Automatic detection and treatment of oscillatory and/or stiff ordinary differential equations /

"Presented at the Differential Equation Workshop, Center for Interdisciplinary Research (Zif), University of Bielefeld, West Germany, April 21, 1980."

A Chinese and English phrase book in the Canton dialect; or, Dialogues on ordinary and familiar subjects for the use of the Chinese resident in America, and of Americans desirous of learning the Chinese language,

Added title-page in Chinese.

The kitchen gardener's instructor : containing a catalogue of garden and herb seed, with practical directions under each head for the cultivation of culinary vegetables and herbs : with a calendar, showing the work necessary to be done in a kitchen garden ... : also, directions for forcing or forwarding vegetables out of the ordinary season : the whole adapted to the climate of the United States /

Advertisement: 1 p. (at end).

The American kitchen-gardener : containing complete practical directions for the cultivation of culinary vegetables and herbs, together with instructions for forcing or forwarding vegetables out of the ordinary season /

Mode of access: Internet.

A new family encyclopedia; : or compendium of universal knowledge: comprehending a plain and practical view of those subjects most interesting to persons in the ordinary professions of life. Illustrated by numberous engravings.

Mode of access: Internet.

The kitchen gardener's instructor : containing a catalogue of garden and herb seeds, with practical directions under each head, for the cultivation of culinary vegetables & herbs : with a calendar, showing the work necessary to be done in a kitchen garden, in every month throughout the season : also, directions for forcing or forwarding vegetables out of the ordinary season /

Includes index.

A Compendious or briefe examination of certayne ordinary complaints of diuers of our countrymen in these our dayes : which although they are in some parte vnjust and friuolous, yet are they all by way of dialogue throughly debated and discussed by William Shakespeare, gentleman.

Reprint. Originally published: London : Thomas Marshe, 1581.

Negotiating social and moral order in internet relay chat

Although internet chat is a significant aspect of many internet users’ lives, the manner in which participants in quasi-synchronous chat situations orient to issues of social and moral order remains to be studied in depth. The research presented here is therefore at the forefront of a continually developing area of study. This work contributes new insights into how members construct and make accountable the social and moral orders of an adult-oriented Internet Relay Chat (IRC) channel by addressing three questions: (1) What conversational resources do participants use in addressing matters of social and moral order? (2) How are these conversational resources deployed within IRC interaction? and (3) What interactional work is locally accomplished through use of these resources? A survey of the literature reveals considerable research in the field of computer-mediated communication, exploring both asynchronous and quasi-synchronous discussion forums. The research discussed represents a range of communication interests including group and collaborative interaction, the linguistic construction of social identity, and the linguistic features of online interaction. It is suggested that the present research differs from previous studies in three ways: (1) it focuses on the interaction itself, rather than the ways in which the medium affects the interaction; (2) it offers turn-by-turn analysis of interaction in situ; and (3) it discusses membership categories only insofar as they are shown to be relevant by participants through their talk. Through consideration of the literature, the present study is firmly situated within the broader computer-mediated communication field. Ethnomethodology, conversation analysis and membership categorization analysis were adopted as appropriate methodological approaches to explore the research focus on interaction in situ, and in particular to investigate the ways in which participants negotiate and co-construct social and moral orders in the course of their interaction. IRC logs collected from one chat room were analysed using a two-pass method, based on a modification of the approaches proposed by Pomerantz and Fehr (1997) and ten Have (1999). From this detailed examination of the data corpus three interaction topics are identified by means of which participants clearly orient to issues of social and moral order: challenges to rule violations, ‘trolling’ for cybersex, and experiences regarding the 9/11 attacks. Instances of these interactional topics are subjected to fine-grained analysis, to demonstrate the ways in which participants draw upon various interactional resources in their negotiation and construction of channel social and moral orders. While these analytical topics stand alone in individual focus, together they illustrate different instances in which participants’ talk serves to negotiate social and moral orders or collaboratively construct new orders. Building on the work of Vallis (2001), Chapter 5 illustrates three ways that rule violation is initiated as a channel discussion topic: (1) through a visible violation in open channel, (2) through an official warning or sanction by a channel operator regarding the violation, and (3) through a complaint or announcement of a rule violation by a non-channel operator participant. Once the topic has been initiated, it is shown to become available as a topic for others, including the perceived violator. The fine-grained analysis of challenges to rule violations ultimately demonstrates that channel participants orient to the rules as a resource in developing categorizations of both the rule violation and violator. These categorizations are contextual in that they are locally based and understood within specific contexts and practices. Thus, it is shown that compliance with rules and an orientation to rule violations as inappropriate within the social and moral orders of the channel serves two purposes: (1) to orient the speaker as a group member, and (2) to reinforce the social and moral orders of the group. Chapter 6 explores a particular type of rule violation, solicitations for ‘cybersex’ known in IRC parlance as ‘trolling’. In responding to trolling violations participants are demonstrated to use affiliative and aggressive humour, in particular irony, sarcasm and insults. These conversational resources perform solidarity building within the group, positioning non-Troll respondents as compliant group members. This solidarity work is shown to have three outcomes: (1) consensus building, (2) collaborative construction of group membership, and (3) the continued construction and negotiation of existing social and moral orders. Chapter 7, the final data analysis chapter, offers insight into how participants, in discussing the events of 9/11 on the actual day, collaboratively constructed new social and moral orders, while orienting to issues of appropriate and reasonable emotional responses. This analysis demonstrates how participants go about ‘doing being ordinary’ (Sacks, 1992b) in formulating their ‘first thoughts’ (Jefferson, 2004). Through sharing their initial impressions of the event, participants perform support work within the interaction, in essence working to normalize both the event and their initial misinterpretation of it. Normalising as a support work mechanism is also shown in relation to participants constructing the ‘quiet’ following the event as unusual. Normalising is accomplished by reference to the indexical ‘it’ and location formulations, which participants use both to negotiate who can claim to experience the ‘unnatural quiet’ and to identify the extent of the quiet. Through their talk participants upgrade the quiet from something legitimately experienced by one person in a particular place to something that could be experienced ‘anywhere’, moving the phenomenon from local to global provenance. With its methodological design and detailed analysis and findings, this research contributes to existing knowledge in four ways. First, it shows how rules are used by participants as a resource in negotiating and constructing social and moral orders. Second, it demonstrates that irony, sarcasm and insults are three devices of humour which can be used to perform solidarity work and reinforce existing social and moral orders. Third, it demonstrates how new social and moral orders are collaboratively constructed in relation to extraordinary events, which serve to frame the event and evoke reasonable responses for participants. And last, the detailed analysis and findings further support the use of conversation analysis and membership categorization as valuable methods for approaching quasi-synchronous computer-mediated communication.

Reasonable adjustment and the assessment of students with disabilities: Australian legal issues and trends

Student assessment is particularly important, and particularly controversial, because it is the means by which student achievement is determined. Reasonable adjustment to student assessment is of equal importance as the means of ensuring the mitigation, or even elimination, of disability related barriers to the demonstration of student achievement. The significance of reasonable adjustment is obvious in the later years of secondary school, and in the tertiary sector, because failure to adjust assessment may be asserted as the reason a student did not achieve as well as anticipated or as the reason a student was excluded from a course and, as a result, from future study and employment opportunities. Even in the early years of schooling, however, assessment and its management are a critical issue for staff and students, especially in an education system like Australia’s with an ever increasing emphasis on national benchmarks testing. This paper will explain the legislation which underpins the right to reasonable adjustment in education in Australian schools. It will give examples of the kinds of adjustment which may be made to promote equality of opportunity in the area of assessment. It will also consider some of the controversies which have confronted, or which, it may be speculated, are likely to confront Australian education institutions as they work towards compliance with reasonable adjustment laws.

Does section 420A impose ‘strict liability’ upon controllers for acts or omissions of agents and experts?

This article addresses in depth the question of whether section 420A of the Corporations Act 2001 (Cth) imposes ‘strict liability’ upon a controller for the failure of an agent or expert to take reasonable care. The weight of existing authority appears to suggest that controllers are liable under s 420A for the carelessness of their agents or expert advisers. However, a closer analysis of the text of the provision and relevant Australian and UK case law demonstrates that this aspect of the statutory construction of s 420A remains very much an open question. This article ultimately contends for a construction of s 420A which requires a controller to adequately supervise and scrutinise, but which does not render a blameless controller strictly liable for all careless acts and omissions of agents and expert advisers.

Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

A bound on the maximum strong order of stochastic Runge-Kutta methods for stochastic ordinary differential equations

In Burrage and Burrage [1] it was shown that by introducing a very general formulation for stochastic Runge-Kutta methods, the previous strong order barrier of order one could be broken without having to use higher derivative terms. In particular, methods of strong order 1.5 were developed in which a Stratonovich integral of order one and one of order two were present in the formulation. In this present paper, general order results are proven about the maximum attainable strong order of these stochastic Runge-Kutta methods (SRKs) in terms of the order of the Stratonovich integrals appearing in the Runge-Kutta formulation. In particular, it will be shown that if an s-stage SRK contains Stratonovich integrals up to order p then the strong order of the SRK cannot exceed min{(p + 1)/2, (s - 1)/2), p greater than or equal to 2, s greater than or equal to 3 or 1 if p = 1.

Spatiotemporal model or time series model for assessing city-wide temperature effects on mortality?

Most studies examining the temperature–mortality association in a city used temperatures from one site or the average from a network of sites. This may cause measurement error as temperature varies across a city due to effects such as urban heat islands. We examined whether spatiotemporal models using spatially resolved temperatures produced different associations between temperature and mortality compared with time series models that used non-spatial temperatures. We obtained daily mortality data in 163 areas across Brisbane city, Australia from 2000 to 2004. We used ordinary kriging to interpolate spatial temperature variation across the city based on 19 monitoring sites. We used a spatiotemporal model to examine the impact of spatially resolved temperatures on mortality. Also, we used a time series model to examine non-spatial temperatures using a single site and the average temperature from three sites. We used squared Pearson scaled residuals to compare model fit. We found that kriged temperatures were consistent with observed temperatures. Spatiotemporal models using kriged temperature data yielded slightly better model fit than time series models using a single site or the average of three sites' data. Despite this better fit, spatiotemporal and time series models produced similar associations between temperature and mortality. In conclusion, time series models using non-spatial temperatures were equally good at estimating the city-wide association between temperature and mortality as spatiotemporal models.