The purpose of this monograph is to show that, in the radiation regime, there exists a Hamiltonian description of the dynamics of a massless scalar field, as well as of the dynamics of the gravitational field. The authors construct such a framework extending the previous work of Kijowski and Tulczyjew. They start by reviewing some elementary facts concerning Hamiltonian dynamical systems and then describe the geometric Hamiltonian framework, adequate for both the usual asymptotically-flat-at-spatial-infinity regime and for the radiation regime. The text then gives a detailed description of the application of the new formalism to the case of the massless scalar field. Finally, the formalism is applied to the case of Einstein gravity. The Hamiltonian role of the Trautman--Bondi mass is exhibited. A Hamiltonian definition of angular momentum at null infinity is derived and analysed.
The subject of this book is the economic backwardness of Poland and Eastern Europe in the modern era. The studies in the first part analyse various aspects of the region's economic and social history in the period from the 16th to the 20th centuries, such as the nature of peasant economics, the character of economic evolution, and the ambiguity of social and economic relations between Poland and "the West". The second part deals with the change following the fall of state socialism. Papers in this part argue that, for understanding the present, it is necessary to take into consideration historical legacies. It is also important to look at the process of this recent change comparatively, both within Eastern Europe and comparing this region with other parts of the world. Professor Kochanowicz's contention in these essays is that the so-called transformation has had to cope not only with the effects of state socialism, but also with a much longer legacy of backwardness.
The purpose of this monograph is to show that, in the radiation regime, there exists a Hamiltonian description of the dynamics of a massless scalar field, as well as of the dynamics of the gravitational field. The authors construct such a framework extending the previous work of Kijowski and Tulczyjew. They start by reviewing some elementary facts concerning Hamiltonian dynamical systems and then describe the geometric Hamiltonian framework, adequate for both the usual asymptotically-flat-at-spatial-infinity regime and for the radiation regime. The text then gives a detailed description of the application of the new formalism to the case of the massless scalar field. Finally, the formalism is applied to the case of Einstein gravity. The Hamiltonian role of the Trautman--Bondi mass is exhibited. A Hamiltonian definition of angular momentum at null infinity is derived and analysed.
A lyrical and moving Polish family saga set against the turbulent backdrop of twentieth-century Europe Lala has lived a dazzling life. Born in Poland just after the First World War and brought up to be a perfect example of her class and generation – tolerant, selfless and brave – Lala is an independent woman who has survived some of the most turbulent events of her times. As she senses the first signs of dementia, she battles to keep her memories alive through her stories, telling her grandson tales of a life filled with love, faithlessness and extraordinary acts of courage. Sweeping from nineteenth-century Kiev to modern-day Poland, Lala is the enthralling celebration of a beautiful life.
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