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.     

On the convergence of cross decomposition

Cross decomposition is a recent method for mixed integer programming problems, exploiting simultaneously both the primal and the dual structure of the problem, thus combining the advantages of Dantzig—Wolfe decomposition and Benders decomposition. Finite convergence of the algorithm equipped with some simple convergence tests has been proved. Stronger convergence tests have been proposed, but not shown to yield finite convergence.In this paper cross decomposition is generalized and applied to linear programming problems, mixed integer programming problems and nonlinear programming problems (with and without linear parts). Using the stronger convergence tests finite exact convergence is shown in the first cases. Unbounded cases are discussed and also included in the convergence tests. The behaviour of the algorithm when parts of the constraint matrix are zero is also discussed. The cross decomposition procedure is generalized (by using generalized Benders decomposition) in order to enable the solution of nonlinear programming problems.     

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.     

Improved description of the Van der Waals interaction in physisorption

The attractive interaction between an atom and a metal surface is calculated, taking into account the d-electron contribution to the metal response, together with an atomic polarizability going beyond the dipole approximation. A numerical calculation is presented for helium on noble metals, giving a slightly deeper physiosorption well compared to the “standard” treatment.     

Levels and transitions in126Te

The decay of¹²⁶Sb to¹²⁶Te is studied by use of Ge(Li) detectors in singles and coincidence arrangements. The gamma-gamma directional correlations of six cascades are measured. A level scheme is constructed where all transitions observed are located. The characteristics of several of the levels are assigned, on basis of the logft values deduced and the directional correlation results. Mixing ratios are deduced for three transitions. From the comparison of the relative intensities ofE1 andE2 transitions depopulating the same levels, threeE1 transitions are concluded to be strongly retarded.     

Nonisotropic L-conversion-electron — X-ray directional correlations in160Dy

The directional correlations betweenL-conversion electrons andL x-rays have been measured. The electrons were emitted in the 86.78keV 2⁺→0⁺ transition in¹⁶⁰Dy, in the decay of¹⁶⁰Tb. The experimental results areA ₂₂(e _L -x _Li )=0.085 (22),A ₂₂(e _L -x _Lα )=0.0066 (29),A ₂₂(e _L -x _Lβ )=0.0000 (27), andA ₂₂(e _L -x _Lγ )=0.0096 78). These results are in disagreement with published theoretical values. It is suggested that the discrepancy is due to a phase inconsistency in the internal conversion matrix elements and there is good agreement withA ₂₂ values calculated in this work.     

Core-electron spectroscopy of alkaline-earth and transition-metal ions in solution

Core-electron spectra of alkaline-earth and transition-metal ions in solution have been recorded. Solvation energies for the core-ionized species are derived using thermodynamic cycles which involve the free-ion to dissolved-ion binding energy shifts. The distinction between “soft” and “hard” ion behaviour is discussed in relation to the solvation energies and multi-line features in the transition-metal core spectra.     

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.