This book reports on the latest advances in using BIM modelling to achieve the semantic enrichment of objects, allowing them to be used both as multidimensional databases - as comprehensive sources of information for finalizing various types of documentation in the building industry - and as modelling tools for the construction of virtual environments. Having advanced to a new stage of development, BIM modelling is now being applied in a range of increasingly complex contexts, and for various new purposes. This book examines the role that virtual reality and related technologies such as AI and IoT can play in preserving and disseminating our cultural heritage and built environment.

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers, where a function field of one variable is the analogue of a finite extension of Q, the field of rational numbers. The author does not ignore the geometric-analytic aspects of function fields, but leaves an in-depth examination from this perspective to others.

Key topics and features:

* Contains an introductory chapter on algebraic and numerical antecedents, including transcendental extensions of fields, absolute values on Q, and Riemann surfaces

* Focuses on the Riemanna "Roch theorem, covering divisors, adeles or repartitions, Weil differentials, class partitions, and more

* Includes chapters on extensions, automorphisms and Galois theory, congruence function fields, the Riemann Hypothesis, the Riemanna "Hurwitz Formula, applications of function fields to cryptography, class field theory, cyclotomic function fields, and Drinfeld modules

* Explains both the similarities and fundamental differences between function fields and number fields

* Includes many exercises and examples to enhance understanding and motivate further study

The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra. The book can serve as a text for a graduate course in number theory or an advanced graduate topics course. Alternatively, chapters 1-4 can serve as the base of an introductory undergraduate course for mathematicsmajors, while chapters 5-9 can support a second course for advanced undergraduates. Researchers interested in number theory, field theory, and their interactions will also find the work an excellent reference.

Terrence Malick's debut film, Badlands, announced the arrival of a unique talent. In the 40 years since that debut, Malick has only made 5 films, but they are distinctive in their beauty. This book is not meant to be a biography of Terrence Malick. The purpose behind the book is to introduce readers to the extraordinary universe of his film-making and to aid them in understanding his work. And to do this through the words of his closest collaborators - cinematographers, set designers, costumers, cameramen, directors, producers, and actors such as Sean Penn, Martin Sheen, Sissy Spacek and Jessica Chastain. As their words flow from one to another, they form a fascinating, kaleidoscopic vision of American film and specifically Malick's artistic world. who make up a film. This book is the fruit of a journey began years ago when Luciano Baracaroli, Carlo Hintermann, Gerardo Panichi and Daniele Villa made a documentary on the work of Terrence Malick, which led to the making of this book as well.

This book reports on the latest advances in using BIM modelling to achieve the semantic enrichment of objects, allowing them to be used both as multidimensional databases - as comprehensive sources of information for finalizing various types of documentation in the building industry - and as modelling tools for the construction of virtual environments. Having advanced to a new stage of development, BIM modelling is now being applied in a range of increasingly complex contexts, and for various new purposes. This book examines the role that virtual reality and related technologies such as AI and IoT can play in preserving and disseminating our cultural heritage and built environment.

How do we react to suffering or betrayal or prosperity? How should we understand a premature death? How can we assimilate a "failure" without being filled with bitterness? How can we live out the demands of our faith in the face of the inequalities of life and its diverse sorrows? The Christian life is a miracle, and as such it is supernatural. We need, therefore, a mind which is also supernatural. We need understanding which goes beyond ordinary human understanding, in order to live up to the norm that our Master demands and not fail in the attempt. Through this book the reader can learn how to obtain the understanding which surpasses human comprehension.