A wavelength-selective directional coupler based on a boundary-condition-modulation grating: proposal,theory, and preliminary results

A nonconventional wavelength-selective grating-assisted vertical coupler is proposed and analysed. Its novelty consists in the grating position: neither between nor above the waveguide cores, but in a lateral region. Analytic and numerical results indicate that, for devices that are not yet optimized, frequency selectivity and/or device length are at least comparable with those of conventional grating-assisted filter-couplers. Potential advantages of the new device, in terms of performance and of manufacturing technology, are discussed.     

On the geometrical structure of Euler-Lagrange equations

Summary We show that the Euler-Lagrange operator and the Poincaré-Cartan form arise in a very simple and natural way from the contact structure of the second order jet space, in a purely differential context, without any reference to a variational problem. By the way we obtain an intrinsic expression of the Euler-Lagrange operator.     

Microcanonical and canonical distributions and finite exchangeable random processes

A pure probabilistic approach to Gibbs' distributions is given, starting from the notion of finite exchangeable random process. The differences between bosons, fermions, and classical particles are ascribed to different values of correlation. The relationship between exchangeability and constraints on the energy distribution is investigated.     

The lattice automorphisms of simple algebraic groups over\bar F_2

We prove that if u is a unipotent element of a connected reductive algebraic group G over , there exists an involution σ in G such that σuσ=u⁻¹. We use this result to determine the group of lattice automorphisms of G, when G is simple.     

Removal of organic pollutants from water via molecular inclusion within a cavitand

The molecular inclusion chemistry of cavitands provides a useful way for the removal of organic pollutants from water. A wide range of lipophilic organic compounds, present at trace level in water, are efficiently extracted by cavitand1, which can be easily reactivated and reused.     

Easy hydrolysis of white phosphorus coordinated to ruthenium

The P4 molecule bound to ruthenium as an eta1-ligand in [CpRu(PPh3)2(eta1-P4)]Y (Y = PF6, CF3SO3) undergoes an easy reaction with water in exceedingly mild conditions to yield PH3, which remains coordinated to the [CpRu(PPh3)2] fragment, and oxygenated derivatives.     

On Constrained Nonlinear Hermite Subdivision

We determine shape-preserving regions and we describe a general setting to generate shape-preserving families for the 2-points Hermite subdivision scheme introduced by Merrien (Numer. Algorithms 2:187–200, [1992]). This general construction includes the shape-preserving families presented in Merrien and Sablonníere (Constr. Approx. 19:279–298, [2003]) and Pelosi and Sablonníere (C ¹ GP Hermite Interpolants Generated by a Subdivision Scheme, Prépublication IRMAR 06–23, Rennes, [2006]). New special families are presented as particular examples. Nonstationary and nonuniform versions of such schemes, which produce smoother limits, are discussed.      

On locally finite Cpp-groups

A group G is called a Cpp-group for a prime number p, if G has elements of order p and the centralizer of every non-trivial p-element of G is a pgroup. In this paper we prove that the only infinite locally finite simple groups that are Cpp-groups are isomorphic either to PSL(2,K) or, if p = 2, to Sz(K), with K a suitable algebraic field over GF(p). Using this fact, we also give some structure theorems for infinite locally finite Cpp-groups.