that upon photolysis, CO is transferred from heme b(3) (nu(CO) = 1956 cm(-1)) to CuB (nu(CO) = 2064 cm(-1)). The decay of the 2065 cm(-1) peak (t(1/2) = 120 +/- 16 ms) and the development of the 1956 cm(-1) peak (t(1/2) = 144 +/- 8 ms ) suggest that formation of the Fe-CO complex is concurrent with the decay of the CuB-CO complex. The intensity ratio of the Fe-CO/CuB-CO (2.15) remains constant for all data points, and thus we conclude that no fraction of CO escapes the binuclear center at 293 K.     

Exponentially divergent trajectories and RRKM behaviour of Ar3 clusters

The rate of exponential divergence of two initially adjacent trajectories has been studied for Ar₂ clusters at low and high energies. It is found that at the dissociation limit energy randomization occurs during two typical vibrational periods. Lifetime distributions for energies not far above the dissociation limit have a random lifetime pattern but highly energized clusters show non-RRKM behaviour     

Water clusters: the (H2O)64 case

Minimum energy structures and dynamics of (H₂O)₆₄ cluster are investigated by molecular dynamics techniques and an empirical potential energy surface. Using plots of the cluster, the oxygen-oxygen distance distribution function, and power spectra, we show the existence of minima with deformed cubic arrangement. These results together with previous calculations on smaller clusters support the conclusion that the cubic type geometries are common among water aggregates.     

Universal frames

For a class of frames we define the notion of a universal element and prove that in the class of all frames of weight less than or equal to a fixed infinite cardinal number τ there are such elements.     

Universality and asymptotics of graph counting problems in non-orientable surfaces

Bender-Canfield showed that a plethora of graph counting problems in orientable/non-orientable surfaces involve two constants tg and pg for the orientable and the non-orientable case, respectively. T.T.Q. Le and the authors recently discovered a hidden relation between the sequence tg and a formal power series solution u(z) of the Painlevé I equation which, among other things, allows to give exact asymptotic expansion of tg to all orders in 1/g for large g. The paper introduces a formal power series solution v(z) of a Riccati equation, gives a non-linear recursion for its coefficients and an exact asymptotic expansion to all orders in g for large g, using the theory of Borel transforms. In addition, we conjecture a precise relation between the sequence pg and v(z). Our conjecture is motivated by the enumerative aspects of a quartic matrix model for real symmetric matrices, and the analytic properties of its double scaling limit. In particular, the matrix model provides a computation of the number of rooted quadrangulations in the 2-dimensional projective plane. Our conjecture implies analyticity of the O(N)- and Sp(N)-types of free energy of an arbitrary closed 3-manifold in a neighborhood of zero. Finally, we give a matrix model calculation of the Stokes constants, pose several problems that can be answered by the Riemann-Hilbert approach, and provide ample numerical evidence for our results.     

Shape resonances in slow electron scattering by aromatic molecules. I. Anthraquinone derivatives

A series of anthraquinone (C(14)O(2)H(8)) derivatives has been studied by means of electron capture negative ion mass spectrometry (ECNI-MS), photoelectron spectroscopy (PES), and AM1 quantum chemical calculations. Mean lifetimes of molecular negative ions M(-.) (MNI) have been measured. The mechanism of long-lived MNI formation in the epithermal energy region of incident electrons has been investigated. A simple model of a molecule (a spherical potential well with the repulsive centrifugal term) has been applied for the analysis of the energy dependence of cross sections at the first stage of the electron capture process. It has been shown that a temporary resonance of MNI at the energy approximately 0.5 eV corresponds to a shape resonance with lifetime 1-2.10(-13) s in the f-partial wave (l = 3) of the incident electron. The next resonant state of MNI at the energy approximately 1.7 eV has been associated with the electron excited Feshbach resonance (whose parent state is a triplet npi* transition). In all cases the initial electron state of the MNI relaxes into the ground state by means of a radiationless transition, and the final state of the MNI is a nuclear excited resonance with a lifetime measurable on the mass spectrometry timescale. Copyright 1999 John Wiley & Sons, Ltd.     

Analytical ab initio potential-energy surfaces for the ground and the first singlet excited states of HeH2

Analytical potential-energy surfaces have been constructed for the ground and the first excited states of HeH₂. The functions fit ab initio MRD CI calculations with standard deviations of 0.05 and 0.13 eV for the ground and the excited surface respectively. Classical trajectory calculations for collisions of ⁴Hc with HD(B ¹Σ_u⁺, υ = 3, J = 2) at the temperature T = 297 K yields the electronic quenching cross section σ_Q = 6.5 A² and the vibrational cross section σ_3→2 = 3.8 A². The results are in qualitative agreement with the experimental values of Fink, Akins and Moore.