The quaternions form a four-dimensional associative and non-commutative algebra over the set of real numbers. In this paper, firstly, we give some relations for k-Pell quaternions and k-Pell-Lucas quaternions. Then, by using Binet's formula, we obtain their sums formulas, their the identities such as Cassini's identity and generating function, also derive relationships between these quaternions.
The aim of this work is to introduce a generalization of dual quaternions called dual bicomplex Horadam quaternions and to present some properties, the Binet’s formula, Catalan’s identity, Cassini’s identity and the summation formula for this type of bicomplex quaternions. Furthermore, several identities for dual bicomplex Fibonacci quaternions are given.
Prosumers are households that are both producers and consumers of electricity. In this paper, an Energy Management System (EMS) for a DC-microgrid-based prosumer is designed and simulated, whose aim is to coordinate operation of a photovoltaic (PV) system and a battery for supplying a DC load; interaction with the utility grid-modelled as an infinitepower source-is minimized, such that power is either injected or drawn only when strictly necessary. The PV system and the battery are paralleled on a common DC-link by means of a boost converter and a synchronous buck converter, respectively, while an inverter ensures connection to the utility grid. In order to design and simulate the individual components of the microgrid, MATLAB ® /Simulink ® tools were used. During the study, different operating scenarios were created with respect to the PV power, load and the state of charge (SoC) of the battery. Thus, the following operation modes were identified: following mode, discharge mode, charging mode-referring to the battery operating modes that depend of its SoC. The aim of the EMS is to ensure the requirements of a prosumer application and switch between these different modes. Simulation results have shown that the developed EMS can achieve effective coordination within the microgrid, and all goals are reached.
In this paper, we introduce the bi-periodic Jacobsthal and Jacobsthal-Lucas quaternions. We give the Binet formulas and the generating functions for these quaternions. We obtain some well-known identities such as the Cassini, Catalan and D’ocagne’s identities. Additionally, we give summation formulas and the relationships between bi-periodic Jacobsthal and Jacobsthal-Lucas quaternions.
This book review is the culmination of a collaborative project between a group of students studying for the MA in Sociology of Childhood and Children's Rights at UCL Institute of Education, University College London. After having read Children's Rights, Educational Research and the UNCRC, we took part in a workshop to learn more about book reviews and how to craft them, facilitated by Rachel Rosen, the Programme Leader. Each student then chose a chapter of the book to review, and these reviews follow below. In this first section, I outline the book, before examining some of the ideas explored in the Introduction. This book came about as a result of the European Educational Research Association annual conference. During this conference, Gillett-Swan and Coppock chaired a roundtable discussion of Network 25, which is dedicated to children's rights in education. This volume brings together a selection of papers from the round table. It is designed to bring together recent thinking about children's rights in educational research, and to appeal to a broad audience of both researchers and educational practitioners. Crucially, the chapters cover an international selection of countries, but only from the minority world. Given debates about the applicability of a single model of childhood, often based on minority world assumptions, and global inequalities in the production of knowledge in childhood research, this is a significant gap. It also raises questions as to whether the book is truly representative of 'diverse and wide-ranging contexts' (10), as the editors claim. The Introduction sets out some of the key themes to be addressed in the book through a structure that echoes the subtitle: past, present and future. The editors introduce the United Nations Convention on the Rights of the Child (UNCRC) and the field of children's rights (the past), before giving an overview of three present debates. These are the drive towards children's participation rights, which draws upon the sociology of childhood for the conceptual shift that has occurred towards viewing children as social actors, the 'dichotomy' of children's rights and parental rights (9) and debates surrounding the decontextualization of children's rights from children's lived experiences. Their summary is perhaps a little undeveloped for researchers in the field, but makes the volume more accessible to readers who are unfamiliar with current debates, fitting well with the intended audience. The future is addressed by proposing to move through and beyond the UNCRC when contextualizing children's rights in education, such as the necessity for adaptability in children's rights research agendas going forward and availing of the possibilities of digital media. The past, present and future structure is useful in that it helps to guide the reader carefully through what could easily become dense theory. However, it does
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