Actions of Polish groups are ubiquitous in mathematics. In certain branches of ergodic theory and functional analysis, one finds a systematic study of the group of measure-preserving transformations and the unitary group. In logic, the analysis of countable models intertwines with results concerning the actions of the infinite symmetric group. This text develops the theory of Polish group actions entirely from scratch, ultimately presenting a coherent theory of the resulting orbit equivalence classes that may allow complete classification by invariants of an indicated form. The book concludes with a criterion for an orbit equivalence relation classifiable by countable structures considered up to isomorphism. This self-contained volume offers a complete treatment of this active area of current research and develops a difficult general theory classifying a class of mathematical objects up to some relevant notion of isomorphism or equivalence.
Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional rigidity theorems and relative ergodicity results in this context.
Contributes to the theory of Borel equivalence relations, considered up to Borel reducibility, and measures preserving group actions considered up to orbit equivalence. This title catalogs the actions of products of the free group and obtains additional rigidity theorems and relative ergodicity results in this context.
Actions of Polish groups are ubiquitous in mathematics. In certain branches of ergodic theory and functional analysis, one finds a systematic study of the group of measure-preserving transformations and the unitary group. In logic, the analysis of countable models intertwines with results concerning the actions of the infinite symmetric group. This text develops the theory of Polish group actions entirely from scratch, ultimately presenting a coherent theory of the resulting orbit equivalence classes that may allow complete classification by invariants of an indicated form. The book concludes with a criterion for an orbit equivalence relation classifiable by countable structures considered up to isomorphism. This self-contained volume offers a complete treatment of this active area of current research and develops a difficult general theory classifying a class of mathematical objects up to some relevant notion of isomorphism or equivalence.
This text reviews many of the aspects of the chemistry of the aromatic hydrocarbons and a consensus evaluation of the data by seven of the leading atmospheric scientists. The book covers topics ranging from the relative importance of the compounds in ozone and haze development to methods of estimating elemantary rate coefficients based on structural features of the compounds to mechanisms of aerosol generation and atmostpheric reaction of the polycyclic compounds to photochemical processes. It identifies features of the aromatic hydrocarbons requiring further study and appendicies give the structural formulas and nomenclature of the compounds reviewed in the book.
Building upon the success of previous editions, this fully revised edition of Sociology lays the foundations for understanding sociology in Australia. The depth and breadth of the book ensures its value not only for first-year students, but for sociology majors requiring on-going reference to a range of theoretical perspectives and current debates. This fifth Australian edition continues to build on the book’s reputation for coverage, clarity and content, drawing upon the work of leading Australian sociologists as well as engaging with global social trends and sociological developments.
We have come to know that our ability to survive and grow as a nation to a very large degree depends upon our scientific progress. Moreover, it is not enough simply to keep 1 abreast of the rest of the world in scientific matters. We must maintain our leadership. President Harry Truman spoke those words in 1950, in the aftermath of World War II and in the midst of the Cold War. Indeed, the scientific and engineering leadership of the United States and its allies in the twentieth century played key roles in the successful outcomes of both World War II and the Cold War, sparing the world the twin horrors of fascism and totalitarian communism, and fueling the economic prosperity that followed. Today, as the United States and its allies once again find themselves at war, President Truman’s words ring as true as they did a half-century ago. The goal set out in the Truman Administration of maintaining leadership in science has remained the policy of the U. S. Government to this day: Dr. John Marburger, the Director of the Office of Science and Technology (OSTP) in the Executive Office of the President, made remarks to that effect during his 2 confirmation hearings in October 2001. The United States needs metrics for measuring its success in meeting this goal of maintaining leadership in science and technology. That is one of the reasons that the National Science Foundation (NSF) and many other agencies of the U. S.
The Natural Philosophy Alliance (NPA) sponsors regular international conferences for presenting high-quality papers discussing aspects of philosophy in the sciences. Many papers offer challenges to accepted orthodoxy in the sciences, especially in physics. Everything from the micro-physics of quantum mechanics to the macro-physics of cosmology is entertained.Though the main interest of the NPA is in challenging orthodoxy in the sciences, it will also feature papers defending such orthodoxy. Our ultimate propose is to enable participants to articulate their own understanding of the truth. All papers are reviewed by society officers, and sometimes by other members, before presentation in conferences and they are edit, sometimes very significantly prior to publication in the Proceedings of the NPA.
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