Grothendieck groups arising from contravariantly finite subcategories

The subject of the paper is the study of the relative homological properties of a given additive category C in relation to a given contravariantly finite subcategory X in C under the assumption that any X-epic has a kernel in C. We introduce the notion of the Grothendieck group relative to the pair (C, X) and also that of the Cartan map cx relative to (C, X) and we show that the cokernel of cx is isomorphic to the corresponding Grothendieck group of the stable category C/Jx We also show that if the right x-dimension of C is finite, then cx is an isomorphism. In case C is a finite dimensional k-additive Krull-Schmidt category, we introduce the notion of the x-dimension vector of an object of C. We give criteria for when an indecomposable object is determined, up to isomorphism, by its x-dimension vector.     

Dielectric and dynamic mechanical studies on homogeneous PBA/PBMA interpenetrating polymer networks

Broadband dielectric relaxation spectroscopy (DRS, 10⁻²‐10⁹ Hz), thermally stimulated depolarization currents (TSDC) techniques and dynamic mechanical analysis (DMA) were employed to investigate the dynamic glass transition and, thus, phase morphology in sequential IPNs of poly(butyl acrylate) (PBA) and poly(butyl methacrylate) (PBMA) with 10 weight % of ethyleneglycol dimethacrylate (EGDMA) as branching agent. In a parallel investigation, similar IPNs with only 0.1% branching agent showed clearly phase separation. In the highly branched IPNs, forced compatibilization induces miscibility of the two components. The results are discussed in terms of suppression of cooperativity and dynamic heterogeneity in the IPNs.     

On confidence intervals from simulation of finite Markov chains

Consider a finite state irreducible Markov reward chain. It is shown that there exist simulation estimates and confidence intervals for the expected first passage times and rewards as well as the expected average reward, with 100% coverage probability. The length of the confidence intervals converges to zero with probability one as the sample size increases; it also satisfies a large deviations property.     

Dominant three-body decays of a heavy higgs and top quark

We calculate the dominant three body Higgs decays,HW ⁺ W ^–(Z ⁰, ) and , in the Standard Model. We find that the branching ratios of these decays are of the order of few percent for large Higgs masses. We comment on the behaviour of the partial decay width below the threshold. Numerical results of the following three body top decays,tW ⁺ b(,g, Z ⁰) andtW ⁺ bH, are also given. We discuss the feasibility of observing these Higgs and top decays at future high energy colliders.     

Mechanically versatile isosorbide-based thermoplastic copolyether-esters with a poly(ethylene glycol) soft segment

Segmented thermoplastic copolyether esters (TPEE's) with a partially renewable hard block containing isosorbide (ISB) and poly(ethylene glycol) (PEG) soft blocks were prepared by melt polycondensation. A range of compositions was accessible despite the relatively low reactivity of the sterically and electronically hindered ISB monomer. The small-scale reactions performed in the melt were limited in terms of achievable molar mass. This is attributed to the challenge of attaining stoichiometric balance in the feed and maintaining this balance throughout the high temperature (>200°C) reactions. Nevertheless, products were isolated that could be manipulated and melt-pressed into specimen for tensile testing. Varying the feed compositions gave rise to copolymers exhibiting a broad range of mechanical properties (elastic modulus from 1–66 MPa). These characteristics are consistent with a segmented polymer architecture with morphological features similar to commercially available TPEE counterparts. These results pave the way for more responsibly sourced building blocks being incorporated into materials with high market value potential.     

Nonlinear optimisation using directional step lengths based on RPROP

A search method based on the backpropagation rule commonly used for training neural networks is proposed here for the optimisation of smooth nonlinear functions. The use of the Resilient backPROPagation (RPROP) heuristic rule for local minimisation is described. The details of employing the directional step length determined by RPROP along with a simple restarting scheme are provided. In the approach proposed here direct use of the directional step determined by the heuristic without using any line search conditions takes place. The overall algorithm has been tested on a number of benchmark functions found in the literature with very positive results. The test problems’ dimension ranges from 100 to 50,000. The results obtained show that the suggested search direction method results to a highly efficient algorithm suitable for large scale optimisation.     

Hydrodynamics in a Gas-Solids Fluidized Bed Using X-Ray Fluoroscopy and Pressure Fluctuation Measurements

In this work, non-intrusive techniques were used to characterize the hydrodynamics in a gas-solids bubbling fluidized bed using polyethylene powder and glass beads of comparable mean diameter (d_p = 360 µm) but different density. X-ray fluoroscopy measurements and pressure fluctuations were performed on a pseudo 2-dimensional gas-solids fluidized bed. Bubble properties were captured from X-ray fluoroscopy measurements. Similarities and differences of flow behavior of the two particle systems were revealed from comparison of bubble properties. Bubble properities normally varied similary with operating conditions for the two particle systems, while bubble sizes for the glass beads system are larger than those for the polyethylene system. Wavelet analysis of pressure fluctuations was applied to investigate the gas and solids phase flow behavior. Multi-scale flow behavior was extracted from the standard deviation of the decomposed coefficient series. Flow behavior due to particles and bubbles of different sizes were captured at different decomposition levels of pressure fluctuations, which is difficult to know from analysis of the original signal. Results extracted from X-ray fluoroscopy and pressure fluctuation measurements were consistent, suggesting that conventional pressure fluctuation measurements can be effectively used for investigation of the bubbling behavior.