A complex of incompressible surfaces for handlebodies and the mapping class group

For a genus g handlebody H _g a simplicial complex, with vertices being isotopy classes of certain incompressible surfaces in H _g , is constructed and several properties are established. In particular, this complex naturally contains, as a subcomplex, the complex of curves of the surface ${\partial H_{g}}$ . As in the classical theory, the group of automorphisms of this complex is identified with the mapping class group of the handlebody.     

Two-loop QCD amplitude for gg-->h, H in the minimal supersymmetric standard model

We present the two-loop QCD amplitude for the interaction of two gluons and a CP-even Higgs boson in the minimal supersymmetric standard model (MSSM). We apply a novel numerical method for the evaluation of Feynman diagrams with infrared, ultraviolet, and threshold singularities. We discuss subtleties in the ultraviolet renormalization of the amplitude with conventional dimensional regularization, dimensional reduction, and the four dimensional helicity scheme. Finally, we show numerical results for scenarios of supersymmetry breaking with a rather challenging phenomenology in which the Higgs signal in the MSSM is suppressed in comparison to the standard model.     

The GHP conformai Killing equations and their integrability conditions,with application to twisting type N vacuum spacetimes

The conformai Killing equations in resolved form and their first and second integrability conditions are obtained in the compact spin coefficient formalism for arbitrary spacetimes. To facilitate calculations an operatorL is introduced which agrees with the Lie derivative only when operating on quantities with GHP weights (0,0). The resulting equations are used to find the conditions for the existence of a two dimensional non-Abelian group of homothetic motions in a twisting typeN vacuum spacetime. The equivalence of two such sets of metrics is established, metrics that were recently the subject of independent investigations by Herlt on the one hand and by Ludwig and Yu on the other.     

Variable step-size implementation of sixth-order Numerov-type methods

The explicit sixth-order Numerov-type family of methods is considered. A new representative from this family is produced and equipped with a cheap step-size changing algorithm. Actually, after the completion of a step, this remains the same, halved, or doubled. The off-step points required for such technique are evaluated through local interpolant. Numerical tests over various problems illustrate the efficiency gained by this approach.     

Explicit hybrid six–step,sixth order,fully symmetric methods for solving y ″ = f (x,y)

A family of explicit, fully symmetric, sixth order, six‐step methods for the numerical solution of y′′ = f(x,y) is studied. This family wastes two function evaluations per step and can be derived through interpolation techniques. An interval of periodicity is possessed and the phase lag is of high order. Numerical instabilities usually present in such type of multistep methods were circumvented. We conclude with extended numerical tests over a set of problems justifying our effort of dealing with the new methods.     

Low‐order,P‐stable,two‐step methods for use with lax accuracies

A semi‐implicit family of two‐step methods is considered for the numerical solution of . These methods are hybrid and waste two stages (function evaluations) per step in order to attain fourth algebraic order while other methods of this type need three stages per step. Exploiting this improvement, we derive a particular method and conclude with a series of numerical tests on stiff periodic problems that illustrate its efficiency.     

On the effect of dead time on the counting statistical error

In X‐ray intensity measurements, the counting statistical error is typically calculated as the square root of the number of counts collected. This, however, is an approximation in the sense that the effect of the dead time in the counting process has been ignored. In this work, the equations for calculation of the counting statistical error in X‐ray fluorescence measurements will be derived, including the effect of the dead time of the counting chain. Copyright © 2016 PANalytical B.V. X‐Ray Spectrometry Published by John Wiley & Sons Ltd.     

Strategies for Enhancing Polyester-Based Materials for Bone Fixation Applications

Polyester-based materials are established options, regarding the manufacturing of bone fixation devices and devices in routine clinical use. This paper reviews the approaches researchers have taken to develop these materials to improve their mechanical and biological performances. Polymer blending, copolymerisation, and the use of particulates and fibre bioceramic materials to make composite materials and surface modifications have all been studied. Polymer blending, copolymerisation, and particulate composite approaches have been adopted commercially, with the primary focus on influencing the in vivo degradation rate. There are emerging opportunities in novel polymer blends and nanoscale particulate systems, to tune bulk properties, and, in terms of surface functionalisation, to optimise the initial interaction of devices with the implanted environment, offering the potential to improve the clinical performances of fracture fixation devices.