Matrix-product codes over Fq

Codes C-1,...,C-M of length it over F-q and an M x N matrix A over F-q define a matrix-product code C = [C-1 (...) C-M] (.) A consisting of all matrix products [c(1) (...) c(M)] (.) A. This generalizes the (u/u + v)-, (u + v + w/2u + v/u)-, (a + x/b + x/a + b + x)-, (u + v/u - v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of /C/, d(C), the minimum Hamming distance of C, and C-perpendicular to. It also reveals an interesting connection with MDS codes. We determine /C/ when A is non-singular. To underbound d(C), we need A to be 'non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary 'Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C-perpendicular to can be described using C-1(perpendicular to),...,C-M(perpendicular to) and a transformation of A. This yields d(C-perpendicular to). Finally we show that an NSC matrix-product code is a generalized concatenated code.

On the direct product of two weak uniquely completable partial latin squares

In this note we show by counter-example that the direct product of two weak uniquely completable partial latin squares is not necessarily a uniquely completable partial latin square. This counter-example rejects a conjecture by Gower (see [3]) on the direct product of two uniquely completable partial latin squares.

A servicing strategy for items sold under warranty

When repairable items sold under warranty fail, the rectification action taken by the manufacturer can be either a repair or a replacement, In this paper a new repair-replacement strategy is proposed for the manufacturer when the items are sold with a non-renewing free replacement warranty policy. The strategy involves splitting the warranty period into two intervals where only repairs are carried out, separated by a third interval with at most one replacement.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

Effect of supplementation with a by-product of molasses fermentation or a non-protein nitrogen/mineral mix on feed intake and microbial protein supply in sheep consuming chopped oat (Avena sativa) hay

Crossbred ewes, weighing 30-40 kg, were assigned to three groups of six animals. One group of sheep was fed chopped oat hay (control), the second group was fed the control diet plus 30 g per head per day spray dried residue from the fermentation of molasses and the third group was fed the control diet plus 30 g per head per day of a non-protein nitrogen/mineral mix. Voluntary feed intake, digestibility of DM, OM and nitrogen, nitrogen balance and microbial nitrogen flow to the intestines were significantly increased by supplementation but efficiency of microbial protein production was not affected. (C) 2001 Elsevier Science BN. All rights reserved,

R-matrices and the tensor product graph method

A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

Calculation of resonances and product state distributions for the unimolecular dissociation of H2S

Resonance phenomena associated with the unimolecular dissociation of H2S --> SH + H have been investigated quantum mechanically by the Lanczos homogeneous filter diagonalization method using a newly developed potential energy surface (J. Chem. Phys. 2001, 114, 320). Resonance energies, widths (rates), and product state distributions have been obtained. Both dissociation rates and product state distributions of SH show, strong fluctuations, indicating that the dissociation of H2S is essentially irregular. Statistical analysis of neighboring level spacing and width distributions also confirms this behavior. The dissociation rates and product state distributions are compared to the predictions of quantum phase space theory.

Prediction of absolute rate coefficients and product branching ratios for the C(P-3) plus allene reaction system

Complex chemical reactions in the gas phase can be decomposed into a network of elementary (e.g., unimolecular and bimolecular) steps which may involve multiple reactant channels, multiple intermediates, and multiple products. The modeling of such reactions involves describing the molecular species and their transformation by reaction at a detailed level. Here we focus on a detailed modeling of the C(P-3)+allene (C3H4) reaction, for which molecular beam experiments and theoretical calculations have previously been performed. In our previous calculations, product branching ratios for a nonrotating isomerizing unimolecular system were predicted. We extend the previous calculations to predict absolute unimolecular rate coefficients and branching ratios using microcanonical variational transition state theory (mu-VTST) with full energy and angular momentum resolution. Our calculation of the initial capture rate is facilitated by systematic ab initio potential energy surface calculations that describe the interaction potential between carbon and allene as a function of the angle of attack. Furthermore, the chemical kinetic scheme is enhanced to explicitly treat the entrance channels in terms of a predicted overall input flux and also to allow for the possibility of redissociation via the entrance channels. Thus, the computation of total bimolecular reaction rates and partial capture rates is now possible. (C) 2002 American Institute of Physics.

A new preventive maintenance strategy for items sold under warranty

When products are sold under warranty, the manufacturer incurs additional costs for warranty servicing. Preventive maintenance actions can be used to reduce this cost and these are worthwhile only if the extra cost incurred is less than the reduction achieved. In this paper we propose a new preventive maintenance policy where the parameters are selected optimally to minimize the total warranty servicing cost.

A normative study of distortion product otoacoustic emissions in six-year-old school children

Evoked otoacoustic emissions have demonstrated potential for application in the community-based hearing screening of paediatric populations. Distortion-product otoacoustic emissions (DPOAEs), as opposed to transient evoked otoacoustic emissions (TEOAEs), have not been extensively researched in this regard. The current study aimed to describe the range of DPOAE values obtained in a large cohort (1576 ears) of 6-year-old children in school settings and to examine possible ear asymmetry, gender and history of ear infection effects on the data. Results indicated a variety of significant effects, particularly in the high frequencies, for DPOAE signal-to-noise ratio. The measurement parameter, DPOAE amplitude (DP-amp), was found to display potentially less clinical applicability due to large standard deviation values. Use of descriptive normative data, as derived in the present investigation, may contribute toward future improvements in the hearing screening of 6-year-old schoolchildren

Polymer product engineering utilising oscillatory baffled reactors

The Oscillatory baffled reactor (OBR) can be used to produce particles with controlled size and morphology, in batch or continuous flow. This is due to the effect of the superimposed oscillations that radially mixes fluid but still allows plug-flow (or close to plug flow) behaviour in a continuous system. This mixing, combined with a close to a constant level of turbulence intensity in the reactor, leads to tight droplet and subsequent product particle size distributions. By applying population balance equations together with experimental droplet size distributions, breakage rates of droplets can be determined and this is a useful tool for understanding the product engineering in OBRs. (C) 2002 Elsevier Science B.V All rights reserved.