This book provides a gentle introduction to fractional Sobolev spaces which play a central role in the calculus of variations, partial differential equations, and harmonic analysis. The first part deals with fractional Sobolev spaces of one variable. It covers the definition, standard properties, extensions, embeddings, Hardy inequalities, and interpolation inequalities. The second part deals with fractional Sobolev spaces of several variables. The author studies completeness, density, homogeneous fractional Sobolev spaces, embeddings, necessary and sufficient conditions for extensions, Gagliardo-Nirenberg type interpolation inequalities, and trace theory. The third part explores some applications: interior regularity for the Poisson problem with the right-hand side in a fractional Sobolev space and some basic properties of the fractional Laplacian. The first part of the book is accessible to advanced undergraduates with a strong background in integration theory; the second part, to graduate students having familiarity with measure and integration and some functional analysis. Basic knowledge of Sobolev spaces would help, but is not necessary. The book can also serve as a reference for mathematicians working in the calculus of variations and partial differential equations as well as for researchers in other disciplines with a solid mathematics background. It contains several exercises and is self-contained.
The Conference OC Bologna 2000: Structure of the Nucleus at the Dawn of the CenturyOCO was devoted to a discipline which has seen a strong revival of research activities in the last decade. New experimental results and theoretical developments in nuclear physics will certainly make important contributions to our knowledge and understanding of Nature's fundamental building blocks. The interest aroused by the Conference among the scientific community was clearly reflected in the large number of participants. These represented the most important nuclear physics laboratories in the world. The Conference covered five major topics of modern nuclear physics: nuclear structure, nucleusOConucleus collisions, hadron dynamics, nuclear astrophysics, and transdisciplinary and peaceful applications of nuclear science. It reviewed recent progress in the field and provided a forum for the discussion of current and future research projects. Contents: Structure of Nuclei Far from the Valley of Beta-Stability; Nuclear Structure; Physics of High Spin States; Symmetries in Nuclear Structure; Collective Excitations; Nuclear Structure at Finite Temperature. Readership: Nuclear physicists.
The present book analyses the work of Ezio Tarantelli, a remarkable Italian scientist and economist killed by the Red Brigades in 1985 after only a short life (1941-1985). Tarantelli’s work and its implications are not only of importance for Italian researchers, but also represents a contribution of interest to economists worldwide. The first chapter of this volume shows the most important features of the European and Italian economy from 1970 to 1985. The contribution of Tarantelli, in fact, was his attempt to address the questions arising from such a context, incorporating the thought of F. Modigliani and J. Robinson in the process. After some brief biographical notes in the second chapter, the third and the fourth concentrate on Tarantelli’s theoretical contribution. The fifth chapter and the conclusions, finally, show how, from his economic analysis, he derived some economic policy proposals that still hold relevance today. The text includes a complete bibliography of his scientific writings.
The extent of John Ruskin's influence has long been acknowledged, though his impact on the development of Anglo-American modernism has received little systematic attention. In this volume, published to mark the centenary of Ruskin's death, a group of international scholars consider what is often an awkward and conflicted relation. Ruskin's voluminous writings are seen to shelter an incipient modernism whose antipathy to a degraded modernity, powerfully predicts a major current within the work of the new century.
In this book Stanghellini argues that to be human means to be in dialogue with alterity, that mental pathology is the outcome of a crisis of one's dialogue with alterity, and that care is a method wherein dialogues take place whose aim is to re-enact interrupted dialogue with alterity within oneself and with the external world.
This book proposes a novel technique, named artifact-driven process monitoring, by which multi-party processes, involving non-automated activities, can be continuously and autonomously monitored. This technique exploits the Internet of Things (IoT) paradigm to make the physical objects, participating in a process, smart. Being equipped with sensors, a computing device, and a communication interface, such smart objects can then become self-aware of their own conditions and of the process they participate in, and exchange this information with the other smart objects and the involved organizations. To allow organizations to reuse preexisting process models, a method to instruct smart objects given Business Process Model and Notation (BPMN) collaboration diagrams is also presented. The work constitutes a revised version of the PhD dissertation written by the author at the PhD School of Information Engineering of Politecnico di Milano, Italy. In 2019, the PhD dissertation won the “CAiSE PhD award”, granted to outstanding PhD theses in the field of Information Systems Engineering.
This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.
A comprehensive guide to the theory, practice and applications of optical tweezers, combining state-of-the-art research with a strong pedagogic approach.
The goal of Boccaccio’s Genealogy of the Pagan Gods is to plunder ancient and medieval literary sources to create a massive synthesis of Greek and Roman mythology. This is volume 1 of a three-volume set of Boccaccio’s complete 15-book work. It contains a famous defense of the value of studying ancient pagan poetry in a Christian world.
Emotions and values are considered the keys to understanding peoples' experiences and actions within the world they inhabit. The traditional symptom-led clinical interview is frequently criticised for ignoring the narrative of a patient's experience in favour of ticking-off symptoms that can be reduced or controlled. In response, this important new book seeks to understand a patient's sufferings through their individual experiences and values. The Therapeutic Interview in Mental Health is about the art of asking questions. This comprehensive book will equip psychologists, psychiatrists and clinicians with the tools to begin unlocking the emotions and experiences of their patients. The method of the therapeutic interview is explained in a step-by-step way, allowing the reader to understand the clinical interview as a means of beginning a shared understanding between patient and clinician. This book is an essential read for all psychologists, psychiatrists, general clinicians, and medical trainees.
Since the nineteenth century, scholars have debated the controversial relationships between humanism, the Renaissance and the Reformation. Challenging the dominant narrative on the subject, Giovanni Tortoriello reconstructs the debates that characterized the early Reformation movements. He shows that Martin Luther's theology of the cross developed in reaction to the irenic tendencies of the Renaissance. With the spread of Platonism, Hermeticism, and Kabbalah in the fifteenth century, the identity of Christianity shifted and the boundaries between the different religions thinned. In response to this attempt to minimize the differences among the various religions, Luther reiterated the centrality and uniqueness of the salvific event of the cross. Confessional biases and theological prejudices have obliterated the role that Platonism, Hermeticism, and Christian Kabbalah played in the early Reformation debates. The author reconstructs these controversies and situates Luther's theology of the cross in this historical context.
The aims of this thesis were to test the adsorption efficiency of cyanobacterial biomasses of polysaccharide producing strains and to realize a pilot plant for galvanic waste treatment based on biosorption. First of all the different strains were tested at laboratory scale with solutions containing one or more metals, in order to gradually approach the reality of galvanic industries, where several metals at different concentrations are present at the same time in the wastes. To realize the pilot plant we tried to combine the protocols established during laboratory experiments with the necessities of the final user, the industry, by designing and realizing three prototypes. It was moreover evaluated the possibility to recover the adsorbed metal in a form easy and convenient for recycling.
First published in 1964, Beard's Massage is a classic physical therapy massage text originally authored by Gertrude Beard, a pioneering physical therapist in the 1920s who treated patients using soft tissue massage techniques that remain the basis of practice today. Now in its fifth edition, with a new title, this classic text has been expanded and updated throughout to provide you with an overview of massage, a description of massage techniques, information on the benefits of massage, and specific techniques for a variety of conditions. - Practical step-by-step guidance to help you develop massage sequences that best meet the needs of your patients. - Sections on massage strokes show the direction and sequence of each stroke, allowing you the benefit of using one comprehensive resource instead of several texts. - Includes guidance in Swedish Remedial Massage techniques to help you develop proper massage techniques and sequences that best meet the needs of each individual client. - Nearly 500 line drawings and photos demonstrate how to perform all of the basic strokes, the physiologic and therapeutic effects of each technique, and how to apply the most appropriate massage sequences to specific regions of the body. - Photos include directional arrows that show hand position and movement across the patient. - Updated references facilitate further study and demonstrate currency of the text. - The new companion DVD with narrated video clips demonstrates each of the various techniques discussed in the text allowing you to visually comprehend proper timing and techniques. - Icons in the text link the text to the DVD so they can function together as a complete learning tool. - New chapter on Anatomical Landmarks for Soft Tissue Massage demonstrates the important anatomical landmarks and structures involved during the application of soft tissue massage techniques. - New chapter on Focal Massage Sequences describes the use of various massage techniques for specific pathologies to help enhance your assessment skills for those clients who present with specific injuries and/or conditions. - New chapter on Decongestive Therapy for the Treatment of Lymphedema shows how massage can be an effective part of lymphedema treatment. - New chapter on Massage in Sport explains the different strokes and methods required for sports massage in rehabilitation. - New chapter on Massage for the Baby and Infant describes different methods for safe massage. - New chapter on Massage in Palliative Care explains the role of massage, especially pain relief and relaxation, in the care of the terminally ill. - New chapter on Soft Tissue Manipulation in Complementary/Alternative Medicine (CAM) describes different massage techniques in CAM therapies.
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