On the problem of algebraic completeness for the invariants of the Riemann Tensor: I

We present a new determining set, CZ, of Riemann invariants which possesses the minimum degree property. From an analysis on the possible independence of CZ, we are led to the division of all space-times into two distinct, invariantly characterized, classes: a general class M_G+, and a special, singular class M_S For each class, we provide an independent set of invariants (I_G+) ⊂ CZ and I_S ⊂ CZ, respectively) which, with the results of a sequel paper, will be shown to be algebraically complete.

On the problem of algebraic completeness for the invariants of the Riemann tensor. III.

We study the set CZ of invariants [Zakhary and Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space-times whose Ricci tensors possess a null eigenvector. We show that all cases are maximally backsolvable, in terms of sets of invariants from CZ, but that some cases are not completely backsolvable and these all possess an alignment between an eigenvector of the Ricci tensor with a repeated principal null vector of the Weyl tensor. We provide algebraically complete sets for each canonically different space-time and hence conclude with these results and those of a previous article [Carminati, Zakhary, and McLenaghan, J. Math. Phys. 43, 492 (2002)] that the CZ set is determining or maximal.

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}

Characterising derivative-based loan arrangements

The income tax and GST laws contain an array of rules that apply to debt and gains in the nature of interest. The definitions of 'debt' or 'loan' and amounts in the nature of 'interest' vary across the provisions and tax officials, taxpayers and courts must decide whether the terms should be read as applying to debt, loans or interest in a narrow legal sense or should be read more broadly to catch multi-element arrangements that give effect to a debt or loan relationship in an economic or commercial sense but not in conventional single document form. This article reviews the UK, US and Australian approaches to interpreting multi-element transactions and considers whether four tax provisions dealing with debt should be interpreted to apply to multi-element, derivative-based loan arrangements.

The determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. II. mixed invariants of Eeven degree in the Ricci Spinor

We continue our analysis of the polynomial invariants of the Riemann tensor in a four-dimensional Lorentzian space. We concentrate on the mixed invariants of even degree in the Ricci spinor Φ_ABȦḂ and show how, using constructive graph-theoretic methods, arbitrary scalar contractions between copies of the Weyl spinor ψ_ABCD, its conjugate ψ_ȦḂĊḊ and an even number of Ricci spinors can be expressed in terms of paired contractions between these spinors. This leads to an algorithm for the explicit expression of dependent invariants as polynomials of members of the complete set. Finally, we rigorously prove that the complete set as given by Sneddon [J. Math. Phys. 39, 1659-1679 (1998)] for this case is both complete and minimal.

Correct weight? analysing Australian football through a derivative global or cultural cringe model

The application of a 'global' model, in practice usually British or American, and generalised sociological concepts to a particular sport and its social and cultural context is not always appropriate. In Australian academia, the custom is particularly appealing, due to the Australian colonial 'cultural cringe', the pattern of automatic deference to overseas (termed 'international') knowledge. This article argues that 'Fresh Prince of Coloma! Dome: Indigenous Logic in the AFL' (Football Studies, 8(1), 2005) inappropriately applies American sociological, and American football, logic to the indigenous Australian game Australian football, which differs in character both as a game and in its social, cultural and political context. The three researchers do not take account of the factors of height and weight in Australian football, and the average size of Aboriginal players, and of the relationship between speed and strength in the game as strategies and tactics change. Both omissions constitute fundamental flaws. American football and sports sociology's ideas of 'central position theory', with a suggestion of underlying racism, is of limited relevance to Australian football. It is also possible that the American sitcom, Fresh Prince of Bel Air, was neither a helpful muse nor a suitable metaphor for research into this subj ect. In Australian football, a game in which few 'central positions' are crucial and in which 'leadership positions' can be found in many parts of the ground, including the half-back flank and the wing, neither size nor position are the only major determinants of significance in the team.

On the determinants of derivative usage by Australian companies

This paper provides an examination of the determinants of derivative use by Australian corporations. We analysed the characteristics of a sample of 469 firm/year observations drawn from the largest Australian publicly listed companies in 1999 and 2000 to address two issues: the decision to use financial derivatives and the extent to which they are used. Logit analysis suggests that a firm's leverage (distress proxy), size (financial distress and setup costs) and liquidity (financial constraints proxy) are important factors associated with the decision to use derivatives. These findings support the financial distress hypothesis while the evidence on the underinvestment hypothesis is mixed. Additionally, setup costs appear to be important, as larger firms are more likely to use derivatives. Tobit results, on the other hand, show that once the decision to use derivatives has been made, a firm uses more derivatives as its leverage increases and as it pays out more dividends (hedging substitute proxy). The overall results indicate that Australian companies use derivatives with a view to enhancing the firms' value rather than to maximizing managerial wealth. In particular, corporations' derivative policies are mostly concerned with reducing the expected cost of financial distress and managing cash flows. Our inability to identify managerial influences behind the derivative decision suggests a competitive Australian managerial labor market.

Derivative actions as a mechanism for the protection of minority shareholders in China: a result of convergence or divergence

The protection of minority shareholders has become one of the key features of company law reform in many countries in recent years. Various mechanisms have been created to achieve this objective. Australia has introduced the statutory derivative action procedure mainly based on models drawn from Canada and New Zealand; this provision was inserted into the Corporations Act in March 2000. China has also adopted a similar mechanism – known as the shareholder representative action; this scheme was based upon China’s understanding of statutory derivative actions in Western countries. China’s derivative action mechanism is reflected in amendments to the 2005 PRC Company Law and 2005 Securities Law that both were passed on 27 October 2005 and came into effective on 1 January 2006. The development of statutory derivative actions in different countries demonstrates the interaction between forces of convergence and divergence in company law reforms. This article reviews different mechanisms adopted in the Chinese law for the protection of minority shareholders. It especially focuses on an analysis of the nature of the shareholder representative action and the procedures for its utilisation in China – the equivalent to Western countries’ derivative actions. In comparison with statutory derivative actions in Australia, this article argues that the concept of the shareholder representative action in China rests upon a misunderstanding of Western derivative actions; this has involved a compromise between the dire need to protect shareholders and the ambiguities of a weak court system. As a consequence, China’s reforms in this area are largely a tentative gesture and are therefore unlikely to be very effective.

Determination of all syzygies for the dependent polynomial invariants of the Riemann Tensor. III. mixed invariants of arbitrary degree in the Ricci Spinor

In this paper, we rigorously prove that the complete set of Riemann tensor invariants given by Sneddon [J. Math. Phys. 40, 5905 (1999)] is both minimal and complete. Furthermore, we provide a two-stage algorithm for the explicit construction of polynomial syzygies relating any dependent Riemann tensor invariant to members of the complete set.

Does the type of derivative instrument used by companies impact firm value?

We explore the relationship between the type of derivative instrument used and firm value, in a sample of Australian firms. Specifically, we examine the impact of the corporate use of swaps, futures, forwards and options, and the extent of such usage, on firm value. Our findings suggest that a 'discount' is most severely imposed on users of swaps.

On the problem of algebraic completeness for the invariants of the Riemann tensor. II

We study the set of invariants CZ [E. Zakhary and J. Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space-times whose Ricci tensors do not possess a null eigenvector. We show that all cases are completely backsolvable in terms of sets of invariants from CZ. We provide algebraically complete sets for each canonically different space-time.

Aspergillus species, cyclic dimeric dipeptide derivative substance P antagonist biosynthetic products thereof, and process for preparation thereof

A novel Aspergillus species, cyclic dimeric dipeptide derivatives which are biosynthetic products thereof and are useful as Substance P antagonists and therefore as analgesic and/or antiinflammatory agents, and a process for preparation of the biosynthetic products are disclosed.

Syzygies of the polynomial invariants of the Riemann tensor

This thesis introduces a novel way of writing polynomial invariants as network graphs, and applies this diagrammatic notation scheme, in conjunction with graph theory, to derive algorithms for constructing relationships (syzygies) between different invariants. These algorithms give rise to a constructive solution of a longstanding classical problem in invariant theory.