By Pierre Adler, Howard Brenner
The target of "Porous Media: Geometry and Transports" is to supply the foundation of a rational and sleek method of porous media. This e-book emphasizes a number of geometrical buildings (spatially periodic, fractal, and random to reconstructed) and the 3 significant single-phase transports (diffusion, convection, and Taylor dispersion). "Porous Media" serves numerous reasons. for college kids it introduces simple info on constitution and transports. Engineers will locate this ebook valuable as a with no trouble available assemblage of al the most important experimental effects bearing on single-phase transports in porous media. For scientists it offers the newest advancements within the box, a few of that have by no means earlier than been released
By Rolf Berndt
Symplectic geometry is a significant subject of present examine in arithmetic. certainly, symplectic equipment are key constituents within the learn of dynamical structures, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie teams. This booklet is a real advent to symplectic geometry, assuming just a normal heritage in research and familiarity with linear algebra. It begins with the fundamentals of the geometry of symplectic vector areas. Then, symplectic manifolds are outlined and explored. as well as the basic vintage effects, akin to Darboux's theorem, more moderen effects and ideas also are incorporated right here, equivalent to symplectic ability and pseudoholomorphic curves. those rules have revolutionized the topic. the most examples of symplectic manifolds are given, together with the cotangent package, Kähler manifolds, and coadjoint orbits. additional important principles are conscientiously tested, corresponding to Hamiltonian vector fields, the Poisson bracket, and connections with touch manifolds. Berndt describes many of the shut connections among symplectic geometry and mathematical physics within the final chapters of the e-book. particularly, the instant map is outlined and explored, either mathematically and in its relation to physics. He additionally introduces symplectic aid, that's a big device for lowering the variety of variables in a actual procedure and for developing new symplectic manifolds from outdated. the ultimate bankruptcy is on quantization, which makes use of symplectic the right way to take classical mechanics to quantum mechanics. This part encompasses a dialogue of the Heisenberg staff and the Weil (or metaplectic) illustration of the symplectic team. a number of appendices supply history fabric on vector bundles, on cohomology, and on Lie teams and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a transparent and concise creation to the foremost tools and purposes of the topic, and calls for just a minimal of must haves. This publication will be an outstanding textual content for a graduate path or as a resource for someone who needs to profit approximately symplectic geometry.
By Radu, Dragos Hrimiuc, Kideo Shimada and Sorin V. Sabau Miron
The identify of this ebook is not surprising for individuals operating within the box of Analytical Mechanics. notwithstanding, the geometric recommendations of Lagrange area and Hamilton house are thoroughly new. The geometry of Lagrange areas, brought and studied in ,, used to be ext- sively tested within the final 20 years by way of geometers and physicists from Canada, Germany, Hungary, Italy, Japan, Romania, Russia and U.S.A. Many foreign meetings have been dedicated to debate this topic, court cases and monographs have been released , , , ,... a wide quarter of applicability of this geometry is advised through the connections to Biology, Mechanics, and Physics and likewise via its common surroundings as a generalization of Finsler and Riemannian geometries. the idea that of Hamilton area, brought in ,  used to be intensively studied in , , ,... and it's been winning, as a geometrical thought of the Ham- tonian functionality the elemental entity in Mechanics and Physics. The classical Legendre’s duality makes attainable a ordinary connection among Lagrange and - miltonspaces. It finds new techniques and geometrical gadgets of Hamilton areas which are twin to these that are related in Lagrange areas. Following this duality Cartan areas brought and studied in , ,..., are, approximately talking, the Legendre duals of sure Finsler areas , , . The above arguments make this monograph a continuation of , , emphasizing the Hamilton geometry.
By American Mathematical Society, János Kollár, Robert Lazarsfeld
By Hugh (of Saint-Victor), Frederick A. Homann
By Rainer Oloff
Die Relativit?tstheorie ist in ihren Kernaussagen nicht mehr umstritten, gilt aber noch immer als kompliziert und nur schwer verstehbar. Das liegt unter anderem an dem aufwendigen mathematischen Apparat, der schon zur Formulierung ihrer Ergebnisse und erst recht zum Nachvollziehen der Argumentation notwendig ist. In diesem Lehrbuch werden die mathematischen Grundlagen der Relativit?tstheorie systematisch entwickelt, das ist die Differentialgeometrie auf Mannigfaltigkeiten einschlie?lich Differentiation und Integration. Die Spezielle Relativit?tstheorie wird als Tensorrechnung auf den Tangentialr?umen dargestellt. Die zentrale Aussage der Allgemeinen Relativit?tstheorie ist die Einsteinsche Feldgleichung, die die Kr?mmung zur Materie in Beziehung setzt. Ausf?hrlich werden die relativistischen Effekte im Sonnensystem einschlie?lich der Schwarzen L?cher behandelt. Der textual content richtet sich an Studierende der Physik und der Mathematik und setzt nur Grundkenntnisse aus der klassischen Differential- und Integralrechnung und der Linearen Algebra voraus.
By George Gasper
A fantastic reference at the topic. fabric on generalized hypergeometric features (starting with Gauss' hypergeometric functionality) is gifted via the q analogy's. the fabric is complicated and is easily written with a good and readable typeface. The creation to q sequence will fulfill the newbie. The record of approximately 500 references protecting the total topic is definitely worth the rate alone.
Lorenz H. Menke, Jr.
By Shigeyuki Kondō (auth.), Radu Laza, Matthias Schütt, Noriko Yui (eds.)
In fresh years, learn in K3 surfaces and Calabi–Yau forms has noticeable stunning growth from either mathematics and geometric issues of view, which in flip maintains to have an incredible impact and effect in theoretical physics—in specific, in string idea. The workshop on mathematics and Geometry of K3 surfaces and Calabi–Yau threefolds, held on the Fields Institute (August 16-25, 2011), aimed to offer a state of the art survey of those new advancements. This complaints quantity features a consultant sampling of the large diversity of subject matters coated via the workshop. whereas the topics variety from mathematics geometry via algebraic geometry and differential geometry to mathematical physics, the papers are certainly similar via the typical topic of Calabi–Yau forms. With the wide range of branches of arithmetic and mathematical physics touched upon, this region unearths many deep connections among matters formerly thought of unrelated.
Unlike such a lot different meetings, the 2011 Calabi–Yau workshop all started with three days of introductory lectures. a variety of four of those lectures is integrated during this quantity. those lectures can be utilized as a kick off point for the graduate scholars and different junior researchers, or as a advisor to the topic.