This book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stéphane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian fields after Mandelbrot and Van Ness's seminal paper. Fundamental properties of fractional Brownian fields are then stated and proved. The second central notion of this book is the so-called local asymptotic self-similarity (in short lass), which is a local version of self-similarity, defined in the third chapter. A lengthy study is devoted to lass fields with finite variance. Among these lass fields, we find both Gaussian fields and non-Gaussian fields, called Lévy fields. The Lévy fields can be viewed as bridges between fractional Brownian fields and stable self-similar fields. A further key issue concerns the identification of fractional parameters. This is the raison d'être of the statistics chapter, where generalized quadratic variations methods are mainly used for estimating fractional parameters. Last but not least, the simulation is addressed in the last chapter. Unlike the previous issues, the simulation of fractional fields is still an area of ongoing research. The algorithms presented in this chapter are efficient but do not claim to close the debate.
Provides a wide range of mathematical models currently used in the life sciences Each model is thoroughly explained and illustrated by example Includes three appendices to allow for independent reading
Collected Studies CS1070 The present book collects 31 articles that Jacques van der Vliet, a leading scholar in the field of Coptic Studies (Leiden University / Radboud University, Nijmegen), has published since 1999 on Christian inscriptions from Egypt and Nubia. These inscriptions are dated between the third/fourth and the fourteenth centuries, and are often written in Coptic and/or Greek, once in Latin, and sometimes (partly) in Arabic, Syriac or Old Nubian. They include inscriptions on tomb stones, walls of religious buildings, tools, vessels, furniture, amulets and even texts on luxury garments. Whereas earlier scholars in the field of Coptic Studies often focused on either Coptic or Greek, Van der Vliet argues that inscriptions in different languages that appear in the same space or on the same kind of objects should be examined together. In addition, he aims to combine the information from documentary texts, archaeological remains and inscriptions, in order to reconstruct the economic, social and religious life of monastic or civil communities. He practiced this methodology in his studies on the Fayum, Wadi al-Natrun, Sohag, Western Thebes and the region of Aswan and Northern Nubia, which are all included in this book.
To write this history of the imagination, Le Goff has recreated the mental structures of medieval men and women by analyzing the images of man as microcosm and the Church as mystical body; the symbols of power such as flags and oriflammes; and the contradictory world of dreams, marvels, devils, and wild forests. "Le Goff is one of the most distinguished of the French medieval historians of his generation . . . he has exercised immense influence."—Maurice Keen, New York Review of Books "The whole book turns on a fascinating blend of the brutally materialistic and the generously imaginative."—Tom Shippey, London Review of Books "The richness, imaginativeness and sheer learning of Le Goff's work . . . demand to be experienced."—M. T. Clanchy, Times Literary Supplement
The apocryphal Apocalypse of Paul plunges us right into the heart of early-Christian conceptions of heaven and hell. This book presents the previously hardly accessible Coptic version and argues that it is the best available witness of the ancient text.
Translated and revised by respected scholar of Chinese religions Franciscus Verellen, who has worked closely with Gernet, this edition includes new references, an extensive, up-to-date bibliography, and a comprehensive index.
Noting that the doctrine of Purgatory does not appear in the Latin theology of the West before the late twelfth century, the author identifies the profound social and intellectual changes which caused its widespread acceptance.
The Liber mahameleth is a work in Latin written in the mid-12th century based (mainly) on Arabic sources from Islamic Spain. It is now our principal source on mathematics in Islamic Spain at that time; There are few extant Arabic texts and no one is as complete as the LM. It is also the second largest mathematical work from the Latin Middle Ages (the other is by Fibonacci, some 50 years later). Since the three main manuscripts preserving it are incomplete and there are many scribal errors, a reliable Latin text has been established, which reports (in notes) the various readings of the manuscripts and the errors in them. This is how a so-called critical edition is made. This edition of the Latin text is preceded by General Introduction, describing the various manuscripts, the content of the work and what we know about its author. Part Two of the volume is a translation of the text and ends with a glossary of Latin terms. The glossary will be of great importance for the knowledge of Latin scientific terms from that time, since there is no other mathematical text of this size from the 12th century. Part Three begins with a short introduction and then analyzes all the problems from the text, with a summary of the mathematical methods involved in each chapter. The commentary is a companion to the translation and explains the author's solving methods.
This book focuses mainly on fractional Brownian fields and their extensions. It has been used to teach graduate students at Grenoble and Toulouse's Universities. It is as self-contained as possible and contains numerous exercises, with solutions in an appendix. After a foreword by Stéphane Jaffard, a long first chapter is devoted to classical results from stochastic fields and fractal analysis. A central notion throughout this book is self-similarity, which is dealt with in a second chapter with a particular emphasis on the celebrated Gaussian self-similar fields, called fractional Brownian fields after Mandelbrot and Van Ness's seminal paper. Fundamental properties of fractional Brownian fields are then stated and proved. The second central notion of this book is the so-called local asymptotic self-similarity (in short lass), which is a local version of self-similarity, defined in the third chapter. A lengthy study is devoted to lass fields with finite variance. Among these lass fields, we find both Gaussian fields and non-Gaussian fields, called Lévy fields. The Lévy fields can be viewed as bridges between fractional Brownian fields and stable self-similar fields. A further key issue concerns the identification of fractional parameters. This is the raison d'être of the statistics chapter, where generalized quadratic variations methods are mainly used for estimating fractional parameters. Last but not least, the simulation is addressed in the last chapter. Unlike the previous issues, the simulation of fractional fields is still an area of ongoing research. The algorithms presented in this chapter are efficient but do not claim to close the debate.
Provides a wide range of mathematical models currently used in the life sciences Each model is thoroughly explained and illustrated by example Includes three appendices to allow for independent reading
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