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The purpose of this paper is to propose some a posteriori residual error estimators (REEs)to evaluate the accuracy of the finite element method for quasi-static electromagnetic problems with mixed boundary conditions. Both classical magnetodynamic A-ϕ and T-Ω formulations in harmonic case are analysed. As an example of application the estimated error maps of an electromagnetic system are studied. At last, a remeshing process is done according to the estimated error maps.

The paper proposes to analyze the efficiency of numerical REEs in the case of magnetodynamic harmonic formulations. The deal is to determine the areas where it is necessary to improve the mesh. Moreover the error estimators are applied for structures with mixed boundary conditions.

The studied application shows the possibilities of the residual error estimators in the case of electromagnetic structures. The comparison of the remeshed show the improvement of the obtained solution when the authors compare with a reference one.

The paper provides some interesting results in the case of magnetodynamic harmonic formulations in terms of potentials. Both classical formulations are studied.

The paper provides some informations to develop the proposed formulations in the software using finite element method.

The paper deals with the possibility to improve the determination of the meshes in the analysis of electromagnetic structure with the finite element method. The proposed method can be a good solution to obtain an optimal mesh for a given numerical error.

The paper proposes some elements of solution for the numerical analysis of electromagnetic structures. More particularly the results can be used to determine the good meshes of the finite element method.

This article presents a locally conservative projection method which aims to preserve the integral of a function and one operator among grad, div, or curl.

After a theoretical description of the projection methods, the locally conservative projection is analytically tested and compared with the orthogonal method. In the second part, the implementation of the methods is described, and improvements are proposed. An industrial application of the present work, consisting in a magneto-thermal coupled problem, is then presented.

The implementation of the conservative method is simpler than the implementation of the orthogonal method while presenting similar behaviour in terms of accuracy and conservation.

The locally conservative method is extended to curl-conform and div-conform elements. Furthermore, three-dimensional studies are proposed.

In this paper, the aim is to propose a residual‐based error estimator to evaluate the numerical error induced by the computation of the electromagnetic systems using a finite element method in the case of the harmonic A‐φ formulation.

The residual based error estimator used in this paper verifies the mathematical property of global and local error estimation (reliability and efficiency).

This estimator used is based on the evaluation of quantities weakly verified in the case of harmonic A‐φ formulation.

In this paper, it is shown that the proposed estimator, based on the mathematical developments, is hardness in the case of the typical applications.

In FEM computations, the mesh quality improves the accuracy of the approximation solution and reduces the computation time. The dynamic bubble system meshing technique can provide high-quality meshes, but the packing process is time-consuming. This paper aims to improve the running time of the bubble meshing by using the advantages of parallel computing on graphics processing unit (GPU).

This paper is based on the analysis of the processing time on CPU. A massively parallel computing-based CUDA architecture is proposed to improve the bubble displacement and database updating. Constraints linked to hardware considerations are taken into account. Finally, speedup factors are provided on test cases and real scale examples.

The numerical experiences show the efficiency of parallel performance reaches a speedup of 35 compared to the serial implementation.

This contribution is so far limited to two-dimensional (2D) geometries although the extension to three-dimension (3D) is straightforward regarding the meshing technique itself and the GPU implementation. The authors’ works are based on a CUDA environment which is widely used by developers. C\C++ and Java were the programming languages used. Other languages may of course lead to slightly different implementations.

This approach makes it possible to use bubble meshing technique for both initial design and optimization, as excellent meshes can be built in few seconds.

Compared to previous works, this contribution shows that the scalability of the bubble meshing technique needs to solve two key issues: reach a T(N) global cost of the implementation and reach a very fast size map interpolation strategy.

This chapter examines how opponents of same-sex marriage have used rights discourse to construct an identity of themselves as victims, and construct gays and lesbians as deviant “others.” I find that conservative rights discourse has been more effective outside the courtroom than in it. This is because these arguments rely on implicit discriminatory stereotypes which are frequently exposed under the scrutiny of dispassionate judicial actors. However, in a popular arena, they are free to operate with considerably less scrutiny. Here, rights discourse is used to mask discriminatory stereotypes and lend legitimacy to positions that would be rejected if made explicitly.

Drawing on his personal experience as a police officer and a range of literature, the author applies Caulkins' and Reuter's paper in this edition to the UK experience. In particular he draws on the work of Goldstein, which places drug‐related crime into three categories: psychopharmacological, economic‐compulsive and systemic.

Northern Ireland (NI) has pervasively been a fragile and often disputed city-regional nation. Despite NI's slim majority in favour of remaining in the European Union, de facto Brexit, post-pandemic challenges and the Northern Ireland Protocol (NIP) have revealed a dilemma: people of all political hues have started to question aspects of their own citizenship. Consequently, this chapter suggests an innovative approach called ‘Algorithmic Nations’ to better articulate its emerging/complex citizenship regimes for this divided and post-conflict society in which identity borders and devolution may be facilitated through blockchain technology. This chapter assesses implications of this dilemma for a city-regionalised nation enmeshed within the UK, Ireland and Europe: NI through Belfast, its main metropolitan hub. The chapter explores digital citizenship in NI by applying ‘Algorithmic Nations’ framework particularly relating to intertwined (1) cross-bordering, (2) critical awareness, (3) digital activism and (4) post-pandemic realities and concludes with three dilemmas and how ‘Algorithmic Nations’ framing could better integrate NI's digital citizenship.

The goal of this article is to introduce the notion of a grey relation between grey sets using grey numbers.

This study uses the grey number to create novel ideas of grey sets. We suggest several operations that can be performed on it, including the union, intersection, join, merge, and composition of grey relations. In addition, we present the definitions of reflexive, symmetric, and transitive grey relations and analyze certain characteristics associated with them. Furthermore, we formulate the concept of the grey equivalence relation, apply it to the study of the grey equivalence class over the grey relation, and go over some of its features.

We present new algebraic aspects of grey system theory by defining grey relations and then analyzing their characteristic features.

This paper proposes a new theoretical direction for grey sets according to grey numbers, namely, grey relations. This paper proposes a new theoretical direction for grey sets according to grey numbers, namely, grey relations. As such, it can be applied to create rough approximations as well as congruences in algebras, topologies, and semigroups.

The presented notions are regarded as new algebraic approaches in grey system theory for the first time. Additionally, some fundamental operations on grey relations are also investigated. Consequently, different types of grey relations, such as reflexive, symmetric, and transitive relations, are discussed. Then, the grey equivalence class derived from the grey equivalence relation is demonstrated, and its properties are examined.

This research study aims to explore the trends in the use of appropriate adults (AAs) for persons with mental disabilities (PMDs) during law enforcement investigation interviews in Singapore and examine the profile of PMDs who were supported by AAs through the investigation process. AAs play a vital role in facilitating communication and providing emotional support to PMDs during investigation interviews.

A descriptive analysis was conducted on data collected from 2016 to 2019.

The findings of the study indicate a growing demand for AA services to support PMDs with some variations across different geographical regions. Approximately three-quarters of all completed interviews supported PMDs who were suspects/accused. Interviewees who received AA support were largely Chinese, male, in their adolescent or early adulthood years and had an intellectual disability. More than half of the interviews supported by AAs involved offences that were sexual in nature or property related.

These results reflect a growing awareness of the role and importance of AAs for PMDs and have practical implications on service delivery and development. This paper’s findings on the profile of PMDs supported by AAs also set the groundwork for further research to investigate how PMDs interface with the criminal justice system.

The purpose of this paper is twofold. First to ascertain the efficacy of current police reception screening to detect detainees with intellectual disability (ID). Second to assess the validity of a short targeted screen for ID among police custody detainees.

The study comprised three stages. First, 248 police custody detainees were assessed for a range of health morbidities, including a pragmatic clinical evaluation of ID. For those with suspected ID, the police custody screens were scrutinised for evidence that this had been detected. Second, a new police health screen, incorporating a short screen for ID, was piloted. Totally, 351 detainees were assessed in the same way as in part 1 with the new screens being scrutinised for evidence that ID had been detected where relevant. Third, the new police screen for ID was validated among a sample of 64 inpatients, some with ID and some without, from forensic inpatient services. Parts 1 and 2 were carried out in the Metropolitan Police Service, London. Part 3 took place in one NHS Trust.

In parts 1 and 2, the rate of detainees with suspected ID was 2-3 per cent. The standard police screen detected 25 per cent of these detainees in part 1. When the new screen was introduced in part 2, the sensitivity for ID increased to 83 per cent. However, there was no requisite improvement in the proportion of detainees with ID receiving an Appropriate Adult. In the inpatient study, the new screen showed a good level of sensitivity (91 per cent) and reasonable specificity (63 per cent).

It is possible to improve the detection rate of detainees with suspected ID by introducing a short ID screen into the police custody officers’ reception health screen.

The Health Screening of People in Police Custody (HELP-PC) study is a project evaluating screening for health morbidity among police custody detainees. Other data from this study have been reported elsewhere, but this is the first time the data pertaining to ID screening has been reported in detail.