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.     

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.     

The Cosmological Constant in the Framework of Gravito-Magnetodynamic Waves in Weak Gravitational Fields

Using the linearization of Einstein's equations for weak gravitational fields, a specific model of gravito-magnetofluid is elaborated. The study of wave formation and propagation in such a medium is necessarily connected to the existence of the cosmological constant.     

Maximal σ‐polynomials of connected 3‐chromatic graphs

In the set of graphs of order n and chromatic number k the following partial order relation is defined. One says that a graph G is less than a graph H if c_i(G) ≤ c_i(H) holds for every i, k ≤ i ≤ n and at least one inequality is strict, where c_i(G) denotes the number of i‐color partitions of G. In this paper the first ? n/2 ? levels of the diagram of the partially ordered set of connected 3‐chromatic graphs of order n are described. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 210–222, 2003     

Farkas-type results for fractional programming problems

Considering a constrained fractional programming problem, within the present paper we present some necessary and sufficient conditions, which ensure that the optimal objective value of the considered problem is greater than or equal to a given real constant. The desired results are obtained using the Fenchel–Lagrange duality approach applied to an optimization problem with convex or difference of convex (DC) objective functions and finitely many convex constraints. These are obtained from the initial fractional programming problem using an idea due to Dinkelbach. We also show that our general results encompass as special cases some recently obtained Farkas-type results.     

Non-Darcian effects on conjugate natural convection between horizontal concentric cylinders filled with a porous medium

An analysis is presented of steady conjugate free convection between two horizontal concentric cylinders filled with a fluid-saturated porous medium; the innermost cylinder surface is maintained at a high temperature and the outermost cylinder surface at a lower one. The velocity-pressure-gradient relation is taken to be nonlinear, with departure from the linear Darcy situation measured by a parameter F₀. The investigation is based on the numerical solution, by a finite-difference method, of the full momentum and energy equations. The streamline and isotherm patterns as well as the local and mean Nusselt numbers are plotted for several physical parameters to show some of the flow and heat transfer characteristics. It is found that all parameters play an important role in the flow and heat transfer characteristics. The model can be applied to a variety of engineering problems.     

Synthesis and characterization of mid‐ and end‐chain functional telechelics by controlled polymerization methods and coupling processes

Well‐defined polystyrene‐ (PSt) or poly(ε‐caprolactone) (PCL)‐based polymers containing mid‐ or end‐chain 2,5 or 3,5‐ dibromobenzene moieties were prepared by controlled polymerization methods, such as atom transfer radical polymerization (ATRP) or ring opening polymerization (ROP). 1,4‐Dibromo‐2‐(bromomethyl)benzene, 1,3‐dibromo‐5‐(bromomethyl)benzene, and 1,4‐dibromo‐2,5‐di(bromomethyl)benzene were used as initiators in ATRP of styrene (St) in conjunction with CuBr/2,2′‐bipyridine as catalyst. 2,5‐Dibromo‐1,4‐(dihydroxymethyl)benzene initiated the ROP of ε‐caprolactone (CL) in the presence of stannous octoate (Sn(Oct)₂) catalyst. The reaction of these polymers with amino‐ or aldehyde‐functionalized monoboronic acids, in Suzuki‐type couplings, afforded the corresponding telechelics. Further functionalization with oxidable groups such as 2‐pyrrolyl or 1‐naphthyl was attained by condensation reactions of the amino or aldehyde groups with low molecular weight aldehydes or amines, respectively, with the formation of azomethine linkages. Preliminary attempts for the synthesis of fully conjugated poly(Schiff base) with polymeric segments as substituents, by oxidative polymerization of the macromonomers, are presented. All the starting, intermediate, or final polymers were structurally analyzed by spectral methods (¹H NMR, ¹³C NMR, and IR). © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 727–743, 2006