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Special topic volume with invited peer reviewed papers only
J -holomorphic curves revolutionized the study of symplectic geometry when Gromov first introduced them in 1985. Through quantum cohomology, these curves are now linked to many of the most exciting new ideas in mathematical physics. This book presents the first coherent and full account of the theory of J -holomorphic curves, the details of which are presently scattered in various research papers. The first half of the book is an expository account of the field, explaining the main technical aspects. McDuff and Salamon give complete proofs of Gromov's compactness theorem for spheres and of the existence of the Gromov-Witten invariants. The second half of the book focuses on the definition of quantum cohomology. The authors establish that the quantum multiplication exists and is associative on appropriate manifolds. They then describe the Givental-Kim calculation of the quantum cohomology of flag manifolds, leading to quantum Chern classes and Witten's calculation for Grassmanians, which relates to the Verlinde algebra. The Dubrovin connection, Gromov-Witten potential on quantum cohomology, and curve counting formulas are also discussed.
International Russian Conference on Materials Science and Metallurgical Technology (RusMetalCon 2019) Selected, peer reviewed papers from the International Russian Conference on Materials Science and Metallurgical Technology (RusMetalCon-2019), October 1-4, 2019, Chelyabinsk, Russian Federation
The knowledge on the ecology of ungulates (orders Perissodactyla and Artiodactyla) inhabiting eastern Europe and northern and central Asia is of special importance for those interested in zoology, ecology, nature conservation, hunting and management. There are 26 species of ungulates 2 oE-169°W within the 22. 4 million km area, between 35-82°N and 20 and they occupy several vegetation zones from arctic deserts to the subtropics. In our opinion, the advancement of science can be retarded and general conclusions will be difficult to make, if the knowledge of the organisms inhabiting one sixth of the world'sland surface, covered by this vast region, is not included. The language barrier, as w...
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This book presents the original proof of Gromov's compactness theorem for pseudo-holomorphic curves in detail. Local properties of pseudo-holomorphic curves are investigated and proved from a geometric viewpoint. Properties of particular interest are isoperimetric inequalities, a monotonicity formula, gradient bounds and the removal of singularities.
The first NATO Science Forum was held in Biarritz in September 1990. This Taormina Conference is the second in a series that we wish to be a long one and I believe that it has equalled the success of its predecessor. In setting up these meetings the NATO Science Committee wanted to gather leading experts to review fields of strong present interest. It was intended that presentations and discussions should pay special attention to potential developments. This "forward look" is indeed precious to us in mapping out the evolution of our Science Programme but more importantly, it is an essential part of the progress of Science. I believe that NATO, being able to bring together eminent scientists ...
Selected, peer reviewed papers from the International Conference on Industrial Engineering, May 19-20, 2016, Chelyabinsk, Russian Federation
This interdisciplinary book gives a comprehensive survey of the state-of-the-art: from applications and trends in fluorescence techniques in science to medicine and engineering. Written for practitioners and researchers in industry and academia, it covers fields like environmental and materials science, biology, medicine, physics and chemistry. Moreover, it reports on such new and breathtaking methods as ultra-fast time-resolved or single molecule spectroscopy, gives examples of applications in the fields of electroluminescent polymers, visualization of membrane potentials in neurons and fluorescence imaging of the brain.