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3311016 results

Page 220 of 165551

  • 108.45 The golden section from three congruent semicircles

  • Tran Quang Hung, Michel Bataille
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 573 / November 2024
    Published online by Cambridge University Press:
    12 November 2024, pp. 530-532
    Print publication:
    November 2024
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  • A generalisation of a theorem of al-Kuhi

  • Sadi Abu-Saymeh, Mowaffaq Hajja
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 573 / November 2024
    Published online by Cambridge University Press:
    12 November 2024, pp. 460-469
    Print publication:
    November 2024
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  • Several problems that were composed and/or solved by the tenth century Islamic mathematician Abu Sahl al-Kuhi reached us via the writings of Abd al-Jalil al-Sijzi, another tenth century Islamic mathematician who, according to [1], was presumably a student of al-Kuhi’s. Twelve of these (sets of) problems and theorems are discussed in [1] and are referred to as The Fragments. The theorem of al-Kuhi alluded to in the title is Fragment #9, which is presented below, together with Fragment #5 and their proofs, in Section 2. Section 3 is devoted to the generalisation referred to in the title. Section 4 describes a relation to angle trisection and Sections 5 and 7 a relation too a configuration of Serenus. Section 6 contains a speculation on what motivated Fragment #9.

  • Another generalisation of Stewart's Theorem

  • Panagiotis T. Krasopoulos
  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 573 / November 2024
    Published online by Cambridge University Press:
    12 November 2024, pp. 478-483
    Print publication:
    November 2024
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  • The aim of this Article is to present a natural generalisation of a well-known result from plane geometry, called Stewart's Theorem. We will present our result in the Euclidean space , but we will prove it only for n = 3. Since its proof for n > 3 is involved, our intention is to give the details in another Article. A search in the relative literature returns many articles which generalise Stewart's Theorem in different directions. We first refer the reader to [1], where a collection of generalisations of Stewart's theorem is presented. In [2], two results are given, which describe a relation between k points in the Euclidean space and their weighted average. If we apply these theorems to the plane, we straightforwardly get Stewart's Theorem. Another result is given in [3], which is also reproduced in [1]. This result considers n + 1 points in which belong to a hyperplane U of dimension n − 1 and another point A ∉ U , and presents an interesting relation that combines distances between each of these points and A, hypervolumes of simplices and powers of points with respect to hyperspheres. Another relative result which involves convex quadrilaterals on the plane is proved in [4]. Lastly, in [5], a generalisation of [4] is proved for 2k points in , and a relation is found between distances of these points and the distance of two corresponding averages (of these points). These articles support the fact that there can be many interesting generalisations of Stewart's Theorem in different directions.

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  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 573 / November 2024
    Published online by Cambridge University Press:
    12 November 2024, p. 542
    Print publication:
    November 2024
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  • MAG volume 108 issue 573 Cover and Back matter

  • Journal:
    The Mathematical Gazette / Volume 108 / Issue 573 / November 2024
    Published online by Cambridge University Press:
    12 November 2024, pp. b1-b3
    Print publication:
    November 2024
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LGBTQ+ Affirmative Counseling
  • A Student and Practitioner Handbook
  • Edited by Jeffry Moe, Amber L. Pope, Dilani M. Perera, Narketta Sparkman-Key
  • Published online:
    31 October 2024
    Print publication:
    04 July 2024
  • Addressing a need for LGBTQ+ affirmative counselling in training, this meticulously crafted book is designed for graduate counselling students, new practitioners, and cross-disciplinary professionals. Authored by top researchers and clinicians, this collection synthesizes best practices in training and intervention, presenting a blueprint to seamlessly integrate affirmative counselling into academic curricula. Individual chapters cover topics including history, culture, assessment, treatment planning, crisis response, international perspectives, technology, and training. Enriched with resources, real-life case examples, and thoughtful reflection questions, the book moves beyond theory to provide actionable insights for effective LGBTQ+ affirmative counselling in diverse organizational settings. Tailored for graduate programs, this book equips future practitioners to adeptly navigate the complexities of affirmative counselling.

Clinical Case Studies in Long-Term Care Psychiatry
  • Navigating Common Mental Health Challenges in Geriatric Care
  • Matthew Gibfried, George T. Grossberg
  • Published online:
    31 October 2024
    Print publication:
    14 November 2024
  • The mental healthcare of older adults can lead to age specific challenges, however, many healthcare settings have limited access to expert geriatric psychiatric consultation. This compelling book provides a comprehensive compilation of real-life cases involving the psychiatric care of older adults in the long-term care setting. Providing practical guidance for healthcare professionals who work regularly with older adults, the chapters cover key topics such as neurocognitive disorders, mood disorders, anxiety disorders, psychotic disorders, end-of-life mental health care, and sexuality issues in older adults. Offering all the information necessary for the diagnosis and formulation of treatment plans for a wide variety of psychiatric presentations, the book covers pharmacologic and non-pharmacologic options for each disorder to assist healthcare professionals in providing well-rounded care. For all those involved in the prevention, assessment, diagnosis, and management of neuropsychiatric disorders in long-term care populations.

Functional Analysis Revisited
  • An Essay on Completeness
  • Adam Bobrowski
  • Published online:
    31 October 2024
    Print publication:
    04 July 2024
  • 'Functional Analysis Revisited' is not a first course in functional analysis – although it covers the basic notions of functional analysis, it assumes the reader is somewhat acquainted with them. It is by no means a second course either: there are too many deep subjects that are not within scope here. Instead, having the basics under his belt, the author takes the time to carefully think through their fundamental consequences. In particular, the focus is on the notion of completeness and its implications, yet without venturing too far from areas where the description 'elementary' is still valid. The author also looks at some applications, perhaps just outside the core of functional analysis, that are not completely trivial. The aim is to show how functional analysis influences and is influenced by other branches of contemporary mathematics. This is what we mean by 'Functional Analysis Revisited.'

Introduction to Clinical Psychology
  • Bridging Science and Practice
  • 10th edition
  • Douglas A. Bernstein, Bethany A. Teachman, Bunmi O. Olatunji, Andres De Los Reyes
  • Published online:
    31 October 2024
    Print publication:
    31 October 2024
  • Fully updated and revised, the tenth edition of this bestselling textbook introduces clinical psychology as a bridge between science and practice. Featuring over 1000 new references, the revised text includes additional coverage of digital mental health, diversity, and identity, and the practice of evidence-based clinical science. Coverage of such topics as emerging models for clinical training and accreditation, new approaches to diagnosing and classifying mental illness, and changes in healthcare legislation ensure that students will understand the very latest trends in the subject. The pedagogical focus of previous editions is maintained. 'Thinking Scientifically' sections in each chapter break down how to evaluate conflicting findings and use them to draw conclusions, while clinical vignettes bring concepts and theories to life. 'In Review' tables at the end of each major section prompt students to review material and test their comprehension. The text is accompanied by a full suite of online teaching supports.

The Art of Working with the Mathieu Group M24
  • Robert T. Curtis
  • Published online:
    31 October 2024
    Print publication:
    14 November 2024
  • The Leech lattice Λ, the Conway group ∙O, and the Monster group M are immensely famous structures. They each grow out of the Mathieu group M24 and its underlying combinatorial structure, and play an important role in various branches of mathematics and in theoretical physics. Written by an expert in the field, this book provides a new generation of mathematicians with the intimate knowledge of M24 needed to understand these beautiful objects, and many others. It starts by exploring Steiner systems, before introducing the Miracle Octad Generator (MOG) as a device for working with the Steiner system S(5,8,24). Emphasizing how theoretical and computational approaches complement one another, the author describes how familiarity with M24 leads to the concept of 'symmetric generation' of groups. The final chapter brings together the various strands of the book to produce a nested chain of groups culminating in the largest Conway simple group Co1.

Three Consuls
  • Capitalism, Empire, and the Rise and Fall of America's Mediterranean Community, 1776–1840
  • Lawrence A. Peskin
  • Published online:
    31 October 2024
    Print publication:
    21 November 2024
  • For two generations after independence, Americans viewed the Mediterranean as the new commercial frontier. From common sailors to wealthy merchants, hundreds of Americans flocked to live and work there. Documenting the eventful lives of three American consuls and their families at the ports of Tangier, Livorno, and Alicante, Lawrence A. Peskin portrays the rise and fall of America's Mediterranean community from 1776 to 1840. We learn how three ordinary merchants became American consuls; how they created flourishing communities; built social and business networks; and interacted with Jews, Muslims, and Catholics. When the bubble burst during the Napoleonic Wars and the War of 1812, American communities across the Mediterranean rapidly declined, resulting in the demise of the consuls' fortunes and health. A unique look into early American diplomacy, Three Consuls provides a much-needed overview of early consular service that highlights the importance of US activities in the Mediterranean region.

The Cambridge Companion to Jack Kerouac
  • Edited by Steven Belletto
  • Published online:
    31 October 2024
    Print publication:
    27 June 2024
  • Jack Kerouac is among the most important and influential writers to emerge from mid-twentieth century America. Founder of the Beat Generation literary movement, Kerouac's most famous novel, On the Road, was known as the bible of this generation, and inspired untold people to question the rigid social and cultural expectations of 1950s America. And yet despite its undeniable influence, On the Road is only a small piece of Kerouac's literary achievement, and there are now well over forty Kerouac books published. The centerpiece to this work is Kerouac's multi-volume Duluoz Legend, named for his fictional alter-ego, Jack Duluoz, and comprising numerous books written over decades that together tell the story of Duluoz's life and times. This volume offers fresh perspectives on his multifaceted body of work, ranging from detailed analyses of his most significant books to wide-angle perspectives that place Kerouac in key literary, theoretical, and cultural contexts.

The Dialectical Agroecologist
  • John Vandermeer, Ivette Perfecto
  • Published online:
    31 October 2024
    Print publication:
    14 November 2024
  • This book examines contradictions within the fields of food studies and agroecology, from the differences between traditional and scientific knowledge, to habitat fragmentation and connection, monocultures versus diverse farming systems, pest regulation, and the rural/urban dialectic. Building and expanding on the work of Richard Levins and Richard Lewontin, who used the dialectical method in the field of biology, this analysis includes examples from the authors' own pioneering research in Mexico, Nicaragua, and Puerto Rico, to demonstrate the benefits of applying the dialectical method to agroecology in practice. Exploring themes in studies that are currently the subject of rigorous debate among academics and activists alike, especially related to food production and distribution, this book is indispensable for practitioners and activists seeking to transform the food system, as well as for social and natural scientists.

Myth and Territory in the Spartan Mediterranean
  • 2nd edition
  • Irad Malkin
  • Foreword by Nicholas Purcell
  • Published online:
    31 October 2024
    Print publication:
    13 June 2024
  • Greek attitudes to settlement and territory were often articulated through myths and cults. This book emphasizes less the poetic, timeless qualities of the myths than their historical function in the archaic and Classical periods, covering the spectrum from explicit charter myths legitimating conquest, displacement, and settlement to the 'precedent-setting' and even aetiological myths, rendering new landscapes 'Greek'. This spectrum is broadest in the world of Spartan colonization – the Spartan Mediterranean – where the greater challenges to territorial possession and Sparta's acute self-awareness of its relative national youthfulness elicited explicit responses in the form of charter myths. The concept of a Spartan Mediterranean, in contrast to the image of a land-locked Sparta, is a major contribution of this book. This revised edition contains a substantial new Introduction which engages with critical and scholarly developments on Sparta since the original publication.

The Poet's Voice
  • Essays on Poetics and Greek Literature
  • 2nd edition
  • Simon Goldhill
  • Foreword by Emma Greensmith
  • Published online:
    31 October 2024
    Print publication:
    13 June 2024
  • How are poetry and the figure of the poet represented, discussed, contested within the poetry of ancient Greece? From what position does a poet speak? With what authority? With what debts to the past? With what involvement in the present? Through a series of interrelated essays on Homer, lyric poetry, Aristophanes, Theocritus and Apollonius of Rhodes, this landmark volume discusses key aspects of the history of poetics: tale-telling and the representation of man as the user of language; memorial and praise; parody, comedy and carnival; irony, masks and desire; the legacy of the past and the idea of influence. Detailed readings of major works of Greek literature and liberal use of critical writings from outside Classics help to align modern and ancient poetics in enlightening ways. This revised edition contains a substantial new Introduction which engages with critical and scholarly developments in Greek literature since the original publication.

Understanding Visuals in the Life Sciences
  • Han Yu
  • Published online:
    31 October 2024
    Print publication:
    21 November 2024
  • From photographs to micrographs, from the various types of graphs to fun, interactive visuals and games, there are many different forms in which science can be visualised. However, all of these forms of visualisation in the Life Sciences are susceptible to misunderstandings and misinformation. This accessible and concise book demonstrates the misconceptions surrounding the visuals used in popular life science communication. Richly illustrated in colour, this guide is packed with examples of commonly used visual types: photographs, micrographs, illustrations, graphs, interactive visuals, and infographics allowing visual creators to produce more effective visuals that aspire to being both attractive and informative for their target audience. It also encourages non-specialist readers to be more empowered and critical, to ask difficult questions, and to cultivate true engagement with science. This book is an invaluable resource for life scientists and science communicators, and anyone who creates visuals for public or non-specialist readers.

‘Unruly’ Children
  • Historical Fieldnotes and Learning Morality in a Taiwan Village
  • Jing Xu
  • Published online:
    31 October 2024
    Print publication:
    14 November 2024
  • How do we become moral persons? What about children's active learning in contrast to parenting? What can children teach us about knowledge-making more broadly? Answer these questions by delving into the groundbreaking ethnographic fieldwork conducted by anthropologists Arthur and Margery Wolf in a martial law era Taiwanese village (1958-60), marking the first-ever study of ethnic Han children. Jing Xu skillfully reinterprets the Wolfs' extensive fieldnotes, employing a unique blend of humanistic interpretation, natural language processing, and machine-learning techniques. Through a lens of social cognition, this book unravels the complexities of children's moral growth, exposing instances of disobedience, negotiation, and peer dynamics. Writing through and about fieldnotes, the author connects the two themes, learning morality and making ethnography, in light of social cognition, and invites all of us to take children seriously. This book is ideal for graduate and undergraduate students of anthropology and educational studies.

Thermal Radiation
  • From Macro to Nano
  • Changying Zhao
  • Published online:
    31 October 2024
    Print publication:
    14 November 2024
  • Thermal radiation studies have progressed rapidly, not only in theoretical and experimental exploration beyond the conventional use but also in advanced applications. This is a one-stop resource for capturing and discussing these cutting-edge developments exploring the theory, experiments, and applications of thermal radiation from macro- to nanoscale. Presented in a systematic framework, this book is divided into two parts: the first on macroscopic thermal radiation and the second on micro- and nanoscale thermal radiation. Each part delivers basic theory, numerical methods, advanced experimental techniques, and promising applications, making this an easy-to-follow guide meeting both basic and advanced needs. Supported by more than 180 colorful illustrations, readers can clearly visualize the theory, experiments, and applications in practice. A book for all, written at a graduate level but undoubtedly a useful tool for researchers, professionals, and even engineers who are interested in this fast-developing area.

The Theology of the Books of Ezra and Nehemiah
  • Roger S. Nam
  • Published online:
    31 October 2024
    Print publication:
    21 November 2024
  • In the opening verses of the Book of Ezra-Nehemiah, King Cyrus exhorts the exiled Judeans to return to Jerusalem to restore worship in Jerusalem. It then narrates this restoration through the construction of the temple, the repair of the city walls, and the commitment to the written Torah. In this volume, Roger Nam offers a new and compelling argument regarding the theology of Ezra-Nehemiah:  that the Judeans' return migration, which extended over several generations, had a totalizing effect on the people. Repatriation was not a single event, but rather a multi-generational process that oscillated between assimilation and preservation of culture. Consequently, Ezra-Nehemiah presents a unique theological perspective. Nam explores the book's prominent theological themes, including trauma, power, identity, community, worship, divine presence, justice, hope, and others – all of which take on a nuanced expression in diaspora.  He also shows how and why Ezra-Nehemiah naturally found a rich reception among emerging early Christian and Jewish interpretive communities.

Spectral and Spectral Element Methods for Fractional Ordinary and Partial Differential Equations
  • Mohsen Zayernouri, Li-Lian Wang, Jie Shen, George Em Karniadakis
  • Published online:
    31 October 2024
    Print publication:
    14 November 2024
  • This comprehensive introduction to global spectral methods for fractional differential equations from leaders of this emerging field is designed to be accessible to graduate students and researchers across math, science, and engineering. The book begins by covering the foundational fractional calculus concepts needed to understand and model anomalous transport phenomena. The authors proceed to introduce a series of new spectral theories and new families of orthogonal and log orthogonal functions, then present corresponding spectral and spectral element methods for fractional differential equations. The book also covers the fractional Laplacian in unbounded and bounded domains and major developments in time-integration of fractional models. It ends by sampling the wide variety of real-world applications of fractional modeling, including concentration transport in surface/subsurface dynamics, complex rheology and material damage, and fluid turbulence and geostrophic transport.

Page 220 of 165551