Determining when the absolute state complexity of a Hermitian code achieves its DLP bound

Let g be the genus of the Hermitian function field H/F(q)2 and let C-L(D,mQ(infinity)) be a typical Hermitian code of length n. In [Des. Codes Cryptogr., to appear], we determined the dimension/length profile (DLP) lower bound on the state complexity of C-L(D,mQ(infinity)). Here we determine when this lower bound is tight and when it is not. For m less than or equal to n-2/2 or m greater than or equal to n-2/2 + 2g, the DLP lower bounds reach Wolf's upper bound on state complexity and thus are trivially tight. We begin by showing that for about half of the remaining values of m the DLP bounds cannot be tight. In these cases, we give a lower bound on the absolute state complexity of C-L(D,mQ(infinity)), which improves the DLP lower bound. Next we give a good coordinate order for C-L(D,mQ(infinity)). With this good order, the state complexity of C-L(D,mQ(infinity)) achieves its DLP bound (whenever this is possible). This coordinate order also provides an upper bound on the absolute state complexity of C-L(D,mQ(infinity)) (for those values of m for which the DLP bounds cannot be tight). Our bounds on absolute state complexity do not meet for some of these values of m, and this leaves open the question whether our coordinate order is best possible in these cases. A straightforward application of these results is that if C-L(D,mQ(infinity)) is self-dual, then its state complexity (with respect to the lexicographic coordinate order) achieves its DLP bound of n /2 - q(2)/4, and, in particular, so does its absolute state complexity.

The future role of government in knowledge-based economies

In this article, we draw together aspects of contemporary theories of knowledge (particularly organisational knowledge) and complexity theory to demonstrate how appropriate conceptual rigor enables both the role of government and the directions of policy development in knowledge-based economies to be identified. Specifically we ask, what is the role of government in helping shape the knowledge society of the future? We argue that knowledge policy regimes must go beyond the modes of policy analysis currently used in innovation, information and technology policy because they are based in an industrial rather than post-industrial analytical framework. We also argue that if we are to develop knowledge-based economies, more encompassing images of the future than currently obtain in policy discourse are required. We therefore seek to stimulate and provoke an array of lines of thought about government and policy for such economies. Our objective is to focus on ideas more than argument and persuasion.

Economics teaching in Australian universities: Rewards and outcomes

This paper presents evidence from two survey's to help explain the poor ratings consistently given to the teaching of economics at Australian universities. The evidence suggests that the Poor ratings of economics teaching can be attributed to two related factors: inappropriate pedagogical practices and lack of rewards for allocating additional time to teaching. The survey data oil pedagogy, in economics consist of 205 responses from graduates from two Queensland universities. The time elapsed since graduation ranges from 1 to 10 years. The survey data on academics' time allocation consist of 290 responses from academic economists across a wide range of Australian universities.

Effects of slurry rheology on industrial grinding performance

To determine the effect of slurry rheology on industrial grinding performance, 45 surveys were conducted on 16 full-scale grinding mills in five sites. Four operating variables - mill throughput, slurry density, slurry viscosity and feed fines content-were investigated. The rheology of the mill discharge slurries was measured either on-line or off-line, and the data were processed using a standard procedure to obtain a full range of flow curves. Multi-linear regression was employed as a statistical analysis tool to determine whether or not rheological effects exert an influence on industrial grinding, and to assess the influence of the four mill operating conditions on mill performance in terms of the Grinding Index, a criterion describing the overall breakage of particles across the mill. The results show that slurry rheology does influence industrial grinding. The trends of these effects on Grinding Index depend upon the rheological nature of the slurry-whether the slurries are dilatant or pseudoplastic, and whether they exhibit a high or low yield stress. The interpretation of the regression results is discussed, the observed effects are summarised, and the potential for incorporating rheological principles into process control is considered, Guidelines are established to improve industrial grinding operations based on knowledge of the rheological effects. This study confirms some trends in the effect of slurry rheology on grinding reported in the literature, and extends these to a broader understanding of the relationship between slurry properties and rheology, and their effects on industrial milling performance. (C) 2002 Elsevier Science B.V. All rights reserved.

Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

A variable stepsize implementation for stochastic differential equations

Stochastic differential equations (SDEs) arise from physical systems where the parameters describing the system can only be estimated or are subject to noise. Much work has been done recently on developing higher order Runge-Kutta methods for solving SDEs numerically. Fixed stepsize implementations of numerical methods have limitations when, for example, the SDE being solved is stiff as this forces the stepsize to be very small. This paper presents a completely general variable stepsize implementation of an embedded Runge Kutta pair for solving SDEs numerically; in this implementation, there is no restriction on the value used for the stepsize, and it is demonstrated that the integration remains on the correct Brownian path.