Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation and waves) with particular regard to models based on fractional calculus. It serves as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature. In particular the relevant role played by some special functions is pointed out along with their visualization through plots. Graphics are extensively used in the book and a large general bibliography is included at the end.This new edition keeps the structure of the first edition but each chapter has been revised and expanded, and new additions include a novel appendix on complete monotonic and Bernstein functions that are known to play a fundamental role in linear viscoelasticity.This book is suitable for engineers, graduate students and researchers interested in fractional calculus and continuum mechanics.
The 2nd edition of this book is essentially an extended version of the 1st and provides a very sound overview of the most important special functions of Fractional Calculus. It has been updated with material from many recent papers and includes several surveys of important results known before the publication of the 1st edition, but not covered there. As a result of researchers’ and scientists’ increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have caught the interest of the scientific community. Focusing on the theory of Mittag-Leffler functions, this volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular, the Mittag-Leffler functions make it possible to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and related special functions. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, control theory and several other related areas.
The many technical and computational problems that appear to be constantly emerging in various branches of physics and engineering beg for a more detailed understanding of the fundamental mathematics that serves as the cornerstone of our way of understanding natural phenomena. The purpose of this Special Issue was to establish a brief collection of carefully selected articles authored by promising young scientists and the world's leading experts in pure and applied mathematics, highlighting the state-of-the-art of the various research lines focusing on the study of analytical and numerical mathematical methods for pure and applied sciences.
Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation and waves) with particular regard to models based on fractional calculus. It serves as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature. In particular the relevant role played by some special functions is pointed out along with their visualization through plots. Graphics are extensively used in the book and a large general bibliography is included at the end.This new edition keeps the structure of the first edition but each chapter has been revised and expanded, and new additions include a novel appendix on complete monotonic and Bernstein functions that are known to play a fundamental role in linear viscoelasticity.This book is suitable for engineers, graduate students and researchers interested in fractional calculus and continuum mechanics.
As a result of researchers’ and scientists’ increasing interest in pure as well as applied mathematics in non-conventional models, particularly those using fractional calculus, Mittag-Leffler functions have recently caught the interest of the scientific community. Focusing on the theory of the Mittag-Leffler functions, the present volume offers a self-contained, comprehensive treatment, ranging from rather elementary matters to the latest research results. In addition to the theory the authors devote some sections of the work to the applications, treating various situations and processes in viscoelasticity, physics, hydrodynamics, diffusion and wave phenomena, as well as stochastics. In particular the Mittag-Leffler functions allow us to describe phenomena in processes that progress or decay too slowly to be represented by classical functions like the exponential function and its successors. The book is intended for a broad audience, comprising graduate students, university instructors and scientists in the field of pure and applied mathematics, as well as researchers in applied sciences like mathematical physics, theoretical chemistry, bio-mathematics, theory of control and several other related areas.
The main goal of this work is to revisit the proof of the global stability of Minkowski space by D. Christodoulou and S. Klainerman, [Ch-KI]. We provide a new self-contained proof of the main part of that result, which concerns the full solution of the radiation problem in vacuum, for arbitrary asymptotically flat initial data sets. This can also be interpreted as a proof of the global stability of the external region of Schwarzschild spacetime. The proof, which is a significant modification of the arguments in [Ch-Kl], is based on a double null foliation of spacetime instead of the mixed null-maximal foliation used in [Ch-Kl]. This approach is more naturally adapted to the radiation features of the Einstein equations and leads to important technical simplifications. In the first chapter we review some basic notions of differential geometry that are sys tematically used in all the remaining chapters. We then introduce the Einstein equations and the initial data sets and discuss some of the basic features of the initial value problem in general relativity. We shall review, without proofs, well-established results concerning local and global existence and uniqueness and formulate our main result. The second chapter provides the technical motivation for the proof of our main theorem.
In the 1980s, the world of riding, training, and competing with horses took a major turn with the spread of natural horsemanship, which at its most basic foundation rejects the use of abusive techniques and relies on methods derived from understanding the dynamics of free-roaming horse herds. Since then, equestrians across disciplines have incorporated elements of natural horsemanship into their work. But despite what was certainly an advancement in human-equine interaction that has improved the lives of many horses, Italian animal behaviorists Francesco de Giorgio and José de Giorgio-Schoorl dare to now ask, What if much of what we think we know about horses is, in fact, wrong? What if the premise of herd hierarchy is a myth? What if “conditioning” the horse’s behavior in the ways we’ve grown accustomed is undercutting his potential for development? What if there is another—better—level of partnership to which we can aspire? Their provocative book takes us into a dimension where we shed our assumptions of leadership, dominance, and control, convincingly showing a way forward that acknowledges that a horse, when allowed, is driven by his own inner motivation to explore and understand the world around him, including his relationship with humans.
International ISAAC (International Society for Analysis, its Applications and Computation) Congresses have been held every second year since 1997. The proceedings report on a regular basis on the progresses of the field in recent years, where the most active areas in analysis, its applications and computation are covered. Plenary lectures also highlight recent results. This volume concentrates mainly on partial differential equations, but also includes function spaces, operator theory, integral transforms and equations, potential theory, complex analysis and generalizations, stochastic analysis, inverse problems, homogenization, continuum mechanics, mathematical biology and medicine. With over 350 participants attending the congress, the book comprises 140 papers from 211 authors. The volume also serves for transferring personal information about the ISAAC and its members. This volume includes citations for O Besov, V Burenkov and R P Gilbert on the occasion of their anniversaries.
Benvenuto Olivieri was a Florentine banker active in Rome during the first half of the sixteenth century. A self made man without any great family patrimony, he rose to prominence during the pontificate of Pope Paul III, becoming involved with a variety of papal enterprises which allowed him to get to the heart of the mechanisms governing the papal finances. Amassing a considerable fortune along the way, Olivieri soon built himself a role as co-ordinator of the appalti (revenue farms) and became one of the most powerful players in the complex network that connected bankers and the papal revenue. This book explores the indissoluble link that had developed between the papacy and bankers, illuminating how the Apostolic Chamber, increasingly in need of money, could not meet its debts, without farming out the rights to future income. Utilising documents from a rich corpus of unpublished sources in Florence and Rome, Guidi Bruscoli unravels the web of financial connections that bound together Florentine and Genoese bankers with the papacy, and looks at how money was raised and the appalti managed.
This book presents and analyses twelve different writings from 19th century Italian literature on the topic of translation. With the exception of their original publication and some earlier reissues, these texts have never been republished in the 20th or 21st centuries and have remained in the shadows for about two centuries. Nevertheless, they provide a very important testimony to the lively interest in translation and the debate that characterized this specific period of Italian literary culture. The few international studies that deal with 19th century theoretical reflection on translation in Italy often focus only on some scattered contributions of a few influential writers (e.g. Leopardi and Foscolo). In this regard, this book could spark new investigations on the subject. While it is commonly thought that reflections on translation during the century analysed in this book came almost exclusively from Germany, France, and England, the debate on this topic was alive and well in Italy during that time and produced many interesting original ideas. Some of the topics discussed by the authors presented here, such as language hospitality, foreign translation, authorial translation, importance of translation in the receiving culture, among others, are presented in an original way that anticipates twentieth-century reflection. Above all, they demonstrate Italian intellectuals’ awareness of the observations on translation originating from other time periods and nations. Although studies on the theory of translation in Italy are often hoped for, they are still rare and undeveloped, and have yet to examine the texts published in this book. The academic awareness of the origins of translation studies in other countries, on the other hand, is more advanced. This book aims to be among these studies.
Consummate painter, draftsman, sculptor, and architect, Michelangelo Buonarroti (1475–1564) was celebrated for his disegno, a term that embraces both drawing and conceptual design, which was considered in the Renaissance to be the foundation of all artistic disciplines. To his contemporary Giorgio Vasari, Michelangelo was “the divine draftsman and designer” whose work embodied the unity of the arts. Beautifully illustrated with more than 350 drawings, paintings, sculptures, and architectural views, this book establishes the centrality of disegno to Michelangelo’s work. Carmen C. Bambach presents a comprehensive and engaging narrative of the artist’s long career in Florence and Rome, beginning with his training under the painter Domenico Ghirlandaio and the sculptor Bertoldo and ending with his seventeen-year appointment as chief architect of Saint Peter’s Basilica at the Vatican. The chapters relate Michelangelo’s compositional drawings, sketches, life studies, and full-scale cartoons to his major commissions—such as the ceiling frescoes and the Last Judgment in the Sistine Chapel, the church of San Lorenzo and its New Sacristy (Medici Chapel) in Florence, and Saint Peter’s—offering fresh insights into his creative process. Also explored are Michelangelo’s influential role as a master and teacher of disegno, his literary and spiritual interests, and the virtuoso drawings he made as gifts for intimate friends, such as the nobleman Tommaso de’ Cavalieri and Vittoria Colonna, the marchesa of Pescara. Complementing Bambach’s text are thematic essays by leading authorities on the art of Michelangelo. Meticulously researched, compellingly argued, and richly illustrated, this book is a major contribution to our understanding of this timeless artist.
This book outlines the legal status of Muslims in Italy. In particular, it highlights that, when it comes to Islam, the Italian legal system exacerbates the dilemma of contemporary constitutional democracies, increasingly caught between the principle of equality and the right to have rights, which implies the respect of diversity. It provides readers with a deep understanding of how domestic and external socio-political factors may muddle the interpretation of Italy’s constitutional provisions, starting with those relating to state secularism and religious freedom. It is argued that today, as never before, these provisions are torn between the principle of equality and the right to be different. This situation has been exacerbated by incessant states of emergency, from immigration to religion-inspired terrorism, in light of which the presence of Islam in the peninsula has been highly politicized. Italy’s experience on the legal status of Muslims provides an interesting case study and, as such, a valuable source of empirical information for a functioning and pluralistic constitutional democracy, especially when dealing with conditions of fear and insecurity. The book will be of interest to researchers, academics, and policy-makers working in the areas of law and religion, constitutional law, comparative law, and human rights.
These memories, handwritten by Elmo Cermaria (Nonno Peppe) for his grandson Checco (Francesco Nicolini), tell of when, as a young man of 20, he found himself hurled into the inferno of the First World War. In those days, you could cry your heart out for a bread roll denied, then miraculously regained thanks to the compassion of a German soldier, “the hated enemy”. These recollections are terse, without a trace of rhetoric and devoid of recriminations. Nonno Peppe tells the facts just as he experienced them first hand, without expressing any condemnation of those responsible for them, even though an awareness of the large-scale massacre he witnessed transpires from his account. When Nonno Peppe delivered the manuscript to his grandson on his wedding day, he asked him to make a promise: “Let the President of the Republic know what we did for Italy.” A hundred years ago, whole generations of young Italian men were stripped of human honor and dignity. Only a few of these young men would live on and become our grandfathers; and only a few of us would be fortunate enough to become “grandchildren of the Great War” and bear witness to their ordeal.
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