Relative Equilibria In The 3 Dimensional Curved N Body Problem
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Relative Equilibria In The 3 Dimensional Curved N Body Problem
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Author : Florin Diacu
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-03-05
Relative Equilibria In The 3 Dimensional Curved N Body Problem written by Florin Diacu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-05 with Mathematics categories.
Considers the 3 -dimensional gravitational n -body problem, n32 , in spaces of constant Gaussian curvature k10 , i.e. on spheres S 3 ?1 , for ?>0 , and on hyperbolic manifolds H 3 ?1, for ?
Relative Equilibria Of The Curved N Body Problem
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Author : Florin Diacu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-17
Relative Equilibria Of The Curved N Body Problem written by Florin Diacu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-17 with Mathematics categories.
The guiding light of this monograph is a question easy to understand but difficult to answer: {What is the shape of the universe? In other words, how do we measure the shortest distance between two points of the physical space? Should we follow a straight line, as on a flat table, fly along a circle, as between Paris and New York, or take some other path, and if so, what would that path look like? If you accept that the model proposed here, which assumes a gravitational law extended to a universe of constant curvature, is a good approximation of the physical reality (and I will later outline a few arguments in this direction), then we can answer the above question for distances comparable to those of our solar system. More precisely, this monograph provides a mathematical proof that, for distances of the order of 10 AU, space is Euclidean. This result is, of course, not surprising for such small cosmic scales. Physicists take the flatness of space for granted in regions of that size. But it is good to finally have a mathematical confirmation in this sense. Our main goals, however, are mathematical. We will shed some light on the dynamics of N point masses that move in spaces of non-zero constant curvature according to an attraction law that naturally extends classical Newtonian gravitation beyond the flat (Euclidean) space. This extension is given by the cotangent potential, proposed by the German mathematician Ernest Schering in 1870. He was the first to obtain this analytic expression of a law suggested decades earlier for a 2-body problem in hyperbolic space by Janos Bolyai and, independently, by Nikolai Lobachevsky. As Newton's idea of gravitation was to introduce a force inversely proportional to the area of a sphere the same radius as the Euclidean distance between the bodies, Bolyai and Lobachevsky thought of a similar definition using the hyperbolic distance in hyperbolic space. The recent generalization we gave to the cotangent potential to any number N ofbodies, led to the discovery of some interesting properties. This new research reveals certain connections among at least five branches of mathematics: classical dynamics, non-Euclidean geometry, geometric topology, Lie groups, and the theory of polytopes.
Relative Equilibria In The 3 Dimensional Curved N Body Problem
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Author : Florin Diacu
language : en
Publisher:
Release Date : 2014-10-03
Relative Equilibria In The 3 Dimensional Curved N Body Problem written by Florin Diacu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-03 with Celestial mechanics categories.
Julia Sets And Complex Singularities Of Free Energies
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Author : Jianyong Qiao
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-06
Julia Sets And Complex Singularities Of Free Energies written by Jianyong Qiao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-06 with Mathematics categories.
The author studies a family of renormalization transformations of generalized diamond hierarchical Potts models through complex dynamical systems. He proves that the Julia set (unstable set) of a renormalization transformation, when it is treated as a complex dynamical system, is the set of complex singularities of the free energy in statistical mechanics. He gives a sufficient and necessary condition for the Julia sets to be disconnected. Furthermore, he proves that all Fatou components (components of the stable sets) of this family of renormalization transformations are Jordan domains with at most one exception which is completely invariant. In view of the problem in physics about the distribution of these complex singularities, the author proves here a new type of distribution: the set of these complex singularities in the real temperature domain could contain an interval. Finally, the author studies the boundary behavior of the first derivative and second derivative of the free energy on the Fatou component containing the infinity. He also gives an explicit value of the second order critical exponent of the free energy for almost every boundary point.
Critical Population And Error Threshold On The Sharp Peak Landscape For A Moran Model
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Author : Raphaël Cerf
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20
Critical Population And Error Threshold On The Sharp Peak Landscape For A Moran Model written by Raphaël Cerf and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.
The goal of this work is to propose a finite population counterpart to Eigen's model, which incorporates stochastic effects. The author considers a Moran model describing the evolution of a population of size of chromosomes of length over an alphabet of cardinality . The mutation probability per locus is . He deals only with the sharp peak landscape: the replication rate is for the master sequence and for the other sequences. He studies the equilibrium distribution of the process in the regime where
Sheaves On Graphs Their Homological Invariants And A Proof Of The Hanna Neumann Conjecture
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Author : Joel Friedman
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-12-20
Sheaves On Graphs Their Homological Invariants And A Proof Of The Hanna Neumann Conjecture written by Joel Friedman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-20 with Mathematics categories.
In this paper the author establishes some foundations regarding sheaves of vector spaces on graphs and their invariants, such as homology groups and their limits. He then uses these ideas to prove the Hanna Neumann Conjecture of the 1950s; in fact, he proves a strengthened form of the conjecture.
Effective Hamiltonians For Constrained Quantum Systems
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Author : Jakob Wachsmuth
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-06-05
Effective Hamiltonians For Constrained Quantum Systems written by Jakob Wachsmuth and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-05 with Mathematics categories.
The authors consider the time-dependent Schrödinger equation on a Riemannian manifold with a potential that localizes a certain subspace of states close to a fixed submanifold . When the authors scale the potential in the directions normal to by a parameter , the solutions concentrate in an -neighborhood of . This situation occurs for example in quantum wave guides and for the motion of nuclei in electronic potential surfaces in quantum molecular dynamics. The authors derive an effective Schrödinger equation on the submanifold and show that its solutions, suitably lifted to , approximate the solutions of the original equation on up to errors of order at time . Furthermore, the authors prove that the eigenvalues of the corresponding effective Hamiltonian below a certain energy coincide up to errors of order with those of the full Hamiltonian under reasonable conditions.
Combinatorial Floer Homology
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Author : Vin de Silva
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-06-05
Combinatorial Floer Homology written by Vin de Silva and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-05 with Mathematics categories.
The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented -manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology. Their proof uses a formula for the Viterbo-Maslov index for a smooth lune in a -manifold.
Polynomial Approximation On Polytopes
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Author : Vilmos Totik
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-09-29
Polynomial Approximation On Polytopes written by Vilmos Totik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-29 with Mathematics categories.
Polynomial approximation on convex polytopes in is considered in uniform and -norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the -case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate -functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.
Transfer Of Siegel Cusp Forms Of Degree 2
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Author : Ameya Pitale
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-09-29
Transfer Of Siegel Cusp Forms Of Degree 2 written by Ameya Pitale and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-29 with Mathematics categories.
Let be the automorphic representation of generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and be an arbitrary cuspidal, automorphic representation of . Using Furusawa's integral representation for combined with a pullback formula involving the unitary group , the authors prove that the -functions are "nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations have a functorial lifting to a cuspidal representation of . Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of to a cuspidal representation of . As an application, the authors obtain analytic properties of various -functions related to full level Siegel cusp forms. They also obtain special value results for and