The idea of structure-preserving algorithms appeared in the 1980's. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or the existence of conservation laws or some other qualitative feature of the dynamics. Another area that has kept growing in importance within Geometric Numerical Integration is the study of highly-oscillatory problems: problems where the solutions are periodic or quasiperiodic and have to be studied in time intervals that include an extremely large number of periods. As is known, these equations cannot be solved efficiently using conventional methods. A further study of novel geometric integrators has become increasingly important in recent years. The objective of this monograph is to explore further geometric integrators for highly oscillatory problems that can be formulated as systems of ordinary and partial differential equations. Facing challenging scientific computational problems, this book presents some new perspectives of the subject matter based on theoretical derivations and mathematical analysis, and provides high-performance numerical simulations. In order to show the long-time numerical behaviour of the simulation, all the integrators presented in this monograph have been tested and verified on highly oscillatory systems from a wide range of applications in the field of science and engineering. They are more efficient than existing schemes in the literature for differential equations that have highly oscillatory solutions. This book is useful to researchers, teachers, students and engineers who are interested in Geometric Integrators and their long-time behaviour analysis for differential equations with highly oscillatory solutions.

This book intensively examines the efficacy of plant-derived products that have been used for over a thousand years by practitioners of so-called Traditional Chinese Medicine in the light of recent chemotherapeuticals. The chapters were written by renowned Chinese medical researchers and are supplemented by results obtained in German antiparasitic research projects. Parasites and emerging diseases are a major threat of our time, which is characterized by an enormous increase in the size of the human population and by an unbelievably rapid globalization that has led to the daily transport of millions of humans and containers with goods from one end of the earth to the other. Furthermore the slow but constant global warming offers new opportunities for many agents of diseases to become established in new areas. Therefore it is essential that we develop precautions in order to avoid epidemics or even pandemics in overcrowded megacities or at the large-scale farm animal confinements that are needed to secure a steady flow of food in the crowded regions of the world. Of course intensive research in the field of chemotherapy since 1900 has produced unbelievable breakthroughs in therapies for formerly untreatable and thus deadly diseases. However, a large number of untreatable diseases remain, as well as a constantly growing number of agents of disease that have developed resistances to standard chemical compounds. As such, it is not only worthwhile but also vital to consider the enormous amounts of information that have been obtained by human "high cultures" in the past. Examples from the past (like quinine) or present (like artemisinin, a modern antimalarial drug) show that plant extracts may hold tremendous potential in the fight against parasites and/or against vector-transmitted agents of diseases.

The main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the latest advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods, and symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the context of structure preservation. All the new methods introduced in this book are proven to be highly effective compared with the well-known codes in the scientific literature. This book also addresses challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.

After thirty years of economic reform, China has reached a crossroads in its development process, and faces many challenges in the use of natural resources, the living environment, and the economic, social and political systems. The sustainability of China's reform and development is even more salient in the face of the global financial crisis and economic recession. Taking the 2008 Olympic Games in Beijing as an iconic turning-point, the book explores key themes such as economic reform and sustainability, innovation and sustainability, globalisation and social development, and analyses the prospects for sustainable reform and development in Post-Olympic China. The book includes topics such as Chinese banking reforms; the issue of regional inequalities; energy and environmental challenges; industry development and corporate social responsibility, and democracy and media bloggers. With analysis written by experts from a wide range of disciplines, the book will appeal to a wide range of readers interested in China's environment and sustainable development, economic and political reform, and international relations.

After thirty years of economic reform, China has reached a crossroads in its development process, and faces many challenges in the use of natural resources, the living environment, and the economic, social and political systems. The sustainability of China s reform and development is even more salient in the face of the global financial crisis and economic recession. Taking the 2008 Olympic Games in Beijing as an iconic turning-point, the book explores key themes such as economic reform and sustainability, innovation and sustainability, globalisation and social development, and analyses the prospects for sustainable reform and development in Post-Olympic China.

The book includes topics such as Chinese banking reforms; the issue of regional inequalities; energy and environmental challenges; industry development and corporate social responsibility, and democracy and media bloggers. With analysis written by experts from a wide range of disciplines, the book will appeal to a wide range of readers interested in China s environment and sustainable development, economic and political reform, and international relations."

The main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the latest advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods, and symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the context of structure preservation. All the new methods introduced in this book are proven to be highly effective compared with the well-known codes in the scientific literature. This book also addresses challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.

This book intensively examines the efficacy of plant-derived products that have been used for over a thousand years by practitioners of so-called Traditional Chinese Medicine in the light of recent chemotherapeuticals. The chapters were written by renowned Chinese medical researchers and are supplemented by results obtained in German antiparasitic research projects. Parasites and emerging diseases are a major threat of our time, which is characterized by an enormous increase in the size of the human population and by an unbelievably rapid globalization that has led to the daily transport of millions of humans and containers with goods from one end of the earth to the other. Furthermore the slow but constant global warming offers new opportunities for many agents of diseases to become established in new areas. Therefore it is essential that we develop precautions in order to avoid epidemics or even pandemics in overcrowded megacities or at the large-scale farm animal confinements that are needed to secure a steady flow of food in the crowded regions of the world. Of course intensive research in the field of chemotherapy since 1900 has produced unbelievable breakthroughs in therapies for formerly untreatable and thus deadly diseases. However, a large number of untreatable diseases remain, as well as a constantly growing number of agents of disease that have developed resistances to standard chemical compounds. As such, it is not only worthwhile but also vital to consider the enormous amounts of information that have been obtained by human "high cultures" in the past. Examples from the past (like quinine) or present (like artemisinin, a modern antimalarial drug) show that plant extracts may hold tremendous potential in the fight against parasites and/or against vector-transmitted agents of diseases.

The idea of structure-preserving algorithms appeared in the 1980's. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or the existence of conservation laws or some other qualitative feature of the dynamics. Another area that has kept growing in importance within Geometric Numerical Integration is the study of highly-oscillatory problems: problems where the solutions are periodic or quasiperiodic and have to be studied in time intervals that include an extremely large number of periods. As is known, these equations cannot be solved efficiently using conventional methods. A further study of novel geometric integrators has become increasingly important in recent years. The objective of this monograph is to explore further geometric integrators for highly oscillatory problems that can be formulated as systems of ordinary and partial differential equations. Facing challenging scientific computational problems, this book presents some new perspectives of the subject matter based on theoretical derivations and mathematical analysis, and provides high-performance numerical simulations. In order to show the long-time numerical behaviour of the simulation, all the integrators presented in this monograph have been tested and verified on highly oscillatory systems from a wide range of applications in the field of science and engineering. They are more efficient than existing schemes in the literature for differential equations that have highly oscillatory solutions. This book is useful to researchers, teachers, students and engineers who are interested in Geometric Integrators and their long-time behaviour analysis for differential equations with highly oscillatory solutions.