The diffraction of elastic waves by an imperfect fusion bond

We consider diffraction by a semi-infinite crack located alonga fusion interface between two differing elastic media. Twotypes of crack, namely open and partially closed cracks, areinvestigated. An open crack is modelled by a stress-free contactboundary condition and a partially closed crack is modelledby a spring contact boundary condition. For the latter, thejump in the stress across the crack is assumed to be proportionalto the jump in the displacement across the crack. This situationarises in, for example, a K-weld where the fine grain of theparent material (for example, ferritic or forged austeniticsteel) is in stark contrast with the coarse-grained weld metal(for example, austenitic weld metal). In the metal weld thedirection of the grain axis varies through the metal. However,diffraction is a local phenomenon and so the austenitic steelis assumed to have a zonal axis so that it may be modelled bya transversely isotropic composite. The ferritic or forged austeniticsteel will be modelled as an isotropic material.     

A quantum spin system with random interactions I

We study a quantum spin glass as a quantum spin system with random interactions and establish the existence of a family of evolution groups {τ_t(ω)}_ω∈/Ω of the spin system. The notion of ergodicity of a measure preserving group of automorphisms of the probability space Ω, is used to prove the almost sure independence of the Arveson spectrum Sp(τ(ω)) of τ_t(ε). As a consequence, for any family of (τ(ω),β) — KMS states {ρ(ω)}, the spectrum of the generator of the group of unitaries which implement τ(ω) in the GNS representation is also almost surely independent of ω.     

Derivatives of M(η5-C5H5)2 (M = Mo,W) with alkenylpyridines and related ligands

Reactions of ligands 2-vinylpyridine 1, 4-vinylpyridine 2, 2-allylpyridine 3, 1-allylpyrazole 4, acrylonitrile 5 and allylcyanide 6 with the metallocene derivatives [Mo(η⁵-C₅H₅)₂H₃][PF₆] 7, [Mo(η⁵-C₅H₅)₂HI] 8, [W(η⁵-C₅H₅)₂H₃] [PF₆] 9, [Mo(η⁵-C₅H₅)₂H₂] 10, [M(η⁵-C₅H₅)₂Br₂], M = Mo 11, M = W 12 are described. Reaction of 7 with 1, 8 with 1, 3 with 8 and 4 with 8 gave mixtures of metallocyle isomers resulting from coordination of the nitrogen atom to molybdenum followed by internal hydrometallation; reaction of 11 with 1 gave an olefinic π complex; reaction of either 9 or 11 with 1 gave intractable oils; reactions of 8 with 2, 11 with 5, 12 with 5, 11 with 6 and 12 with 6 yielded monosubstituted products in which the ligand is N-coordinated.     

Indestructibility of compact spaces

In this article we investigate which compact spaces remain compact under countably closed forcing. We prove that, assuming the Continuum Hypothesis, the natural generalizations to _ω1${\omega }_1$-sequences of the selection principle and topological game versions of the Rothberger property are not equivalent, even for compact spaces. We also show that Tall and Usuba?s “_ℵ1${\aleph }_1$-Borel Conjecture” is equiconsistent with the existence of an inaccessible cardinal.     

Two-player simultaneous location game: Preferential rights and overbidding

Competitive location problems can be characterized by the fact that the decisions made by others will affect our own payoffs. In this paper, we address a discrete competitive location game in which two decision-makers have to decide simultaneously where to locate their services without knowing the decisions of one another. This problem arises in a franchising environment in which the decision-makers are the franchisees and the franchiser defines the potential sites for locating services and the rules of the game. At most one service can be located at each site, and one of the franchisees has preferential rights over the other. This means that if both franchisees are interested in opening the service in the same site, only the one that has preferential rights will open it. We consider that both franchisees have budget constraints, but the franchisee without preferential rights is allowed to show interest in more sites than the ones she can afford. We are interested in studying the influence of the existence of preferential rights and overbidding on the outcomes for both franchisees and franchiser. A model is presented and an algorithmic approach is developed for the calculation of Nash equilibria. Several computational experiments are defined and their results are analysed, showing that preferential rights give its holder a relative advantage over the other competitor. The possibility of overbidding seems to be advantageous for the franchiser, as well as the inclusion of some level of asymmetry between the two decision-makers.     

Use of the hole-drilling method for measuring residual stresses in highly stressed shot-peened surfaces

The same shot-peening treatment was applied to five steels with different mechanical properties. The induced residual stress profiles were analyzed using X-ray diffraction and incremental hole drilling (IHD). The results of both techniques showed that IHD can still be successfully used for measuring shot-peening residual stresses, even if these exceed the yield strength of the bulk material. Expected errors due to the plasticity effect are reduced by the strain hardening of the surface. For an assessment of the reliability of IHD data, strain-hardening variation was quantified by microhardness measurements to estimate the yield strength of the plastified layer. All the main calculation methods for IHD were applied. The results were compared and discussed with respect to the characteristics of each method.     

Science Conference Presenters’ Images of Inquiry

Inquiry‐focused professional development and conceptions of inquiry held by eight professional development leaders were investigated within the context of a state science teacher conference. The prominent session format involved session leaders modeling classroom experiences. In all sessions, classroom inquiry was portrayed as a teacher‐guided activity with the primary goal being to increase motivation for engaging students in classroom inquiry. The leaders’ conceptualized inquiry primarily as a teaching approach with various goals, characteristics, and potential barriers. The findings of this study provide evidence of how inquiry, a prominent feature of science education reform, was portrayed in sessions at a conference sponsored by a state affiliate of the National Science Teachers Association and thought about by persons who led these sessions. The findings have implications for teacher learning from conference‐based professional development and its potential influence on science teacher thinking and practice.     

A Quasilinear System Related with the Asymptotic Equation of the Nematic Liquid Crystal’s Director Field*

In this paper, the author studies the local existence of strong solutions and their possible blow-up in time for a quasilinear system describing the interaction of a short wave induced by an electron field with a long wave representing an extension of the motion of the director field in a nematic liquid crystal’s asymptotic model introduced in [Saxton, R. A., Dynamic instability of the liquid crystal director. In: Current Progress in Hyperbolic Systems (Lindquist, W. B., ed.), Contemp. Math., Vol.100, Amer. Math.Soc., Providence, RI, 1989, pp.325–330] and [Hunter, J. K. and Saxton, R. A., Dynamics of director fields, SIAM J. Appl. Math., 51, 1991, 1498–1521] and studied in [Hunter, J. K. and Zheng, Y., On a nonlinear hyperbolic variational equation I, Arch. Rat. Mech. Anal.,129, 1995, 305–353], [Hunter, J. K. and Zheng, Y., On a nonlinear hyperbolic variational equation II, Arch. Rat. Mech. Anal., 129, 1995, 355–383] and in [Zhang, P. and Zheng,Y., On oscillation of an asymptotic equation of a nonlinear variational wave equation,Asymptotic Anal., 18, 1998, 307–327] and, more recently, in [Bressan, A., Zhang, P. and Zheng, Y., Asymptotic variational wave equations, Arch. Rat. Mech. Anal., 183, 2007,163–185].     

Search for singlet-triplet bistability or biradicaloid properties in polycyclic conjugated hydrocarbons: a valence-bond analysis

Two classes of molecules displaying singlet-triplet biradical bistability (i.e. species having significant biradicaloid properties) can be designed as follows. Alternant conjugated polycyclic hydrocarbons with numerous fixed double bonds (double bonds that remain unchanged in all its Kekulé resonance structures), a large number of Dewar resonance structures which measures the corresponding diradical resonance, and a small HOMO-LUMO band gap which measures the ease of thermal spin inversion are candidates for singlet triplet biradical bistability. Chichibabin's hydrocarbon ( 1 ) is an example. In addition, in the search for candidate molecules having singlet triplet bistability, one should also examine polycyclic conjugated systems having nonalternant induced spin frustration. Spin frustrated nonalternant polycyclic conjugated hydrocarbons will display singlet-triplet bistability (biradicaloid properties) and are generated from alternant valence-bond diradicals or Hückel molecular orbital diradicals having classical Kekulé structures by appropriate intramolecular joining of two starred or nonstarred positions with bonds, respectively.