The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems. "Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters. For each topic the theoretical framework is carefully explained using examples and applications. The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises. This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences. Herb Kunze is a professor of mathematics at the University of Guelph in Ontario. Davide La Torre is an associate professor of mathematics in the Department of Economics, Management and Quantitative Methods of the University of Milan. Franklin Mendivil is a professor of mathematics at Acadia University in Nova Scotia. Edward Vrscay is a professor in the department of Applied Mathematics at the University of Waterloo in Ontario. The major focus of their research is on fractals and the applications of fractals.
The idea of modeling the behaviour of phenomena at multiple scales has become a useful tool in both pure and applied mathematics. Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems. "Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters. For each topic the theoretical framework is carefully explained using examples and applications. The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises. This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course. The other chapters illustrate many extensions and applications of fractal-based methods to different areas. This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences. Herb Kunze is a professor of mathematics at the University of Guelph in Ontario. Davide La Torre is an associate professor of mathematics in the Department of Economics, Management and Quantitative Methods of the University of Milan. Franklin Mendivil is a professor of mathematics at Acadia University in Nova Scotia. Edward Vrscay is a professor in the department of Applied Mathematics at the University of Waterloo in Ontario. The major focus of their research is on fractals and the applications of fractals.
Industrial policies are the key element underlying today’s geopolitical scramble and a pillar of national security.Reacting to Western weaknesses and bottlenecks in the global supply chains, highlighted by multiple shocks such as the pandemic, the war in Ukraine, and the recent Israel-Hamas war, the US in first place and the EU later have started to introduce new industrial legislation aimed at making up for lost ground with respect to other industrialpowerhouses, such as China. Besides being policy tools to accelerate the green and digital transitions, however, the US Inflation Reduction Act and the Net Zero Industry Act, as well as the US and the EU Chips Acts, entail subsidies, local content requirements and export controls targeted at strengthening the domestic industrial base for critical technologies, fostering strategic autonomy and de-risking from excessive foreign dependencies.This race poses risks for the weaponisation of industrial policies and fragmentation of international trade and also potentially jeopardises technological development. How can we strike a balance between economic security and efficiency? Which sectors are the most critical and which ones are the leading global powers pursuing? What will the consequences be for global value chains and international trade? Is it possible to reach an agreement on rules for a new level playing field to prevent economic competition turning into economic warfare?
This 2006 book is a controversial reappraisal of the Italian occupation of the Mediterranean during the Second World War, which Davide Rodogno examines within the framework of fascist imperial ambitions. He focuses on the European territories annexed and occupied by Italy between 1940 and 1943: metropolitan France, Corsica, Slovenia, Croatia, Dalmatia, Montenegro, Albania, Kosovo, Western Macedonia, and mainland and insular Greece. He explores Italy's plans for Mediterranean expansion, its relationship with Germany, economic exploitation, the forced 'Italianisation' of the annexed territories, collaboration, repression, and Italian policies towards refugees and Jews. He also compares Fascist Italy and Nazi Germany through their dreams of imperial conquest, the role of racism and anti-Semitism, and the 'fascistization' of the Italian Army. Based on previously unpublished sources, this is a groundbreaking contribution to genocide, resistance, war crimes and occupation studies as well as to the history of the Second World War more generally.
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