Chemical bonding in representative astrophysically relevant neutral,cation, and anion HCnH chains

Most existing studies assign a polyynic and cumulenic character of chemical bonding in carbon-based chains relying on values of the bond lengths. Building on our recent work, in this paper we add further evidence on the limitations of such an analysis and demonstrate the significant insight gained via natural bond analysis. Presently reported results include atomic charges, natural bond order and valence indices obtained from ab initio computations for representative members of the astrophysically relevant neutral and charged HC_2k/2k+1H chain family. They unravel a series of counter-intuitive aspects and/or help naive intuition in properly understanding microscopic processes, e.g., electron removal from or electron attachment to a neutral chain. Demonstrating that the Wiberg indices adequately quantify the chemical bonding structure of the HC_2k/2k+1H chains—while the often heavily advertised Mayer indices do not—represents an important message conveyed by the present study.     

First integrals for Finsler metrics with vanishing $$\chi $$ -curvature

Annals of Global Analysis and Geometry - We prove that in a Finsler manifold with vanishing $$\chi $$ -curvature (in particular with constant flag curvature) some non-Riemannian geometric...     

Sufficient conditions of non‐uniqueness for the Coulomb friction problem

We consider the Signorini problem with Coulomb friction in elasticity. Sufficient conditions of non‐uniqueness are obtained for the continuous model. These conditions are linked to the existence of real eigenvalues of an operator in a Hilbert space. We prove that, under appropriate conditions, real eigenvalues exist for a non‐local Coulomb friction model. Finite element approximation of the eigenvalue problem is considered and numerical experiments are performed. Copyright © 2003 John Wiley & Sons, Ltd.     

Hardy type inequalities with exponential weights for a class of convolution operators

In this paper we consider operators of the form H=λ(-i∇), with λ analytic in a strip and with some specific growth conditions at infinity, and prove Hardy type estimates in L ²(ℝ ⁿ ) with exponential weights. In fact we extend our previous results [19] from bounded analytic functions on a strip to analytic functions with polynomial growth in that strip.     

On Genuine Bernstein–Durrmeyer Operators

We continue the studies on the so–called genuine Bernstein–Durrmeyer operators U _n by establishing a recurrence formula for the moments and by investigating the semigroup T(t) approximated by U _n . Moreover, for sufficiently smooth functions the degree of this convergence is estimated. We also determine the eigenstructure of U _n , compute the moments of T(t) and establish asymptotic formulas. Received: January 26, 2007.     

A result on sets,with applications to vector optimization

In this paper there is stated a result on sets in ordered linear spaces which can be used to show that some properties of the sets are inherited by their convex hulls under suitable conditions. As applications one gives a characterization of weakly efficient points and a duality result for nonconvex vector optimization problems.