Extensions of Modules over Schur Algebras, Symmetric Groups and Hecke Algebras

We study the relation between the cohomology of general linear and symmetric groups and their respective quantizations, using Schur algebras and standard homological techniques to build appropriate spectral sequences. As our methods fit inside a much more general context within the theory of finite-dimensional algebras, we develop our results first in that general setting, and then specialize to the above situations. From this we obtain new proofs of several known results in modular representation theory of symmetric groups. Moreover, we reduce certain questions about computing extensions for symmetric groups and Hecke algebras to questions about extensions for general linear groups and their quantizations.     

Measurement of apex angle of the prism using total internal reflection

Total internal reflection technique is examined critically for the measurement of apex angle of the prism. Recognition of the critical boundary completely specifies the apex angle ‘A’ of the prism by keeping constant the ratio of refractive index of sample fluid (n₁=1.4) to that of glass (n₂=1.7). Recording of observations in the laboratory is dependent upon whether the apex angle ‘A’ of prism is greater than or less than or equal to critical angle ‘r_c’. The minimum value of error function ‘χ’ in the proximity of Abbe angle explain the choice of Abbe type instruments and shown invariant by relating positive ‘₊’ and the negative angle of emergence ‘₋’. Using ray-tracing technique, an expression for the length of the critical boundary ‘l’ is derived and is shown as a measure of the apex angle ‘A’ of the prism.

The choice of the realistic grazing condition leads us to two turning points for which error function ‘χ’ is minimal and yields appropriate option of the measurement of apex angle ‘A’ of the prism. It is further shown that the small error ‘ζ’ crept in the apex angle ‘A’ of the prism can lead to a significant error in the design of Pulfrich type instruments.

Experimental measurements are in-line with the predictions made.     

Influence of seeded impurities on the fusion reactor operation

In order to study the influence of seeded impurities on ITER like reactor operation the COREDIV code has been extended to include the transport of several sputtered and/or injected impurities. In the COREDIV code the core plasma is treated in the frame of 1D radial transport model whereas in the edge the 2D multifluid code EPIT is used. The EPIT code solves in the slab geometry the MHD equations for densities and velocities for all ions species as well as for electron and ion temperatures. The iteration scheme in the code leads to steady state solution of coupled core and SOL system. The numerical results for Carbon and Nickel plate and seeded impurities Silicon and Neon are presented.     

Index Heuristics for Multiclass M/G/1 Systems with Nonpreemptive Service and Convex Holding Costs

We consider the optimal service control of a multiclass M/G/1 queueing system in which customers are served nonpreemptively and the system cost rate is additive across classes and increasing convex in the numbers present in each class. Following Whittle's approach to a class of restless bandit problems, we develop a Langrangian relaxation of the service control problem which serves to motivate the development of a class of index heuristics. The index for a particular customer class is characterised as a fair charge for service of that class. The paper develops these indices and reports an extensive numerical investigation which exhibits strong performance of the index heuristics for both discounted and average costs.     

A novel approach to the acoustic characterisation of porous road surfaces

Porous road surfaces offer an effective means of reducing the generation and propagation of noise from road traffic. However, the porosity of these surfaces can deteriorate over time, leading to a reduction in their noise reducing properties. Efficient methods are therefore required for monitoring this performance. Existing techniques for performing in-situ measurements of acoustic absorption are unsuitable for use within the traffic stream. Static measurements using time domain Maximum Length Sequence (MLS) based techniques have been demonstrated to offer advantages over traditional techniques, presenting the opportunity for measurements under dynamic conditions. This paper describes the design of a system for carrying out dynamic MLS-based measurements. Results are presented which demonstrate that stable dynamic measurements can be carried out at speeds of up to 30 km/h.     

Reciprocating sliding wear behavior of laser-clad small amplitude Mo2Ni3Si/NiSi metal silicide composite coatings

Mo₂Ni₃Si/NiSi metal silicide composite coatings with a fine microstructure consisting of Mo₂Ni₃Si primary dendrites and the interdendritic Mo₂Ni₃Si/NiSi eutectics were fabricated on austenitic stainless steel AISI 321 by laser cladding process. Small amplitude reciprocating sliding wear resistance of the coatings is evaluated as functions of normal load and slip amplitude and the wear mechanisms were discussed based on worn surface morphology observations. Results showed that the Mo₂Ni₃Si/NiSi coatings have excellent small amplitude reciprocating sliding wear resistance.     

Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

Crystallographic report: A new polymorph for bis[bis(N,N‐dibenzyldithiocarbamato)cadmium(II)]

The title compound is a centrosymmetric dimer with each cadmium in a distorted CdS₅ square pyramidal geometry. The Cd–S bond distances range from 2.5626(11) to 2.8459(11) Å. Copyright © 2004 John Wiley & Sons, Ltd.     

The “corset effect” of spin-lattice relaxation in polymer melts confined in nanoporous media

Linear polyethylene oxides with molecular weightsM _w of 1665 and 10170 confined in pores with variable diameters in a solid methacrylate matrix were studied by proton field-cycling nuclear magnetic resonance relaxometry. The pore diameter was varied in the range of 9–57 nm. In all cases, the spin-lattice relaxation time shows a frequency dependence close toT ₁∞ v^3/4 in the range ofv=3·10^?1-2·10¹ MHz as predicted by the tube-reptation model. This protonT ₁ dispersion essentially reproduces that found in a previous deuteron study (R. Kimmich, R.-O. Seitter, U. Beginn, M. Möller, N. Fatkullin: Chem. Phys. Lett. 307, 147, 1999). As a feature particularly characteristic for reptation, this finding suggests that reptation is the dominating chain dynamics mechanism under pore confinement in the corresponding time range. The absolute values of the spin-lattice relaxation times indicate that the diameter of the effective tubes in which reptation occurs is much smaller than the pore diameters on the time scale of spin-lattice relaxation experimens. An estimation leads to a valued ^*～0.5 nm. The impenetrability of the solid pore walls, the uncrossability of polymer chains (“excluded volume”) and the low value of the compressibility in polymer melts create the “corset effect” which reduces the lateral motions of polymer chains to a microscopic scale of only a few tenths of a nanometer.