Positivity and its Applications

Positivity and its Applications
Author: Eder Kikianty
Publisher: Springer Nature
Total Pages: 321
Release: 2021-07-22
Genre: Mathematics
ISBN: 3030709744

This proceedings volume features selected contributions from the conference Positivity X. The field of positivity deals with ordered mathematical structures and their applications. At the biannual series of Positivity conferences, the latest developments in this diverse field are presented. The 2019 edition was no different, with lectures covering a broad spectrum of topics, including vector and Banach lattices and operators on such spaces, abstract stochastic processes in an ordered setting, the theory and applications of positive semi-groups to partial differential equations, Hilbert geometries, positivity in Banach algebras and, in particular, operator algebras, as well as applications to mathematical economics and financial mathematics. The contributions in this book reflect the variety of topics discussed at the conference. They will be of interest to researchers in functional analysis, operator theory, measure and integration theory, operator algebras, and economics. Positivity X was dedicated to the memory of our late colleague and friend, Coenraad Labuschagne. His untimely death in 2018 came as an enormous shock to the Positivity community. He was a prominent figure in the Positivity community and was at the forefront of the recent development of abstract stochastic processes in a vector lattice context.

Total Positivity and Its Applications

Total Positivity and Its Applications
Author: Mariano Gasca
Publisher: Springer Science & Business Media
Total Pages: 510
Release: 2013-03-09
Genre: Mathematics
ISBN: 9401586748

This volume contains both invited lectures and contributed talks presented at the meeting on Total Positivity and its Applications held at the guest house of the University of Zaragoza in Jaca, Spain, during the week of September 26-30, 1994. There were present at the meeting almost fifty researchers from fourteen countries. Their interest in thesubject of Total Positivity made for a stimulating and fruitful exchange of scientific information. Interest to participate in the meeting exceeded our expectations. Regrettably, budgetary constraints forced us to restriet the number of attendees. Professor S. Karlin, of Stanford University, who planned to attend the meeting had to cancel his participation at the last moment. Nonetheless, his almost universal spiritual presence energized and inspired all of us in Jaca. More than anyone, he influenced the content, style and quality of the presentations given at the meeting. Every article in these Proceedings (except some by Karlin hirnself) references his influential treatise Total Positivity, Volume I, Stanford University Press, 1968. Since its appearance, this book has intrigued and inspired the minds of many researchers (one of us, in his formative years, read the galley proofs and the other of us first doubted its value but then later became its totally committed disciple). All of us present at the meeting encourage Professor Karlin to return to the task of completing the anxiously awaited Volume 11 of Total Positivity.

Moments, Positive Polynomials and Their Applications

Moments, Positive Polynomials and Their Applications
Author: Jean-Bernard Lasserre
Publisher: World Scientific
Total Pages: 384
Release: 2010
Genre: Mathematics
ISBN: 1848164467

1. The generalized moment problem. 1.1. Formulations. 1.2. Duality theory. 1.3. Computational complexity. 1.4. Summary. 1.5. Exercises. 1.6. Notes and sources -- 2. Positive polynomials. 2.1. Sum of squares representations and semi-definite optimization. 2.2. Nonnegative versus s.o.s. polynomials. 2.3. Representation theorems : univariate case. 2.4. Representation theorems : mutivariate case. 2.5. Polynomials positive on a compact basic semi-algebraic set. 2.6. Polynomials nonnegative on real varieties. 2.7. Representations with sparsity properties. 2.8. Representation of convex polynomials. 2.9. Summary. 2.10. Exercises. 2.11. Notes and sources -- 3. Moments. 3.1. The one-dimensional moment problem. 3.2. The multi-dimensional moment problem. 3.3. The K-moment problem. 3.4. Moment conditions for bounded density. 3.5. Summary. 3.6. Exercises. 3.7. Notes and sources -- 4. Algorithms for moment problems. 4.1. The overall approach. 4.2. Semidefinite relaxations. 4.3. Extraction of solutions. 4.4. Linear relaxations. 4.5. Extensions. 4.6. Exploiting sparsity. 4.7. Summary. 4.8. Exercises. 4.9. Notes and sources. 4.10. Proofs -- 5. Global optimization over polynomials. 5.1. The primal and dual perspectives. 5.2. Unconstrained polynomial optimization. 5.3. Constrained polynomial optimization : semidefinite relaxations. 5.4. Linear programming relaxations. 5.5. Global optimality conditions. 5.6. Convex polynomial programs. 5.7. Discrete optimization. 5.8. Global minimization of a rational function. 5.9. Exploiting symmetry. 5.10. Summary. 5.11. Exercises. 5.12. Notes and sources -- 6. Systems of polynomial equations. 6.1. Introduction. 6.2. Finding a real solution to systems of polynomial equations. 6.3. Finding all complex and/or all real solutions : a unified treatment. 6.4. Summary. 6.5. Exercises. 6.6. Notes and sources -- 7. Applications in probability. 7.1. Upper bounds on measures with moment conditions. 7.2. Measuring basic semi-algebraic sets. 7.3. Measures with given marginals. 7.4. Summary. 7.5. Exercises. 7.6. Notes and sources -- 8. Markov chains applications. 8.1. Bounds on invariant measures. 8.2. Evaluation of ergodic criteria. 8.3. Summary. 8.4. Exercises. 8.5. Notes and sources -- 9. Application in mathematical finance. 9.1. Option pricing with moment information. 9.2. Option pricing with a dynamic model. 9.3. Summary. 9.4. Notes and sources -- 10. Application in control. 10.1. Introduction. 10.2. Weak formulation of optimal control problems. 10.3. Semidefinite relaxations for the OCP. 10.4. Summary. 10.5. Notes and sources -- 11. Convex envelope and representation of convex sets. 11.1. The convex envelope of a rational function. 11.2. Semidefinite representation of convex sets. 11.3. Algebraic certificates of convexity. 11.4. Summary. 11.5. Exercises. 11.6. Notes and sources -- 12. Multivariate integration 12.1. Integration of a rational function. 12.2. Integration of exponentials of polynomials. 12.3. Maximum entropy estimation. 12.4. Summary. 12.5. Exercises. 12.6. Notes and sources -- 13. Min-max problems and Nash equilibria. 13.1. Robust polynomial optimization. 13.2. Minimizing the sup of finitely many rational cunctions. 13.3. Application to Nash equilibria. 13.4. Exercises. 13.5. Notes and sources -- 14. Bounds on linear PDE. 14.1. Linear partial differential equations. 14.2. Notes and sources

Positive Psychology: Theory, Research And Applications

Positive Psychology: Theory, Research And Applications
Author: Hefferon, Kate
Publisher: McGraw-Hill Education (UK)
Total Pages: 290
Release: 2011-05-01
Genre: Psychology
ISBN: 0335241956

"Kate Hefferon and Ilona Boniwell have done an excellent job on this introduction to Positive Psychology! I encourage educators, students and everyone else interested in an updated, well-written and culturally balanced approach to the scientific study of human flourishing, to read this highly accessible, yet rigorously crafted text; and to get it under your skin by ways of carefully chosen tests and exercises." Hans Henrik Knoop, Aarhus University, Denmark and President, European Network for Positive Psychology "This accessible, yet comprehensive, book provides an excellent new resource in the area of positive psychology. Students, researchers and practitioners alike will benefit from the skilful and lively integration of theory, research and application. The authors are prominent members of the international positive psychology movement and as such are able to deliver a confident, practical and overarching assessment of the area, integrated into psychology more widely." Angela Clow, University of Westminster, UK "This is an exceptional book that synthesizes more than a decade of positive psychology research into chapters that are engaging, accessible, and educational. Hefferon and Boniwell demonstrate a mastery of the literature through the ways in which they have marshaled the evidence from research and practice into this invaluable resource. This book will become an essential reference guide for researchers, educators and practitioners of positive psychology around the world." Professor Alex Linley, Founding Director, Capp "This book is a valuable resource for students looking for an introduction to Positive Psychology, but also wanting to get a comprehensive and updated overview of this innovative approach to the study of human behaviour and experience. It provides a broad coverage of the most relevant theories and constructs developed within Positive Psychology, and of their relevance for intervention and application in the most diverse life domains. Hefferon and Boniwell use a rigorous though accessible and friendly style of presentation. By means of effective learning supports, they stimulate readers' active engagement in critical reflections on each topic. The authors address the several issues and open questions which still characterize Positive Psychology as a relatively recent domain through a balanced and objective approach." Antonella Delle Fave, University of Milano, Italy "Kate Hefferon and Ilona Boniwell have produced the first textbook which has set out purposefully to support students and teachers in higher education in the exciting new area of positive psychology. The authors have experience of teaching the lectures described in each chapter and the book is written in a way that students will find engaging and fun. Each chapter has clear learning objectives, mock essay questions, measurement tools, summaries and a guide to further resources. The content has been well researched and the early chapters cover the main concepts of positive psychology such as emotions, happiness, wellbeing, optimism, and resilience. The later chapters are more novel and cover interventions and applications all with a critical eye. Of particular note is the chapter on the body in positive psychology - a topic which is frequently omitted from the 'thoughts and feelings' approach of other texts in this area. I would strongly recommend this book to all students and teachers of psychology." Nanette Mutrie, Professor of Exercise and Sport Psychology, Strathclyde University, UK Discover the latest research findings and thinking on the topics of happiness, flow, optimism, motivation, character strengths, love and more! Find out how happiness levels can be increased, what stops us from flourishing and how positive psychology can be applied to many professional disciplines. This new textbook combines a breadth of information about positive psychology with reflective questions, critical commentary and up to date research. It is written in a witty, engaging and contemporary manner and includes: Personal development exercises to help you meld together research and application Mock essay questions to get essay writing going Think about it boxes to get you thinking about the concepts and theories discussed Experiments boxes giving you most influential positive psychology experiments to date Suggested resources guiding you where to go next Measurement tools presenting popular positive psychology tools Time out boxes on key issues, concepts and thinkers Chapter summaries to help you check their understanding Review questions to enhance your learning Positive Psychology is key reading for students taking modules in positive psychology and well-being, and will also be of interest to students of applied, coaching and sports psychology, as well as psychologists, coaches, counsellors and researchers interested in this burgeoning field.

Total Positivity and Its Applications

Total Positivity and Its Applications
Author: Mariano Gasca
Publisher: Springer
Total Pages: 518
Release: 1996-03-31
Genre: Mathematics
ISBN: 079233924X

This volume contains both invited lectures and contributed talks presented at the meeting on Total Positivity and its Applications held at the guest house of the University of Zaragoza in Jaca, Spain, during the week of September 26-30, 1994. There were present at the meeting almost fifty researchers from fourteen countries. Their interest in thesubject of Total Positivity made for a stimulating and fruitful exchange of scientific information. Interest to participate in the meeting exceeded our expectations. Regrettably, budgetary constraints forced us to restriet the number of attendees. Professor S. Karlin, of Stanford University, who planned to attend the meeting had to cancel his participation at the last moment. Nonetheless, his almost universal spiritual presence energized and inspired all of us in Jaca. More than anyone, he influenced the content, style and quality of the presentations given at the meeting. Every article in these Proceedings (except some by Karlin hirnself) references his influential treatise Total Positivity, Volume I, Stanford University Press, 1968. Since its appearance, this book has intrigued and inspired the minds of many researchers (one of us, in his formative years, read the galley proofs and the other of us first doubted its value but then later became its totally committed disciple). All of us present at the meeting encourage Professor Karlin to return to the task of completing the anxiously awaited Volume 11 of Total Positivity.

Positivity in Algebraic Geometry I

Positivity in Algebraic Geometry I
Author: R.K. Lazarsfeld
Publisher: Springer Science & Business Media
Total Pages: 414
Release: 2004-08-24
Genre: History
ISBN: 9783540225331

This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.

Positive Systems

Positive Systems
Author: James Lam
Publisher: Springer
Total Pages: 331
Release: 2019-01-12
Genre: Technology & Engineering
ISBN: 3030043274

This book presents high-quality original contributions on positive systems, including those with positivity in compartmental switched systems, Markovian jump systems, Boolean networks, interval observer design, fault detection, and delay systems. It comprises a selection of the best papers from POSTA 2018, the 6th International Conference on Positive Systems, which was held in Hangzhou, China, in August 2018. The POSTA conference series represents a targeted response to the growing need for research that reports on and critically discusses a wide range of topics concerning the theory and applications of positive systems. The book offers valuable insights for researchers in applied mathematics, control theory and their applications.

Positive Psychiatry, Psychotherapy and Psychology

Positive Psychiatry, Psychotherapy and Psychology
Author: Erick Messias
Publisher: Springer Nature
Total Pages: 431
Release: 2020-01-24
Genre: Medical
ISBN: 3030332640

For hundreds of years, psychology has looked into the dysfunctions and symptoms of the mind. It’s only over the last few decades that the field has started to pay attention to what constitutes a functional and content life. Instead of using disease to understand health, positive psychology studies the components of a good life and helps people not only avoid mental health problems but develop happiness. The work done in positive psychology is now at a point where applications are being developed in positive psychotherapy and extended to those with psychiatric diagnoses in positive psychiatry. While these fields are a recent development they hold the promise of helping all of us live a fulfilled life. Medicine in general, and psychiatry in particular, suffers from a worldview that is symptom- and deficit-oriented. By adopting a positive approach, psychology, psychotherapy, and psychiatry add a more holistic, integrative, resource oriented, and preventive perspective. There is great urgency in developing resources and potentials in our patients, not only freeing them from their disorders. Psychiatrists and psychotherapists alike are incorporating these positive tools into their practices with positive clinical outcomes. Standing on the shoulders of pioneers like Nossrat Peseschkian, in positive psychotherapy, and Dilip Jeste, in positive psychiatry, this textbook is the first to bring together these innovations in one volume that will serve as an excellent resource for medical professionals looking to reap the benefits gained by the studies in these areas. Currently, the majority of texts that are available are targeting psychologists and researchers, whereas this book seeks to use positive psychology as the foundation on which the clinical applications are built. As such, this book will be of interest to psychiatrists, psychologists, social workers, and other mental health professionals. It may be used in educating a new generation of mental health professionals in these tenets that are expanding the reach of psychology, the practice of psychotherapy, and the scope of psychiatry.

Positive Intelligence

Positive Intelligence
Author: Shirzad Chamine
Publisher: Greenleaf Book Group
Total Pages: 241
Release: 2012
Genre: Business & Economics
ISBN: 1608322785

Chamine exposes how your mind is sabotaging you and keeping your from achieving your true potential. He shows you how to take concrete steps to unleash the vast, untapped powers of your mind.