Ratios of some domination parameters in trees

We determine upper bounds on the ratios of several domination parameters in trees.     

Application of the schwarz-christoffel mapping to planar gravity: static solutions

Point-like masses on a given initial domain of the complex plane are interacting globally under gravity and as a consequence the initial domain is mapped into a final domain which encodes all effects of localized sources . The mapping between the two domains is a truncated beta function which so far has not been fully investigated. In this paper we propose to know more about the final domain and so we start from the remark that when the masses are put on the real axis of the upper half plane, the mapping in question is the Schwarz-Christoffel mapping (SCM), a popular and useful tool in computational geometry. The linking of planar gravity with the SCM will allow us to use all what we know from this mapping to get answer for certain static solutions in planar gravity. Among the problems we will study we mention: masses distributed on the real axis of the full complex plane, masses distributed on a circle, the dust string either closed or infinite open. Strings with tensions are however not linked to SCM as these mappings do not involve the concept of tension.     

Polyrotaxanes based on polyethers and β‐cyclodextrin

A polyrotaxane in which β‐cyclodextrins (β‐CDs) are threaded onto a polyether chain was prepared by polycondensation of a β‐CD/bisphenol A (BPA) inclusion complex with aromatic dihalides. Two dihalides, with and without a side chain, were used. This polycondensation results in a polyrotaxane (or pseudopolyrotaxane for polymers without stoppers) with a 1:1 threading ratio when the side chain is present and 2:3 when there is none. The long side chain prevents dethreading of the macrocycles. The best yield and a good threading ratio were obtained when the polycondensation was performed by liquid?solid phase transfer catalysis without solvent (L/S PTC) using 2,5‐bi(iodomethyl)‐4‐methoxy‐(1‐octyloxy)benzene as dihalide. The ¹H NMR and FTIR spectra show that the products consist of β‐CD and polyether. The 2D NOESY NMR spectrum shows that the polyether chains are included in the β‐CD cavity. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 4391–4399, 2009     

Discretizing two‐dimensional complex fractured fields for incompressible two‐phase flow

A method is introduced to discretize irregular and complex two‐dimensional fractured media. The geometry of the fractured media is first analysed by searching and treating the complex configurations. Based on that, the method generated a good mesh quality and allows for including finer grids. An incompressible two‐phase flow problem is solved to compare the developed method and a public method based on the approximation of a 1D fracture by the edges of a 2D finite element grid of the porous media. The comparison showed that the developed method (i) represents better the fractured domain by maintaining the geometric integrity of input surfaces and geologic data, (ii) provides, for sample and complex fractured domains, excellent and more accurate results, and (iii) is much less sensitive to the grid sizes. Furthermore, the method has to be more efficient than the other methods for transport problems and has to provide better predictable results; this is mainly based on point (ii) and because the method produces optimal triangular grids. Copyright © 2009 John Wiley & Sons, Ltd.     

Rheology of compatibilized immiscible viscoelastic polymer blends

Rheological behavior of a PS/PE model viscoelastic immiscible blend compatibilized by two types of interfacial modifiers was investigated. Dynamic, steady shear, and transient experiments were performed to probe the effect of the interfacial modification on the rheological behavior of the blend. While the effect was relatively small in dynamic and steady shear experiments, significant signature of the presence of the copolymer was observed in transient experiments after start up of shear flow. The magnitude of the departure from Doi-Otha theory (worked out for non-compatibilized blends) was evaluated. Received: 6 March 2000 Accepted: 15 June 2000     

The relevance of the cosmological constant for lensing

This review surveys some recent developments concerning the effect of the cosmological constant on the bending of light by a spherical mass in Kottler (Schwarzschild–de Sitter) spacetime. Some proposals of how such an effect may be put into a setting of gravitational lensing in cosmology are also discussed. The picture that emerges from this review is that it seems fair to assert that the contribution of Λ to the bending of light has by now been well established, while putting the Λ light-bending terms into a cosmological context is still subject to some interpretation and requires further work and clarification.     

Variable neighborhood search for extremal graphs. 21. Conjectures and results about the independence number

A set of vertices S in a graph G is independent if no neighbor of a vertex of S belongs to S. The independence number α is the maximum cardinality of an independent set of G. A series of best possible lower and upper bounds on α and some other common invariants of G are obtained by the system AGX 2, and proved either automatically or by hand. In the present paper, we report on such lower and upper bounds considering, as second invariant, minimum, average and maximum degree, diameter, radius, average distance, spread of eccentricities, chromatic number and matching number.     

SYNTHESIS OF 7-THIA-1-AZABICYCLO (4,3,0) NONANE DERIVATIVES VIA FREE RADICAL REACTION

Abstract

Several β-aminothiols were prepared by condensation of 3-piperideine and different thiiranes.     

Browder-type Theorems and SVEP

We study the new properties (b) and (gb), which we had introduced in [13], for an operator having the SVEP on the complement of distinguished parts of its spectrum. Classes of operators are considered as illustrating examples.