Benzenoid Molecules with Uniform Distribution of π-Electrons within Rings

In a recent work it was demonstrated that in linear hexagonal chains the distribution of π-electrons into rings (as computed by means of the Randić–Balaban method) is uniform, irrespective of the nature of the terminal fragments. We now establish that an analogous, yet somewhat more complex, uniformity in the π-electron distribution exists also in double linear hexagonal chains, as well as in some other benzenoid systems.     

SDP diagonalizations and perspective cuts for a class of nonseparable MIQP

We present a new approach, requiring the solution of a SemiDefinite Program, for decomposing the Hessian of a nonseparable mixed-integer quadratic problem to permit using perspective cuts to improve its continuous relaxation bound. The new method favorably compares with a previously proposed one requiring a minimum eigenvalue computation.     

Fast computation of a rational point of a variety over a finite field

We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety.

     

XRR and GISAXS study of silicon oxynitride films

Thin films of silicon oxynitride have largely replaced pure silicon oxide films as gate and tunnel oxide films in modern technology due to their superior properties in terms of efficiency as boron barrier, resistance to electrical stress and high dielectric strength. A single chamber system for plasma enhanced chemical vapor deposition was employed to deposit different films of SiO_xN_yH_z with 0.85 < x < 1.91. All films were previously characterized by Rutherford back-scattering and infrared spectroscopy to determine the stoichiometry and the presence of various bonding configurations of constituent atoms. We used X-ray reflectivity to determine the electron density profile across the depth, and we showed that the top layer is densified. Moreover, grazing incidence small-angle X-ray scattering was used to study inhomogeneities (clustering) in the films, and it is shown that plate-like inhomogeneities exist in the top and sphere-like particles at the bottom part of the film. Their shape and size depend on the stoichiometry of the films.     

Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations

In this paper,the Dirichlet problem of Stokes approximate of non-homogeneous incompressibleNavier-Stokes equations is studied.It is shown that there exist global weak solutions as well as global andunique strong solution for this problem,under the assumption that initial density ρ_0(x)is bounded away from0 and other appropriate assumptions(see Theorem 1 and Theorem 2).The semi-Galerkin method is applied toconstruct the approximate solutions and a prior estimates are made to elaborate upon the compactness of theapproximate solutions.     

Some Questions of Heinrich on Ultrapowers of Locally Convex Spaces

In this note we treat some open problems of Heinrich on ultrapowers of locally convex spaces. In section 1 we investigate the localization of bounded sets in the full ultrapower of a locally convex space, in particular the coincidence of the full and the bounded ultrapower, mainly concentrating in the case of (DF)-spaces. In section 2 we provide a partial answer to a question of Heinrich on commutativity of strict inductive limits and ultrapowers. In section 3 we analyze the relation between some natural candidates for the notion of superreflexivity in the setting of Fréchet spaces. We give an example of a Fréchet-Schwartz space which is not the projective limit of a sequence of superreflexive Banach spaces.     

Diffractive dissociation reaction np → Λ0K0p for incident neutron momenta between 30 and 70 GeV/c BIS-2 collaboration

We present results of the exclusive diffractive reaction np ⁰K⁰p at 0·08 < |t|< 0·53 GeV²/c² and momenta between 30–70 GeV/c at the Serpukhov neutron beam. Thet-dependence is exp (Bt) withB= 11·4± 2·3 (GeV/c)^–2 and it exhibits the diffractive minimum at ¦t¦ 0·28 GeV²/c² for ⁰K⁰ massesM < 1·8 GeV/c².B decreases with increasingM. Correlation with the beam direction is observed in the rest frame of the ⁰K⁰ system: the cross section rises for the forward-going ⁰. The rise is more pronounced for higherM. The cross section of reaction np ⁰K⁰p for 0<|t|< 0·53 GeV²/c² is 10·3 ± 2·5 ± 2·8 b.     

Inclusive production of vector mesons in π+ p interactions at 250 GeV/c

We report on a study of ρ⁰, ρ⁺, ω, \(\bar K^{*0} (892)\) andK ^*0 (892) inclusive production in π⁺ p interactions at 250 GeV/c, for ρ⁺, \(\bar K^{*0} (892)\) for the first time in a π⁺ p experiment. The data are compared withK ⁺ p data in the same experiment, with results of other experiments and with quark-parton models. Interesting differences are found between ρ^+,0 and ω production.     

Functional analysis and boundary-value problems: An introductory treatment

Book Review

Functional analysis and boundary-value problems: An introductory treatmentB. Dayanand Reddy: Pitman Monographs and Survey in Pure and Applied Mathematics, Longman Scientific and Technical, 1986, 333 pp., £45.00 net