Diffraction in a cylindrically orthotropic elastic solid containing a stress free crack

A cylindrically orthotropic elastic solid is excited by a point impulsive body force. The solid contains a semi-infinite stress free crack. The resulting anti-plane wave motion problem has been solved in the form of a finite series representing the incident and reflected pulses plus an integral representing the diffraction pulse. The series part of the solution has been previously treated. In the present investigation the diffraction integral is integrated when λ (which measures the anisotropy of the solid) is an odd integer number. The diffraction integral is also integrated when λ is half an odd integer, for the special case in which the source lies in the plane of the crack and parallel to the crack edge. The displacement jump across the circular diffraction wave front is given for unrestricted (positive) values of λ.     

Bodies of constant width in arbitrary dimension

We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n – 1)‐dimensional projection being given. We give a number of examples, like a four‐dimensional body of constant width whose 3D‐projection is the classical Meissner's body. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Macrodefect-Free Materials: Modification of Interfaces in Cement Composites by Polymer Grafting

MDF materials are chemically bonded ceramic materials free of the macrodefects typical of hydraulic cement-based materials. MDF materials arising through reactions of sulfo-aluminate-ferrite belitic (SAFB) clinkers and/or Portland cements (PC) with two types of water-soluble polymer (hydroxy-propylmethyl cellulose {HPMC}, polyphosphate glass {poly-P}) are discussed. Mixes of low energy SAFB clinkers with Portland cement, HPMC and, especially poly-P comprise promising cross-linked compositions additional to the better known MDF materials formed from high alumina cement with polyvinylalcohol/acetate. The principles of co-ordination of P and C atoms (of the polymer) with Al and Fe atoms (originating from the cement) are highlighted from spectroscopic information on next-nearest-neighbour interactions, along with the effects of second co-ordination spheres. Polymers modify the interface through functional bonding/grafting of polymer chains onto the surfaces of cement grains. Both the cross-linked atomic structure and the interface coincide well with the model of functional polymers and represent a new type of atomic-level structure in polymer-modified cements. Interpretation is based on previous magnetic resonance and thermal analysis studies. The compactness of Al(Fe)-O-P cross-links reduces transport through the interfaces, increasing the interfacial interactions and resisting the unfavourable uptake of moisture and carbonation.     

Synthesis and thermal crosslinking of oxazolidine‐functionalized polyurethanes

A new oxazolidine derivative was obtained from phenol, 2‐amino‐2‐methylpropane‐1,3‐diol and paraformaldehyde. The reaction of this novel oxazolidine diol with phenylisocyanate lead to a urethane model compound which can be polymerized thermally by oxazolidine ring opening to give a Mannich bridge structure. Linear segmented polyurethanes were prepared by reaction of different ratios of oxazolidine diol and commercial polyethylenglycol (M_w ～ 400) with 4,4′‐methylenbis (cyclohexylisocyanate) (HMDI, 90% isomers mixture). The polyurethanes were thermally characterized and crosslinked by oxazolidine ring opening to obtain materials which showed improved thermal stability. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4965–4973, 2007     

Ethylene/1‐hexene copolymerization with tetramethyldisiloxane‐bridged bis(indenyl) metallocenes

Ethylene/1‐hexene copolymerizations with disiloxane‐bridged metallocenes, rac‐ and meso‐1,1,3,3‐tetramethyldisiloxanediyl‐bis(1‐indenyl)zirconium dichloride (rac‐ 1 , meso‐ 1 ) activated by modified methylaluminoxane were performed to investigate the influence of conformational dynamics on comonomer selectivity. Although ¹H NOESY (nuclear Overhauser and exchange spectroscopy) analysis indicated that the most stable conformation for the meso isomer in solution was that in which both indenes project over the metal coordination site, this isomer showed higher 1‐hexene selectivity in copolymerization (r_e = 140 ± 30, r_h = 0.024 ± 0.004) than the rac isomer with only one indene over the coordination site (r_e = 240 ± 20, r_h = 0.005 ± 0.001). The meso isomer showed high 1‐hexene selectivity, a high product of reactivity ratios (r_er_h = 3.3 ± 0.5) and produced copolymers that could be separated into fractions with different ethylene content suggesting that the active species exhibited multisite behavior and populated conformations with different comonomer selectivities during the copolymerization. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3323–3331, 2004     

Some remarks on Newton–Sabatier methods

It is shown how Newton–Sabatier methods (arising in inverse scattering at fixed energy) can be related to spectral measures and typically when they correspond to regular potentials. A number of spectral formulae for various transmutation kernels are also given in terms of general Kontorovi?–Lebedev theory and connections to generating functions, generalized orthogonal polynomials, etc. are indicated.