The determination of all syzygies for the dependent polynomial invariants of the Riemann tensor. I. Pure Ricci and pure Weyl invariants

In this paper, we shall consider all pure Ricci and pure Weyl scalar invariants of any degree, in a four-dimensional Lorentzian space. We present a general graph-theoretic based reduction algorithm which decomposes, using syzygies, any pure invariant in terms of the independent base invariants {r₁,r₂,r₃} or {w₁,w₂}

Crime stories: posnerian pragmatism, Rawlsian pure procedural justice, and the fictional problem

There are many different ways in which law and truth may be said to be related. It is perhaps in the criminal trial that connections between them are of most significance. An orthodox way of describing a criminal trial is that the criminal procedure is seeking to establish the truth concerning some past event, and that success of the procedure is measured by how close its outcome converges with that truth. Criminal justice presents the community with challenging dilemmas in this regard, such as those arising from the notion of double jeopardy. This paper discusses the Rawlsian notions of 'imperfect', 'perfect' and 'pure' procedural justice, and suggests against Rawls that it is pure procedural justice that best represents what we want from a criminal justice system. Good procedure makes good criminal law. A comparison is made with the writings of Habermas and Posner, and given that pure procedural justice eschews transcendental truths, some brief comments are made on the convergence of that position with the realm of the fictional.

An experiment using ICT to investigate pure voting power

We present an experiment to evaluate the accuracy of power indices by measuring the political power embodied in blocks of votes per se. The experiment incorporates several players interacting in lCT chat rooms under supervision. The chat rooms and the selection process reduce or eliminate other political forces leaving logroIIing as the primary political force.

An experimental investigation of pure voting power

We evaluate the accuracy of power indices by experimentally measuring the political power embodied in blocks of votes per se.  The experiment incorporates several players interacting in online chat rooms under supervision.  The chat rooms and the selection process reduce or eliminate extraneous political forces leaving logrolling as the primary political force.  Results show that two standard power indices reflect voting power while other power indices and proportionality do not.

Damping properties of open cell microcellular pure Al foams

Damping behaviours of the open cell microcellular pure Al foams fabricated by sintering and dissolution process with the relative density of 0·31-0·42 and the pore size of 112-325 μm were investigated. The damping characterisation was conducted on a multifunction internal friction apparatus. The internal friction (IF) was measured at frequencies of 1·0, 3·0 and 6·0 Hz over the temperature range of 298-725 K. The measured IF shows that the open cell pure Al foam has a damping capacity that is enhanced in comparison with pure Al. At a lower temperature (∼400 K), the IF of the open cell pure Al foams increases with decreasing relative density, with decreasing pore size and with increasing frequency. The IF peak was found at the temperature range of 433-593 K in the IF curves. It is clear that the IF peak is relaxational type and the activation energy associated with the IF peak is about 1·60 ± 0·02 eV. Defect effects can be used to interpret the damping mechanisms.

Grain refinement of pure magnesium using rolled Zirmax® master alloy (MG-33.3ZR)

Owing to the limited solubility of zirconium in molten magnesium, almost all of the zirconium contained in the Zirmax® master alloy (Mg-33.3Zr) is present in the form of nearly pure zirconium particles. Of them, zirconium particle clusters and individual zirconium particles greater than 5

Standard voting power indices work : an experimental investigation of pure voting power

We evaluate power indices by experimentally measuring the political power embodied in blocks of votes per se. Subjects with differing votes divide a fixed purse by majority rule in online chat rooms under supermision. Chat rooms and processes for selecting subjects reduce or eliminate extraeous political forces leaving logrolling as the primary political force. Results show that various power indices bracket voting power which is more than proportionally concentrated in large players.

Pure boron nitride nanowires produced from boron triiodide

A thick layer of pure boron nitride (BN) nanowires with a uniform diameter of 20 nm was synthesized for the first time using a CVD process with a new precursor of boron triiodide (BI3). Transmission electron microscopy revealed a nanocrystalline structure in the BN nanowires and the absence of any catalyst particle. Some BN nanowires self-assembled into thick threads up to several hundred micrometres long on top of the nanowire layer. The nitriding reactions and lack of catalyst suggest new formation mechanisms of the BN nanowires.

Defendants' liability for pure mental harm to third parties in Australia : still a work in progress

In Australia, both common and statutory law allows compensation for negligently occasioned recognised psychiatric injury, but distinguishes between pure mental harm and consequential mental harm. This column briefly discusses the concept of pure "mental harm" and the major Australian cases relating to defendants' liability to third parties for causing them pure mental harm (Jaensch v Coffey (1984) 155 CLR 549 [PDF]; Tame v New South Wales; Annetts v Australian Stations Pty Ltd (2002) 211 CLR 317 [PDF]; Sullivan v Moody (2001) 207 CLR 562 [PDF]; and Gifford v Strang Patrick Stevedoring Pty Ltd (2003) 214 CLR 269 [PDF]). The analysis focuses on judicial approaches to determining liability in these cases, especially causation. Lack of guiding principles and precise tests for attribution of liability are illustrated by Kemp v Lyell McEwin Health Service (2006) 96 SASR 192 [PDF]. This case is analysed first in the context of common law, and then in the light of the reform legislation contained in the Civil Liability Act 1936 (SA) and similar provisions in other jurisdictions.

Biomimetic coating on pure titanium submitted to different surface treatments

Titanium (Ti) plates were firstly treated to form various types of oxide layers on the surface and then immersed into simulated body fluid (SBF) to evaluate the apatite forming ability. The surface morphology and roughness of the different oxide layers were measured by atomic force microscopy (AFM), and the surface energies were determined based on the Owens-Wendt (OW) methods. It was found that Ti samples after Alkali-Heat treatment (AH) achieved the best apatite formation after soaking in SBF for 3 weeks, compared to those without treatment, thermal or H₂O₂ oxidation. Furthermore, contact angle measurement revealed that the oxide layer on the alkali-heat treated Ti samples possessed the highest surface energy. The results indicate that the apatite inducing ability of a titanium oxide layer is linked to its surface energy. Apatite nucleation is easier on a surface with a higher surface energy.

The effect of skin passing on the material behavior of metal strip in pure bending and tension

The metal strip used in roll forming has often been preprocessed by (tension or roller) leveling or by skin-pass rolling, and as a consequence, may contain residual stresses. These stresses are not well observed by the tensile test, but could have a significant effect on the bending and springback behavior. With the advent of improved process design techniques for roll forming, including advanced finite element techniques, the need for precise material property data has become important. The major deformation mode of roll forming is that of bending combined with unloading and reverse bending, and hence property data derived from bend tests could be more relevant than that from tensile testing.

This work presents a numerical study on the effect of skin passing on the material behavior of stainless steel strip in pure bending and tension. A two dimensional (2-D) numerical model was developed using Abaqus Explicit to analyze the affect of skin passing on the residual stress profile across a section for various working conditions. The deformed meshes and their final stress fields were then imported as pre-defined fields into Abaqus Standard, and the post-skin passing material behavior in pure bending was determined. The results show that a residual stress profile is introduced into the steel strip during skin passing, and that its shape and stress level depend on the overall thickness reduction as well as the number of rolling passes used in the skin passing process. The material behavior in bending and the amount of springback changed significantly depending on the skin pass condition.