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.

The line structure of balanced ternary designs with block size three, index three and rho(2) = 1, 2

In this paper necessary and sufficient conditions for a vector to be the fine structure of a balanced ternary design with block size 3, index 3 and rho(2) = 1 and 2 are determined with one unresolved case.

Numerical modelling of single-layer folding: clarification of an issue regarding the possible effect of computer codes and the influence of initial irregularities

The influence of initial perturbation geometry and material propel-ties on final fold geometry has been investigated using finite-difference (FLAC) and finite-element (MARC) numerical models. Previous studies using these two different codes reported very different folding behaviour although the material properties, boundary conditions and initial perturbation geometries were similar. The current results establish that the discrepancy was not due to the different computer codes but due to the different strain rates employed in the two previous studies (i.e. 10(-6) s(-1) in the FLAC models and 10(-14) s(-1) in the MARC models). As a result, different parts of the elasto-viscous rheological field were bring investigated. For the same material properties, strain rate and boundary conditions, the present results using the two different codes are consistent. A transition in Folding behaviour, from a situation where the geometry of initial perturbation determines final fold shape to a situation where material properties control the final geometry, is produced using both models. This transition takes place with increasing strain rate, decreasing elastic moduli or increasing viscosity (reflecting in each case the increasing influence of the elastic component in the Maxwell elastoviscous rheology). The transition described here is mechanically feasible but is associated with very high stresses in the competent layer (on the order of GPa), which is improbable under natural conditions. (C) 2000 Elsevier Science Ltd. All rights reserved.

Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg G less than or equal to n-2/2 or deg G greater than or equal to n-2/2 + 2g then the state complexity of C-L(D, G) is equal to the Wolf bound. For deg G is an element of [n-1/2, n-3/2 + 2g], we use Clifford's theorem to give a simple lower bound on the state complexity of C-L(D, G). We then derive two further lower bounds on the state space dimensions of C-L(D, G) in terms of the gonality sequence of F/F-q. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of C-L(D, G) and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.

Segregation in binary and ternary liquid fluidized beds

The mechanism underlying segregation in liquid fluidized beds is investigated in this paper, A binary fluidized bed system not at a stable equilibrium condition. is modelled in the literature as forming a mixed part-corresponding to stable mixture-at the bottom of the bed and a pure layer of excess components always floating on the mixed part. On the basis of this model: (0 comprehensive criteria for binary particles of any type to mix/segregate, and (ii) mixing, segregation regime map in terms of size ratio and density ratio of the particles for a given fluidizing medium, are established in this work. Therefore, knowing the properties of given particles, a second type of particles can be chosen in order to avoid or to promote segregation according to the particular process requirements. The model is then advanced for multicomponent fluidized beds and validated against experimental results observed for ternary fluidized beds. (C) 2002 Elsevier Science B.V. All rights reserved.

Further evidence for the reliance of catalysis by rabbit muscle pyruvate kinase upon isomerization of the ternary complex between enzyme and products

Isothermal calorimetry has been used to examine the effect of thermodynamic non-ideality on the kinetics of catalysis by rabbit muscle pyruvate kinase as the result of molecular crowding by inert cosolutes. The investigation, designed to detect substrate-mediated isomerization of pyruvate kinase, has revealed a 15% enhancement of maximal velocity by supplementation of reaction mixtures with 0.1 M proline, glycine or sorbitol. This effect of thermodynamic non-ideality implicates the existence of a substrate-induced conformational change that is governed by a minor volume decrease and a very small isomerization constant; and hence, substantiates earlier inferences that the rate-determining step in pyruvate kinase kinetics is isomerization of the ternary enzyme product complex rather than the release of products. (C) 2003 Elsevier Science B.V. All rights reserved.

Mechanical alloying of MoSi2 with ternary alloying elements. Part 1: Experimental

Phase evolution during the mechanical alloying of Mo and Si elemental powders with a ternary addition of Al, Mg, Ti or Zr was monitored using X-ray diffraction. Rietveld analysis was used to quantify the phase proportions. When Mo and Si are mechanically alloyed in the absence of a ternary element, the tetragonal C11b polymorph of MoSi2 (t-MoSi2) forms by a self-propagating combustion reaction. With additional milling, the tetragonal phase transforms to the hexagonal C40 structure (h-MoSi2). The mechanical alloying of Al, Mg and Ti additions with Mo and Si tend to promote a more rapid transformation of t-MoSi2 to h-MoSi2. In high concentrations, the addition of these ternary elements inhibits the initial combustion reaction, instead promoting the direct formation of h-MoSi2. The addition of Zr tends to stabilise the tetragonal phase.

Mechanical alloying of MoSi2 with ternary alloying elements. Part 2 - computer simulation

A computer model of the mechanical alloying process has been developed to simulate phase formation during the mechanical alloying of Mo and Si elemental powders with a ternary addition of Al, Mg, Ti or Zr. Using the Arhennius equation, the model balances the formation rates of the competing reactions that are observed during milling. These reactions include the formation of tetragonal C11(b) MOSi2 (t-MoSi2) by combustion, the formation of the hexagonal C40 MoSi2 polymorph (h-MoSi2), the transformation of the tetragonal to the hexagonal form, and the recovery of t-MoSi2 from h-MoSi2 and deformed t-MoSi2. The addition of the ternary additions changes the free energy of formation of the associated MoSi2 alloys, i.e. Mo(Si, Al)(2), Mo(Mg, Al)(2), (Mo, Ti)Si-2 (Mo, Zr)Si-2 and (Mo, Fe)Si-2, respectively. Variation of the energy of formation alone is sufficient for the simulation to accurately model the observed phase formation. (C) 2003 Elsevier B.V. All rights reserved.

Corporate governance codes in Australia and New Zealand: Propriety and prosperity

Overview of the central features of corporate governance codes, 'Principles of Good Corporate Governance and Best Practice Recommendations' (released by the ASX Corporate Governance Council) and 'Corporate Governance in New Zealand, Principles and Guidelines' (released by New Zealand Securities Commission) - whether the codes address the right problem - are the solutions of independence and disclosure conceptually and practically viable - whether codes pay sufficient attention to wealth creation.

Pseudo-ternary phase diagrams of aqueous mixtures of Quil A, cholesterol and phospholipid prepared by the lipid-film hydration method

Pseudo-ternary phase diagrams of the polar lipids Quil A, cholesterol (Chol) and phosphatidylcholine (PC) in aqueous mixtures prepared by the lipid film hydration method (where dried lipid film of phospholipids and cholesterol are hydrated by an aqueous solution of Quil A) were investigated in terms of the types of particulate structures formed therein. Negative staining transmission electron microscopy and polarized light microscopy were used to characterize the colloidal and coarse dispersed particles present in the systems. Pseudo-ternary phase diagrams were established for lipid mixtures hydrated in water and in Tris buffer (pH 7.4). The effect of equilibration time was also studied with respect to systems hydrated in water where the samples were stored for 2 months at 4degreesC. Depending on the mass ratio of Quil A, Chol and PC in the systems, various colloidal particles including ISCOM matrices, liposomes, ring-like micelles and worm-like micelles were observed. Other colloidal particles were also observed as minor structures in the presence of these predominant colloids including helices, layered structures and lamellae (hexagonal pattern of ring-like micelles). In terms of the conditions which appeared to promote the formation of ISCOM matrices, the area of the phase diagrams associated with systems containing these structures increased in the order: hydrated in water/short equilibration period < hydrated in buffer/short equilibration period < hydrated in water/prolonged equilibration period. ISCOM matrices appeared to form over time from samples, which initially contained a high concentration of ring-like micelles suggesting that these colloidal structures may be precursors to ISCOM matrix formation. Helices were also frequently found in samples containing ISCOM matrices as a minor colloidal structure. Equilibration time and presence of buffer salts also promoted the formation of liposomes in systems not containing Quil A. These parameters however, did not appear to significantly affect the occurrence and predominance of other structures present in the pseudo-binary systems containing Quil A. Pseudo-ternary phase diagrams of PC, Chol and Quil A are important to identify combinations which will produce different colloidal structures, particularly ISCOM matrices, by the method of lipid film hydration. Colloidal structures comprising these three components are readily prepared by hydration of dried lipid films and may have application in vaccine delivery where the functionality of ISCOMs has clearly been demonstrated. (C) 2003 Elsevier B.V. All rights reserved.

A comparison of pseudo-ternary diagrams of aqueous mixtures of Quil A, cholesterol and phospholipid prepared by lipid-film hydration and dialysis

Pseudo-ternary diagrams for Quil A, phospholipid (phosphatidylcholine (PC) or phosphatidylethanolamine (PE)) and cholesterol were established in order to identify combinations that result in the formation of immune-stimulating complex (ISCOM) matrices and other colloidal structures produced by these three components in aqueous systems following lipid-film hydration or dialysis (methods that can be used to produce ISCOMs). In addition, the effect of equilibration time (1 month at 4degreesC) on the structures formed by the various combinations of the three components was investigated. Depending on the ratio of Quil A, cholesterol and phospholipid, different colloidal particles, including ISCOM matrices, liposomes and ring-like micelles, were found irrespective of the preparation method used. In contrast, worm-like micelles were only observed in systems prepared by lipid-film hydration. For samples prepared by dialysis, ISCOM matrices were predominantly found near the Quil A apex of the pseudo-ternary diagram (> 50% Quil A). On the other hand, for samples prepared by lipid-film hydration, ISCOM matrices were predominantly found near the phospholipid apex of the pseudo-ternary diagram (> 50% phospholipid). The regions in the pseudo-ternary diagrams in which ISCOM matrices were observed increased following an extended equilibration time, particularly for samples prepared by lipid-film hydration. Differences were also observed between pseudoternary diagrams prepared using either PE or PC as phospholipids.

Influence of nanowire density on the shape and optical properties of ternary InGaAs nanowires

We have synthesized ternary InGaAs nanowires on (111)B GaAs surfaces by metal-organic chemical vapor deposition. Au colloidal nanoparticles were employed to catalyze nanowire growth. We observed the strong influence of nanowire density on nanowire height, tapering, and base shape specific to the nanowires with high In composition. This dependency was attributed to the large difference of diffusion length on (111)B surfaces between In and Ga reaction species, with In being the more mobile species. Energy dispersive X-ray spectroscopy analysis together with high-resolution electron microscopy study of individual InGaAs nanowires shows large In/Ga compositional variation along the nanowire supporting the present diffusion model. Photoluminescence spectra exhibit a red shift with decreasing nanowire density due to the higher degree of In incorporation in more sparsely distributed InGaAs nanowires.