Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise

In this paper we extend the ideas of Brugnano, Iavernaro and Trigiante in their development of HBVM($s,r$) methods to construct symplectic Runge-Kutta methods for all values of $s$ and $r$ with $s\geq r$. However, these methods do not see the dramatic performance improvement that HBVMs can attain. Nevertheless, in the case of additive stochastic Hamiltonian problems an extension of these ideas, which requires the simulation of an independent Wiener process at each stage of a Runge-Kutta method, leads to methods that have very favourable properties. These ideas are illustrated by some simple numerical tests for the modified midpoint rule.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation

Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples. © 2011 American Mathematical Society.

Numerical methods and analysis for a class of fractional advection-dispersion models

In this paper, a class of fractional advection–dispersion models (FADMs) is considered. These models include five fractional advection–dispersion models, i.e., the time FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0 < γ < 1, the space FADM with two sides Riemann–Liouville derivatives, the time–space FADM and the time fractional advection–diffusion-wave model with damping with index 1 < γ < 2. These equations can be used to simulate the regional-scale anomalous dispersion with heavy tails. We propose computationally effective implicit numerical methods for these FADMs. The stability and convergence of the implicit numerical methods are analysed and compared systematically. Finally, some results are given to demonstrate the effectiveness of theoretical analysis.

The SAGE Handbook of Criminological Research Methods

Conducting research into crime and criminal justice carries unique challenges. This Handbook focuses on the application of 'methods' to address the core substantive questions that currently motivate contemporary criminological research. It maps a canon of methods that are more elaborated than in most other fields of social science, and the intellectual terrain of research problems with which criminologists are routinely confronted. Drawing on exemplary studies, chapters in each section illustrate the techniques (qualitative and quantitative) that are commonly applied in empirical studies, as well as the logic of criminological enquiry. Organized into five sections, each prefaced by an editorial introduction, the Handbook covers: • Crime and Criminals • Contextualizing Crimes in Space and Time: Networks, Communities and Culture • Perceptual Dimensions of Crime • Criminal Justice Systems: Organizations and Institutions • Preventing Crime and Improving Justice Edited by leaders in the field of criminological research, and with contributions from internationally renowned experts, The SAGE Handbook of Criminological Research Methods is set to become the definitive resource for postgraduates, researchers and academics in criminology, criminal justice, policing, law, and sociology.

Responsibilisation and Rights: Explorations in Comparative Youth Criminology

Studies of international youth justice, punishment and control are in their infancy but the issues of globalisation, transnationalisation, policy transfer and localisation are gradually being addressed. There also appears a growing demand in policy and pressure group circles in the UK to learn more about other jurisdictions in order to emulate ‘best practice’ and avoid the worst excesses of punitive populism. However, existing comparative work in this area rarely ventures much beyond country specific descriptions of historical development, powers and procedures. Statistical comparisons – predominantly of custody rates – are becoming more sophisticated but remain beset with problems of partial and inaccurate data collection. The extent to which different countries do things differently, and how and why such difference is maintained, remains a relatively unexcavated territory. This article suggests a conceptually comparative framework in which degrees of international, national and local convergence and divergence can begin to be revealed and assessed.

Illusions of Difference: Comparative Youth Justice in the Devolved UK

Surprisingly, there has been little or no systematic research to date that has explored the significance of UK devolution for youth justice policy and practice. This article explores the extent of differential justice in the United Kingdom, particularly as it is expressed in the myriad action plans, criminal justice reviews, frameworks for action, delivery plans and offending strategies that have surfaced since 1998. In particular, the article considers how far policy convergence and divergence are reflected through the discourses of risk, welfare, restoration and children's rights in the four administrations of England, Scotland, Wales and Northern Ireland. For comparative criminology, the United Kingdom offers a unique opportunity to explore how international and national pressures towards convergence and/or divergence can be challenged, rebranded, versioned, adapted or resisted at sub-national and local levels.

Health status and use of health services among recently arrived men with refugee backgrounds: A comparative analysis of urban and regional settlement in South-east Queensland

Approximately one-third of refugee and humanitarian entrants to Australia are adult men. Many of these men and their families settle in regional areas. Little is known about the health status of refugee men and the use of health services, and whether or not there are differences between those living in urban and regional areas. This paper reports on the cross-sectional differences in health status and use of health services among a group of 233 recently arrived refugee men living in urban and regional areas of South-east Queensland. Overall, participants reported good levels of subjective health status, moderate to good levels of well-being, and low prevalence of mental illness. Men living in urban areas were more likely to have a longstanding illness and report poorer health status than those settled in regional areas. In contrast, men living in regional areas reported poorer levels of well-being in the environment domain and were more likely to visit hospital emergency departments. Targeted health promotion programs will ensure that refugee men remain healthy and develop their full potential as members of the Australian community. Programs that facilitate refugees’ access to primary health care in regional areas may promote more appropriate use of hospital emergency departments by these communities.

Outcomes following operative and non-operative management of humeral midshaft fractures: a prospective, observational cohort study of 47 patients

Background Although the non-operative management of closed humeral midshaft fractures has been advocated for years, the increasing popularity of operative intervention has left the optimal treatment choice unclear. Objective To compare the outcomes of operative and non-operative treatment of traumatic closed humeral midshaft fractures in adult patients. Methods A multicentre prospective comparative cohort study across 20 centres was conducted. Patients with AO type 12 A2, A3 and B2 fractures were treated with a functional brace or a retrograde-inserted unreamed humeral nail. Follow-up measurements were taken at 6, 12 and 52 weeks after the injury. The primary outcome was fracture healing after 1 year. Secondary outcomes included sub-items of the Constant score, general patient satisfaction, complications and cost-effectiveness parameters. Functions of the uninjured extremity were used as reference parameters. Intention-to-treat analysis was applied with the use of t-tests, Fisher’s exact tests, Mann–Whitney U-tests and adjusted analysis of variance (ANOVA). Results Forty-seven patients were included. The patient sample consisted of 23 women and 24 men, with a mean age of 52.7 years (range 17–86 years). Of the 47 cases, 14 were treated non-operatively and 33 operatively. The follow-up rate at 1 year was 81%. After 1 year, 11 fractures (100%) healed in the non-operative group and at least 24 fractures (≥89%) healed in the operative group [1 non-union patient (4%) and no data for 2 patients (7%)]. There were no significant differences in pain, range of motion (ROM) of the shoulder and elbow, and return to work after 6 weeks, 12 weeks and 1 year. Although operatively treated patients showed significantly greater shoulder abduction strength (p = 0.036), elbow flexion strength (p = 0.021), functional hand positioning (p = 0.008) and return to recreational activities (p = 0.043) after 6 weeks, no statistically significant differences existed in any outcome measure at the 1-year follow-up. Conclusions Our findings indicate that the non-operative management of humeral midshaft fractures can be expected to have similar functional outcomes and patient satisfaction at 1 year, despite an early benefit to operative treatment. If no radiological evidence of fracture healing exists in non-operatively treated patients during early follow-up, a switch to surgical treatment results in good functional outcomes and patient satisfaction. Keywords: Humeral shaft fracture, Non-operative treatment, Functional brace, Operative treatment, Unreamed humeral nail (UHN), Prospective, Cohort study