Basefield transforms with the convolution property

We present a general framework for constructing transforms in the field of the input which have a convolution-like property. The construction is carried out over the reals, but is shown to be valid over more general fields. We show that these basefield transforms can be viewed as “projections” of the discrete Fourier transform (DFT). Furthermore, by imposing an additional condition on the projections, one may obtain self-inverse versions of the basefield transforms. Applying the theory to the real and complex fields, we show that the projection of the complex DFT results in the discrete combinational Fourier transform (DCFT) and that the imposition of the self-inverse condition on the DCFT yields the discrete Hartley transform (DHT). Additionally, we show that the method of projection may be used to derive efficient basefield transform algorithms by projecting standard FFT algorithms from the extension field to the basefield. Using such an approach, we show that many of the existing real Hartley algorithms are projections of well-known FFT algorithms     

Influence of Irradiation on the Oxide Film Formed on 316 L Stainless Steel in PWR Primary Water

Oxidation of stainless steel in PWR primary water at 325 °C was studied by investigating the influence of defects created at the alloy subsurface by proton irradiation before corrosion exposure. Corrosion experiments were conducted by sequentially exposing samples, with H ₂ ¹⁸ O used for the second exposure. The oxide layer, formed in these conditions was studied by SEM and TEM and could be divided in two parts: an external discontinuous layer composed of crystallites rich in iron and an internal continuous layer richer in chromium. Tracer experiments revealed that the growth of this protective scale was due to oxygen diffusion in the grain boundary of the oxide layer. Defects created by irradiation have an effect on the two oxide layers. They are a preferential nucleation site for the external layer and so increase the density of the crystallites. They also induce a slower diffusion of oxygen in the internal layer.     

A set of algorithms linking NLMS and block RLS algorithms

This paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares (NLMS) and the block recursive least squares (BRLS) algorithms. All these algorithms use small block lengths, thus allowing easy implementation and small input-output delay. It is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares (LMS) algorithm, while converging much faster. A precise evaluation of the arithmetic complexity is provided, and the adaptive behavior of the algorithm is analyzed. Simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the NLMS algorithm. The conclusions of the theoretical analysis are checked by simulations, illustrating that, even in the case where noise is added to the reference signal, the proposed algorithm allows altogether a faster convergence and a lower residual error than the NLMS algorithm. Finally, a sample-by-sample version of this algorithm is outlined, which is the link between the NLMS and recursive least squares (RLS) algorithms     

A Necessary Condition on the Location of Pilot Tones for Maximizing the Correction Capacity in OFDM Systems

This paper presents a new view of the Bose-Chaudhuri-Hocquengem (BCH) code through the addition of some flexibility to the syndromes distribution in the transmitted sequence. In order to get this flexibility, we derive a necessary condition (NC) on the syndromes distribution for decoding BCH codes, which includes the already known Hartmann-Tzeng proposition. This NC is essentially deduced from the decoding process of BCH code, and is related to the locator polynomial and the requested constraints to guarantee a maximal error-correction capacity. The obtained results have the advantage to be applicable for any considered field (finite or not). Furthermore, we prove that when the correction capacity is equal to 2 or 3, the obtained NC becomes also sufficient. This result is very useful in some practical transmission systems such as orthogonal frequency-division multiplexing systems. Once the pilot tones considered in such systems verify the necessary and sufficient condition, it becomes possible to both reduce the peak-to-average-power rate and correct the impulse noise, present in such multicarrier systems. The usefulness of the presented analysis and the exploitation of the derived condition on the pilot tones distribution is illustrated by simulation results in the case of the Hiperlan2 system     

A multi-start evolutionary local search for the two-dimensional loading capacitated vehicle routing problem

This paper addresses an extension of the capacitated vehicle routing problem where customer demand is composed of two-dimensional weighted items (2L-CVRP). The objective consists in designing a set of trips minimizing the total transportation cost with a homogenous fleet of vehicles based on a depot node. Items in each vehicle trip must satisfy the two-dimensional orthogonal packing constraints. A GRASP×ELS algorithm is proposed to compute solutions of a simpler problem in which the loading constraints are transformed into resource constrained project scheduling problem (RCPSP) constraints. We denote this relaxed problem RCPSP-CVRP. The optimization framework deals with RCPSP-CVRP and lastly RCPSP-CVRP solutions are transformed into 2L-CVRP solutions by solving a dedicated packing problem. The effectiveness of our approach is demonstrated through computational experiments including both classical CVRP and 2L-CVRP instances. Numerical experiments show that the GRASP×ELS approach outperforms all previously published methods.     

Analysis of ductility of nanostructured copper prepared by powder metallurgy

The strain rate sensitivity (m) was determined as a function of the strain rate using mechanical jump tests, on a nanostructured copper (grain size of 90 nm) prepared by powder metallurgy. The largest value is m = 0.050 ± 0.005, measured at 1 × 10⁻⁵ s⁻¹. Apparent activation volume was derived giving an insight of the micromechanisms involved in the plastic deformation. Nanostructured face centred cubic metals exhibit elongation due to their strain rate sensitivity and the related delay in the localisation of the deformation. The present analysis brings elements of the micromechanism involved in the plasticity, providing with the guide to design a relevant ultra-fine grained architecture with improved ductility.     

Influence of fluxing in the preparation of bulk Fe-based glassy alloys

Fe-based master ingots, with composition [(Fe₅₀Co₅₀)₇₅B₂₀Si₅]₉₆Nb₄, have been prepared by arc-melting and subsequently purified using the fluxing technique. Rods, with diameters from 1 to 2.5 mm, ribbons and wires with a maximal diameter of 200 μm have been produced from these purified master ingots. The amorphous structure, thermal stability, hardness and magnetic properties of the specimens were studied. In particular, we show by high-energy synchrotron X-ray diffraction that the rods are fully amorphous up to a maximal diameter of 2 mm. Moreover, the [(Fe₅₀Co₅₀)₇₅B₂₀Si₅]₉₆Nb₄ glassy alloy exhibits high hardness (HV = 1050) combined with good soft-magnetic properties (H_c = 63 A/m).     

The effect of nitrogen on the passivation mechanisms and electronic properties of chromium oxide layers

In this work, several Physical Vapour Deposition (PVD) films of chromium and chromium nitride were grown by adjusting the nitrogen flow rate. It was found that films containing lower nitrogen content exhibited better corrosion behaviour in relation to their microstructure. Moreover, the resistivities of the samples were found to increase with N content due to a decrease in the number of metallic bonds in the coatings and a loss of oxide layer conductivity. The latter is linked to a decrease of charge carrier density by the incorporation of species into the passive layers, which decreases cation vacancy density.