Functional Identities


Book Description

A functional identity can be informally described as an identical relation involving arbitrary elements in an associative ring together with arbitrary (unknown) functions. The theory of functional identities is a relatively new one, and this is the first book on this subject. The book is accessible to a wide audience and touches on a variety of mathematical areas such as ring theory, algebra and operator theory.




Exploring Positive Identities and Organizations


Book Description

In the new world of work and organizations, creating and maintaining a positive identity is consequential and challenging for individuals, for groups and for organizations. New challenges for positive identity construction and maintenance require new theory. This edited volume uncovers new topics and new theoretical approaches to identity through the specific focus on positive identities of individuals, groups, organizations and communities. This volume aims to forge new ground in identity research and organizations through a compilation of new frame-breaking chapters on positive identity written by leading identity scholars. In chapters that build theoretical and empirical bridges between identity and growth, authenticity, relationships, hope, sustainability, leadership, resilience, cooperation, and community reputation and other important variables, the authors jumpstart an exciting domain of research on new ways that work organizations are sites of and contributors to identities that are beneficial or valuable to individuals or collectives. This volume invites readers to consider, "When and how does applying a positive lens to the construct of identity generate new insights for organizational researchers?" A unique feature of this volume is that it brings together explorations of identity from multiple levels of analysis: individual, dyadic, group, organization and community. Commentary chapters integrate the chapters within each level of analysis, illuminate core themes and unearth new questions. The volume is designed to accomplish three objectives: To establish Positive Identities and Organizations as an interdisciplinary, multi-level domain of inquiry To integrate a focus on Positive Identity with existing theory and research on identity and organizations To map out a vibrant new research territory in organizational studies . This volume will appeal to an international community of scholars in Management, Psychology, and Sociology, as well as practitioners who seek to generate positive identity-related dynamics, states and outcomes in work organizations.




Landscapes, Identities and Development


Book Description

Bringing together theoretical and empirical research from 22 countries in Europe, North America, Australia, South America and Japan, this book offers a state-of-the-art survey of conceptual and methodological research and planning issues relating to landscape, heritage, [and] development. It has 30 chapters grouped in four main thematic sections: landscapes as a constitutive dimension of territorial identities; landscape history and landscape heritage; landscapes as development assets and resources; and landscape research and development planning. The contributors are scholars from a wide range of cultural and professional backgrounds, experienced in fundamental and applied research, planning and policy design. They were invited by the co-editors to write chapters for this book on the basis of the theoretical frameworks, case-study research findings and related policy concerns they presented at the 23rd Session of PECSRL - The Permanent European Conference for the Study of the Rural Landscape, organized by TERCUD - Territory, Culture and Development Research Centre, Universidade Lusófona, in Lisbon and Óbidos, Portugal, 1 - 5 September 2008. With such broad inter-disciplinary relevance and international scope, this book provides a valuable overview, highlighting recent findings and interpretations on historical, current and prospective linkages between changing landscapes and natural, economic, cultural and other identity features of places and regions; landscape-related identities as local and regional development assets and resources in the era of globalized economy and culture; the role of landscape history and heritage as platforms of landscape research and management in European contexts, including the implementation of The European Landscape Convention; and, the strengthening of the landscape perspective as a constitutive element of sustainable development.




Rigid Designation and Theoretical Identities


Book Description

Joseph LaPorte offers an original account of the connections between the reference of words for properties and kinds, and theoretical identity statements. He argues that terms for properties, as well as for concrete objects, are rigid designators, and defends the Kripkean tradition of theoretical identities.




Performing Identities


Book Description

Performing Identities brings together essays by scholars, artists and activists engaged in understanding and conserving rapidly disappearing local knowledge forms of indigenous communities across continents. It depicts the imaginative transactions evident in the interface of identity and cultural transformation, raising the issue of cultural rights of these otherwise marginalized communities.




Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory


Book Description

This book includes review articles in the field of elliptic integrals, elliptic functions and modular forms intending to foster the discussion between theoretical physicists working on higher loop calculations and mathematicians working in the field of modular forms and functions and analytic solutions of higher order differential and difference equations.




Social Identities


Book Description

The concept of social identity occupies a central position in contemporary social psychology. Social Identities: Motivational, Emotional, Cultural Influences reports recent developments in the analysis of motivational and affective aspects of social identity processes. The book also examines the cross-cultural generality of Social Identity Theory explanations of intergroup competitiveness, which have strongly influenced international research in this area. People’s social identities and self-evaluation are thought to be largely derived from group memberships; it is presumed that people are motivated to attain positivity in these identities by favouring the ingroup in intergroup comparisons. An increasing stream of research is being devoted to extending the applicability of social identity concepts to intergroup relations and related fields. The editors present here a collection of contributions from leading figures in social psychology which explore the state of the art in social identity theory. The most prominent motivational theories of identification are reported. Central themes concern: motivations which lead individuals to join a group and identify with it the role emotions have in favouring (or hindering) intergroup relations the effect of emotions on intergroup behaviour how people react to social identity threats Shedding new light on important social problems like prejudice, bigotry, and intense conflicts around the world, this unique volume will be indispensable to students and researchers of social psychology, sociology and cultural studies.




Ramanujan's Forty Identities for the Rogers-Ramanujan Functions


Book Description

Sir Arthur Conan Doyle's famous fictional detective Sherlock Holmes and his sidekick Dr. Watson go camping and pitch their tent under the stars. During the night, Holmes wakes his companion and says, ``Watson, look up at the stars and tell me what you deduce.'' Watson says, ``I see millions of stars, and it is quite likely that a few of them are planets just like Earth. Therefore there may also be life on these planets.'' Holmes replies, ``Watson, you idiot. Somebody stole ourtent.'' When seeking proofs of Ramanujan's identities for the Rogers-Ramanujan functions, Watson, i.e., G. N. Watson, was not an ``idiot.'' He, L. J. Rogers, and D. M. Bressoud found proofs for several of the identities. A. J. F. Biagioli devised proofs for most (but not all) of the remaining identities.Although some of the proofs of Watson, Rogers, and Bressoud are likely in the spirit of those found by Ramanujan, those of Biagioli are not. in particular, Biagioli used the theory of modular forms. Haunted by the fact that little progress has been made into Ramanujan's insights on these identities in the past 85 years, the present authors sought ``more natural'' proofs. Thus, instead of a missing tent, we have had missing proofs, i.e., Ramanujan's missing proofs of his forty identities for theRogers-Ramanujan functions. in this paper, for 35 of the 40 identities, the authors offer proofs that are in the spirit of Ramanujan. Some of the proofs presented here are due to Watson, Rogers, and Bressoud, but most are new. Moreover, for several identities, the authors present two or threeproofs. For the five identities that they are unable to prove, they provide non-rigorous verifications based on an asymptotic analysis of the associated Rogers-Ramanujan functions. This method, which is related to the 5-dissection of the generating function for cranks found in Ramanujan's lost notebook, is what Ramanujan might have used to discover several of the more difficult identities. Some of the new methods in this paper can be employed to establish new identities for the Rogers-Ramanujanfunctions.




Shades of Gray


Book Description

"In Shades of Gray Molly Littlewood McKibbin offers a social and literary history of multiracialism in the twentieth-century United States. She examines the African American and white racial binary in contemporary multiracial literature to reveal the tensions and struggles of multiracialism in American life through individual consciousness, social perceptions, societal expectations, and subjective struggles with multiracial identity. McKibbin weaves a rich sociohistorical tapestry around the critically acclaimed works of Danzy Senna, Caucasia (1998); Rebecca Walker, Black White and Jewish: Autobiography of a Shifting Self (2001); Emily Raboteau, The Professor's Daughter (2005); Rachel M. Harper, Brass Ankle Blues (2006); and Heidi Durrow, The Girl Who Fell from the Sky (2010). Taking into account the social history of racial classification and the literary history of depicting mixed race, she argues that these writers are producing new representations of multiracial identity. Shades of Gray examines the current opportunity to define racial identity after the civil rights, black power, and multiracial movements of the late twentieth century changed the sociopolitical climate of the United Statesand helped revolutionize the racial consciousness of the nation. McKibbin makes the case that twenty-first-century literature is able to represent multiracial identities for the first time in ways that do not adhere to the dichotomous conceptions of race that have, until now, determined how racial identities could be expressed in the United States" --




Dense Sphere Packings


Book Description

The 400-year-old Kepler conjecture asserts that no packing of congruent balls in three dimensions can have a density exceeding the familiar pyramid-shaped cannonball arrangement. In this book, a new proof of the conjecture is presented that makes it accessible for the first time to a broad mathematical audience. The book also presents solutions to other previously unresolved conjectures in discrete geometry, including the strong dodecahedral conjecture on the smallest surface area of a Voronoi cell in a sphere packing. This book is also currently being used as a blueprint for a large-scale formal proof project, which aims to check every logical inference of the proof of the Kepler conjecture by computer. This is an indispensable resource for those who want to be brought up to date with research on the Kepler conjecture.