This work is a textbook on Mathematical Analysis written by expert lecturers in the field. This textbook, other than the classical differentiation and integration tools for functions of several real variables, metric spaces, ordinary differential equations, implicit function and so on, also provides opportunities to go deeper into certain topics: among them, the Ascoli-Arzelà theorem, the regularity of convex functions in R^n, L^p spaces and absolutely continuous functions, all topics that are paramount in modern Mathematical Analysis. Other instances include the Weierstrass theorem on polynomial approximation of continuous functions or Peano's existence theorem (typically only existence, without uniqueness) for nonlinear ODEs and systems under general assumptions. The content is discussed in an elementary way and, at a successive stage, some topics are examined from several, more penetrating, angles. The agile organization of the subject matter helps instructors to effortlessly determine which parts to present during lectures and where to stop. The authors believe that any textbook can contribute to the success of a lecture course only to a point, and the choices made by lecturers are decisive in this respect. The book is addressed to graduate or undergraduate honors students in Mathematics, Physics, Astronomy, Computer Science, Statistics and Probability, attending Mathematical Analysis courses at the Faculties of Science, Engineering, Economics and Architecture.
Nonlinear partial differential equations has become one of the main tools of mod ern mathematical analysis; in spite of seemingly contradictory terminology, the subject of nonlinear differential equations finds its origins in the theory of linear differential equations, and a large part of functional analysis derived its inspiration from the study of linear pdes. In recent years, several mathematicians have investigated nonlinear equations, particularly those of the second order, both linear and nonlinear and either in divergence or nondivergence form. Quasilinear and fully nonlinear differential equations are relevant classes of such equations and have been widely examined in the mathematical literature. In this work we present a new family of differential equations called "implicit partial differential equations", described in detail in the introduction (c.f. Chapter 1). It is a class of nonlinear equations that does not include the family of fully nonlinear elliptic pdes. We present a new functional analytic method based on the Baire category theorem for handling the existence of almost everywhere solutions of these implicit equations. The results have been obtained for the most part in recent years and have important applications to the calculus of variations, nonlin ear elasticity, problems of phase transitions and optimal design; some results have not been published elsewhere.
This work is a textbook on Mathematical Analysis written by expert lecturers in the field. This textbook, other than the classical differentiation and integration tools for functions of several real variables, metric spaces, ordinary differential equations, implicit function and so on, also provides opportunities to go deeper into certain topics: among them, the Ascoli-Arzelà theorem, the regularity of convex functions in R^n, L^p spaces and absolutely continuous functions, all topics that are paramount in modern Mathematical Analysis. Other instances include the Weierstrass theorem on polynomial approximation of continuous functions or Peano's existence theorem (typically only existence, without uniqueness) for nonlinear ODEs and systems under general assumptions. The content is discussed in an elementary way and, at a successive stage, some topics are examined from several, more penetrating, angles. The agile organization of the subject matter helps instructors to effortlessly determine which parts to present during lectures and where to stop. The authors believe that any textbook can contribute to the success of a lecture course only to a point, and the choices made by lecturers are decisive in this respect. The book is addressed to graduate or undergraduate honors students in Mathematics, Physics, Astronomy, Computer Science, Statistics and Probability, attending Mathematical Analysis courses at the Faculties of Science, Engineering, Economics and Architecture.
Nonlinear partial differential equations has become one of the main tools of mod ern mathematical analysis; in spite of seemingly contradictory terminology, the subject of nonlinear differential equations finds its origins in the theory of linear differential equations, and a large part of functional analysis derived its inspiration from the study of linear pdes. In recent years, several mathematicians have investigated nonlinear equations, particularly those of the second order, both linear and nonlinear and either in divergence or nondivergence form. Quasilinear and fully nonlinear differential equations are relevant classes of such equations and have been widely examined in the mathematical literature. In this work we present a new family of differential equations called "implicit partial differential equations", described in detail in the introduction (c.f. Chapter 1). It is a class of nonlinear equations that does not include the family of fully nonlinear elliptic pdes. We present a new functional analytic method based on the Baire category theorem for handling the existence of almost everywhere solutions of these implicit equations. The results have been obtained for the most part in recent years and have important applications to the calculus of variations, nonlin ear elasticity, problems of phase transitions and optimal design; some results have not been published elsewhere.
Why did weeds matter in the Carolingian empire? What was their special significance for writers in eighth- and ninth-century Europe and how was this connected with the growth of real weeds? In early medieval Europe, unwanted plants that persistently appeared among crops created extra work, reduced productivity, and challenged theologians who believed God had made all vegetation good. For the first time, in this book weeds emerge as protagonists in early medieval European history, driving human farming strategies and coloring people's imagination. Early medieval Europeans' effort to create agroecosystems that satisfied their needs and cosmologies that confirmed Christian accounts of vegetable creation both had to come to terms with unruly plants. Using diverse kinds of texts, fresh archaeobotanical data, and even mosaics, this interdisciplinary study reveals how early medieval Europeans interacted with their environments.
The book is published as part of the "PRIN 2017 The Dark side of the Law". This volume analyzes the theoretical underpinnings of the academic transhumanism movement, beginning with the relationship between anthropology and technique. The author focuses on the question of immortality, which can be considered the core of transhumanism. The true depth of immortality will be discussed, through which and how many transformations could be produced in order to change our society, which is basically shaped by and for human mortal beings, in a society composed by immortal persons. Some writers have written about what a future populated with immortals might look like, which is far removed from both the bright future painted by transhumanists and from the disappearance of humanity feared by bioconservatives.
At the end of the Second World War, America’s newly acquired status of hegemonic power- together with the launch of ambitious international programs such as the Marshall Plan- significantly altered existing transatlantic relations. In this context, Italian and American architectural cultures developed a fragile dialogue characterized by successful exchanges and forms of collaboration but also by reciprocal wariness. The dissemination of models and ideas concerning architecture generated complex effects and frequently led to surprising misinterpretations, obstinate forms of resistance and long negotiations between the involved parties. Issues of continuity and discontinuity dominated Italian culture and society at the time since at stake was the possible balance between allegedly long-established traditions and the prospect of a radical rupture with recent history. Architectural culture often contributed to reach a compromise between very diverging attitudes. Situated in the larger realm of studies on Americanization, this book questions current interpretations of transatlantic relations in architecture. By reconsidering the means and effects of the dialogue that unfolded between the two sides of the Atlantic during the postwar years, the volume analyzes how cultural and formal models were developed in one context and then modified when transferred to a new one as well as the fortune of this cultural exchange in terms of circulation, amplification, and simplification.
This book presents a comprehensive analysis of the Italian experience of transitional justice examining how the crimes of Fascism and World War II have been dealt with from a comparative perspective. Applying an interdisciplinary and comparative methodology, the book offers a detailed reconstruction of the prosecution of the crimes of Fascism and the Italian Social Republic as well as crimes committed by Nazi soldiers against Italian civilians and those of the Italian army against foreign populations. It also explores the legal qualification and prosecution of the actions of the Resistance. Particular focus is given to the Togliatti Amnesty, the major turning point, through comparisons to the wider European post-WWII transitional scenario and other relevant transitional amnesties, allowing consideration of the intense debate on the legitimacy of amnesties under international law. The book evaluates the Italian experience and provides an ideal framework to assess the complexity of the interdependencies between time, historical memory and the use of criminal law. In a historical moment marked by the resurgence of racism, neo-fascism, falsifications of the past, as well as the desire to amend the faults of the past, the Italian unfinished experience of dealing with the Fascist era can help move the discussion forward. The book will be essential reading for students, researchers and academics in International Criminal Law, Transitional Justice, History, Memory Studies and Political Science.
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