Ionic-charge dependence of the intermolecular coulombic decay time scale for aqueous ions probed by the core-hole clock

Auger electron spectroscopy combined with theoretical calculations has been applied to investigate the decay of the Ca 2p core hole of aqueous Ca(2+). Beyond the localized two-hole final states on the calcium ion, originating from a normal Auger process, we have further identified the final states delocalized between the calcium ion and its water surroundings and produced by core level intermolecular Coulombic decay (ICD) processes. By applying the core-hole clock method, the time scale of the core level ICD was determined to be 33 ± 1 fs for the 2p core hole of the aqueous Ca(2+). The comparison of this time constant to those associated with the aqueous K(+), Na(+), Mg(2+), and Al(3+) ions reveals differences of 1 and up to 2 orders of magnitude. Such large variations in the characteristic time scales of the core level ICD processes is qualitatively explained by different internal decay mechanisms in different ions as well as by different ion-solvent distances and interactions.     

Upper tails for counting objects in randomly induced subhypergraphs and rooted random graphs

General upper tail estimates are given for counting edges in a random induced subhypergraph of a fixed hypergraph ℋ, with an easy proof by estimating the moments. As an application we consider the numbers of arithmetic progressions and Schur triples in random subsets of integers. In the second part of the paper we return to the subgraph counts in random graphs and provide upper tail estimates in the rooted case.     

Some Remarks on the Combinatorics of ISn

\noindent We describe the asymptotic behavior of the cardinalities of the finite symmetric inverse semigroup IS_n and its endomorphism semigroup. This is applied to show that the ratio |IS_n|/|End(IS_n)| is asymptotically 0, answering a question of Schein and Teclezghi. We also apply our results to compute the distributions of elements from IS_n with respect to certain combinatorial properties, and to compute the generating functions for |IS_n| and for the number of nilpotent elements in IS_n.     

Superconductivity in ultrathin films II. Structure in tunneling curves

Additional structure is seen in conductance versus voltage curves when electrons are tunneled into very thin superconducting films. This peak like structure has been detected in several materials; it is observed at multiples of the energy gap above the main conductance maximum. The peak amplitude is very thickness dependent. At roughly half the transition temperature of the ultrathin film the amplitude goes to zero within a narrow temperature range. Effects of magnetic field, an overlay of a non-superconductor, and annealing are less pronounced. The most probable explanation seems to be a model where the tunneling rate is stimulated whenever the relaxation and recombination phonon frequencies equal.Supported by the Swedish Natural Science Research Council.     

Convergence of Discrete Snakes

The discrete snake is an arborescent structure built with the help of a conditioned Galton-Watson tree and random i.i.d. increments Y. In this paper, we show that if and , then the discrete snake converges weakly to the Brownian snake (this result was known under the hypothesis ). Moreover, if this condition fails, and the tails of Y are sufficiently regular, we show that the discrete snake converges weakly to an object that we name jumping snake. In both case, the limit of the occupation measure is shown to be the integrated super-Brownian excursion. The proofs rely on the convergence of the codings of discrete snake with the help of two processes, called tours.     

Log-normal size distributions of ultrafine metal particles

We have produced particles with median diameters well below 5 nm of Al, Fe, Co and Sn, using inert gas evaporation. The logarithm of the particle volume has a Gaussian distribution which can be explained by a theoretical model for coalescence of liquid particles. The standard deviations of these log-normal distributions, as inferred from electron microscopy, always lie close to a common value regardless of the kind of metal or method of evaporation.     

Perfect matchings in random s-uniform hypergraphs

Let E = {X₁, X₂…, X_m} where the X_i ? V for 1 ≤ i ≤ m are distinct. The hypergraph G = (V, E) is said to be s-uniform if |X₁| = s for 1 ≤ i ≤ m. A set of edges M = {X_i : i ? I } is a perfect matching if (i) i ≠ j ? I implies X_i ∩ X_i = 0, and (ii) ∪_i?I X_i = V. In this article we consider the question of whether a random s-uniform hypergraph contains a perfect matching. Let s ≥ 3 be fixed and m/n^4/3 → ∞. We show that an s-uniform hypergraph with m edges chosen uniformly from [74] contains a perfect matching with high probability. This improves an earlier result of Schmidt and Shamir who showed that m/n^3/2 → ∞ suffices. © 1995 John Wiley & Sons, Inc.     

The asymptotic distributions of incomplete U-statistics

Summary An incomplete U-statistic is obtained by sampling the terms of an U-statistic. This paper derives the asymptotic distribution (if the variance is finite). Depending on the number of sampled terms, the resulting distribution is either the same as for the U-statistic, a normal distribution, or something intermediate. Also the case of a non-random sampling of the terms is treated. As an example, a non-parametric test of the independence of two circular random variables is studied. The results are generalized to generalized U-statistics.