Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.

Order of instruction effects - do they make a difference when teaching senior chemistry with computer based visualizations?

This study investigated whether conceptual development is greater if students learning senior chemistry hear teacher explanations and other traditional teaching approaches first then see computer based visualizations or vice versa. Five Canadian chemistry classes, taught by three different teachers, studied the topics of Le Chatelier’s Principle and dynamic chemical equilibria using scientific visualizations with the explanation and visualizations in different orders. Conceptual development was measured using a 12 item test based on the Chemistry Concepts Inventory. Data was obtained about the students’ abilities, learning styles (auditory, visual or kinesthetic) and sex, and the relationships between these factors and conceptual development due to the teaching sequences were investigated. It was found that teaching sequence is not important in terms of students’ conceptual learning gains, across the whole cohort or for any of the three subgroups.

Supplement : Efficient weak second-order stochastic Runge-Kutta methods for non-commutative Stratonvich stochastic differential equations

This paper gives a modification of a class of stochastic Runge–Kutta methods proposed in a paper by Komori (2007). The slight modification can reduce the computational costs of the methods significantly.

Pattern recognition using invariants defined from higher order spectra - one-dimensional inputs

A new approach to pattern recognition using invariant parameters based on higher order spectra is presented. In particular, invariant parameters derived from the bispectrum are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale and amplification invariant, as well. A minimal set of these invariants is selected as the feature vector for pattern classification, and a minimum distance classifier using a statistical distance measure is used to classify test patterns. The classification technique is shown to distinguish two similar, but different bolts given their one-dimensional profiles. Pattern recognition using higher order spectral invariants is fast, suited for parallel implementation, and has high immunity to additive Gaussian noise. Simulation results show very high classification accuracy, even for low signal-to-noise ratios.

Higher order spectral analysis of Chua's circuit

Higher order spectral analysis is used to investigate nonlinearities in time series of voltages measured from a realization of Chua's circuit. For period-doubled limit cycles, quadratic and cubic nonlinear interactions result in phase coupling and energy exchange between increasing numbers of triads and quartets of Fourier components as the nonlinearity of the system is increased. For circuit parameters that result in a chaotic Rossler-type attractor, bicoherence and tricoherence spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. When the circuit exhibits a double-scroll chaotic attractor the bispectrum is zero, but the tricoherences are high, consistent with the importance of higher-than-second order nonlinear interactions during chaos associated with the double scroll.

Higher-order spectral analysis of nonlinear ocean surface gravity waves

Higher-order spectral analysis is used to detect the presence of secondary and tertiary forced waves associated with the nonlinearity of energetic swell observed in 8- and 13-m water depths. Higher-order spectral analysis techniques are first described and then applied to the field data, followed by a summary of the results.

Higher-Order spectra of nonlinear polynomial models for Chua's circuit

Polynomial models are shown to simulate accurately the quadratic and cubic nonlinear interactions (e.g. higher-order spectra) of time series of voltages measured in Chua's circuit. For circuit parameters resulting in a spiral attractor, bispectra and trispectra of the polynomial model are similar to those from the measured time series, suggesting that the individual interactions between triads and quartets of Fourier components that govern the process dynamics are modeled accurately. For parameters that produce the double-scroll attractor, both measured and modeled time series have small bispectra, but nonzero trispectra, consistent with higher-than-second order nonlinearities dominating the chaos.

On the behaviour of higher-order spectral features for object recognition in the presence of various types of noise

This paper presents results on the robustness of higher-order spectral features to Gaussian, Rayleigh, and uniform distributed noise. Based on cluster plots and accuracy results for various signal to noise conditions, the higher-order spectral features are shown to be better than moment invariant features.

Towards testing a new first-order decision making model for the procurement of public sector major infrastructure

Given global demand for new infrastructure, governments face substantial challenges in funding new infrastructure and simultaneously delivering Value for Money (VfM). As background to this challenge, a brief review is given of current practice in the selection of major public sector infrastructure in Australia, along with a review of the related literature concerning the Multi-Attribute Utility Approach (MAUA) and the effect of MAUA on the role of risk management in procurement selection. To contribute towards addressing the key weaknesses of MAUA, a new first-order procurement decision making model is mentioned. A brief summary is also given of the research method and hypothesis used to test and develop the new procurement model and which uses competition as the dependent variable and as a proxy for VfM. The hypothesis is given as follows: When the actual procurement mode matches the theoretical/predicted procurement mode (informed by the new procurement model), then actual competition is expected to match optimum competition (based on actual prevailing capacity vis-à-vis the theoretical/predicted procurement mode) and subject to efficient tendering. The aim of this paper is to report on progress towards testing this hypothesis in terms of an analysis of two of the four data components in the hypothesis. That is, actual procurement and actual competition across 87 road and health major public sector projects in Australia. In conclusion, it is noted that the Global Financial Crisis (GFC) has seen a significant increase in competition in public sector major road and health infrastructure and if any imperfections in procurement and/or tendering are discernible, then this would create the opportunity, through the deployment of economic principles embedded in the new procurement model and/or adjustments in tendering, to maintain some of this higher level post-GFC competition throughout the next business cycle/upturn in demand including private sector demand. Finally, the paper previews the next steps in the research with regard to collection and analysis of data concerning theoretical/predicted procurement and optimum competition.

Practice and Procedure. Self-executing order - construction - whether further judicial at required for self-executing order to take effect

In Mango Boulevard Pty Ltd v Spencer [2010] QCA 207, a self-executing order had been made in consequence of continuing default by parties to the proceedings in meeting their disclosure obligations. The case involved several questions about the construction and implications of the self-executing order. This note focuses on the aspects of the case relating to that order.

Towards human and social innovation: not wanting to know in order to create

The formation of a venture relies, in part, upon the participants reaching a shared understanding of purpose and process. Yet in circumstances of great complexity and uncertainty how can such a shared understanding be created? If the response to complexity and uncertainty is to seek simplicity in order to find commonality then what is lost and what is at risk? Can shared understandings of purpose and process be arrived at by embracing complexity and uncertainty and if so how? These questions led us to explore the process of dialogue and communication of a team in its formative stages. Our interests were not centred upon the behavioural characteristics of the individuals in the 'forming' stage of group dynamics but rather the process of cognitive and linguistic turns, the wax and wan of ideas and, the formation of shared meaning. This process of cognitive and linguistic turns was focused thematically on the areas of foresight, innovation, entrepreneurship, and public policy. This cross disciplinary exploration sought to explore potential synergies between these domains, in particular in developing a conceptual basis for long term thinking that can inform wiser public policy.

Microstrip decoupling networks for low-order multi-port arrays with reduced element spacing

An array of monopole elements with reduced element spacing of λ/6 to λ/20 is considered for application in digital beam-forming and direction-finding. The small element spacing introduces strong mutual coupling between the array elements. This paper discusses that decoupling can be achieved analytically for arrays with three elements and describes Kuroda’s identities to realize the lumped elements of the derived decoupling network. Design procedures and equations are proposed. Experimental results are presented. The decoupled array has a bandwidth of 1% and a superdirective radiation pattern.

An aspect query language model based on query decomposition and high-order contextual term associations

In information retrieval (IR) research, more and more focus has been placed on optimizing a query language model by detecting and estimating the dependencies between the query and the observed terms occurring in the selected relevance feedback documents. In this paper, we propose a novel Aspect Language Modeling framework featuring term association acquisition, document segmentation, query decomposition, and an Aspect Model (AM) for parameter optimization. Through the proposed framework, we advance the theory and practice of applying high-order and context-sensitive term relationships to IR. We first decompose a query into subsets of query terms. Then we segment the relevance feedback documents into chunks using multiple sliding windows. Finally we discover the higher order term associations, that is, the terms in these chunks with high degree of association to the subsets of the query. In this process, we adopt an approach by combining the AM with the Association Rule (AR) mining. In our approach, the AM not only considers the subsets of a query as “hidden” states and estimates their prior distributions, but also evaluates the dependencies between the subsets of a query and the observed terms extracted from the chunks of feedback documents. The AR provides a reasonable initial estimation of the high-order term associations by discovering the associated rules from the document chunks. Experimental results on various TREC collections verify the effectiveness of our approach, which significantly outperforms a baseline language model and two state-of-the-art query language models namely the Relevance Model and the Information Flow model

Third-order theory of spectacle lenses applied to correction of peripheral refractive errors

Purpose: To demonstrate that relatively simple third-order theory can provide a framework which shows how peripheral refraction can be manipulated by altering the forms of spectacle lenses. Method: Third-order equations were used to yield lens forms that correct peripheral power errors, either for the lenses alone or in combination with typical peripheral refractions of myopic eyes. These results were compared with those of finite ray-tracing. Results: The approximate forms of spherical and conicoidal lenses provided by third-order theory were flatter over a moderate myopic range than the forms obtained by rigorous raytracing. Lenses designed to correct peripheral refractive errors produced large errors when used with foveal vision and a rotating eye. Correcting astigmatism tended to give large errors in mean oblique error and vice versa. When only spherical lens forms are used, correction of the relative hypermetropic peripheral refractions of myopic eyes which are observed experimentally, or the provision of relative myopic peripheral refractions in such eyes, seems impossible in the majority of cases. Conclusion: The third-order spectacle lens design approach can readily be used to show trends in peripheral refraction.

Serious fears across cultures about the collapse of the world order

This chapter approaches resilience from an evolutionary psychology (socio-biological) perspective. It argues that the internal constitution and mental toughness of the individual will provide a core protection for life’s inevitable tests in the innumerable micro and macro environments humans find themselves. The many descriptors of the construct of resilience used in various studies are explored. Finally, the difference psychologists can make in the therapy of clients whose resilience is being tested, is examined by means of case examples.