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Mathematical Study Of Degenerate Boundary Layers A Large Scale Ocean Circulation Problem
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Book Synopsis Mathematical Study of Degenerate Boundary Layers: A Large Scale Ocean Circulation Problem by : Anne-Laure Dalibard
Download or read book Mathematical Study of Degenerate Boundary Layers: A Large Scale Ocean Circulation Problem written by Anne-Laure Dalibard and published by American Mathematical Soc.. This book was released on 2018-05-29 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with a complete asymptotic analysis as $E \to 0$ of the Munk equation $\partial _x\psi -E \Delta ^2 \psi = \tau $ in a domain $\Omega \subset \mathbf R^2$, supplemented with boundary conditions for $\psi $ and $\partial _n \psi $. This equation is a simple model for the circulation of currents in closed basins, the variables $x$ and $y$ being respectively the longitude and the latitude. A crude analysis shows that as $E \to 0$, the weak limit of $\psi $ satisfies the so-called Sverdrup transport equation inside the domain, namely $\partial _x \psi ^0=\tau $, while boundary layers appear in the vicinity of the boundary.
Book Synopsis On the Asymptotic Analysis of Large-scale Ocean Circulation by : W. P. M. de Ruijter
Download or read book On the Asymptotic Analysis of Large-scale Ocean Circulation written by W. P. M. de Ruijter and published by . This book was released on 1980 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Theory of Large-Scale Ocean Circulation by : R. M. Samelson
Download or read book The Theory of Large-Scale Ocean Circulation written by R. M. Samelson and published by Cambridge University Press. This book was released on 2011-06-27 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mounting evidence that human activities are substantially modifying the Earth's climate brings a new imperative to the study of the ocean's large-scale circulation. This textbook provides a concise but comprehensive introduction to the theory of large-scale ocean circulation, as it is currently understood and established. Students and instructors will benefit from the carefully chosen chapter-by-chapter exercises. This advanced textbook is invaluable for graduate students and researchers in the fields of oceanic, atmospheric and climate sciences, and other geophysical scientists, as well as physicists and mathematicians with a quantitative interest in the planetary fluid environment.
Book Synopsis Mathematical Modelling of Ocean Circulation by : Guriĭ Ivanovich Marchuk
Download or read book Mathematical Modelling of Ocean Circulation written by Guriĭ Ivanovich Marchuk and published by Springer. This book was released on 1988-10-05 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems of ocean dynamics present more and more com plex tasks for investigators, based on the continuously sophisti cation of theoretical models, which are applied with the help of universal and efficient algorithms of numerical mathematics. The present level of our knowledge in the field of mathemat ical physics and numerical mathematics allows one to give rather complete theoretical analysis of basic statements of problems as well as numerical algorithms. Our task is to perform such analy sis and also to analyze the results of calculations in order to improve our knowledge of the mechanism of large-scale hy drological processes occurring in the World Ocean. The new level of numerical mathematics has essentially influenced , the formation of new solution methods of ocean dynamics prob lems, among which an important one is the splitting method, which has been already widely practised in various fields of science and engineering. A number of monographs by N. N. Yanenko, A. A. Samarsky, G.!. Marchuk (Rozhdestvensky and Yanenko 1968; Samarsky and Andreyev 1976; Marchuk 1970, 1980b) and others are devoted to the description of this methods. But the methods of the splitting theory require extensive creative work for their application to concrete problems, which are peculiar, as a rule, in problem formulation. The success of the application of these methods is related to the deep understanding of the essence of the described processes. In the last decades fundamental works of Arakawa, K.
Book Synopsis Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem by : Gabriella Pinzari
Download or read book Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem written by Gabriella Pinzari and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author proves the existence of an almost full measure set of -dimensional quasi-periodic motions in the planetary problem with masses, with eccentricities arbitrarily close to the Levi–Civita limiting value and relatively high inclinations. This extends previous results, where smallness of eccentricities and inclinations was assumed. The question had been previously considered by V. I. Arnold in the 1960s, for the particular case of the planar three-body problem, where, due to the limited number of degrees of freedom, it was enough to use the invariance of the system by the SO(3) group. The proof exploits nice parity properties of a new set of coordinates for the planetary problem, which reduces completely the number of degrees of freedom for the system (in particular, its degeneracy due to rotations) and, moreover, is well fitted to its reflection invariance. It allows the explicit construction of an associated close to be integrable system, replacing Birkhoff normal form, a common tool of previous literature.
Book Synopsis Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations by : T. Alazard
Download or read book Strichartz Estimates and the Cauchy Problem for the Gravity Water Waves Equations written by T. Alazard and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir is devoted to the proof of a well-posedness result for the gravity water waves equations, in arbitrary dimension and in fluid domains with general bottoms, when the initial velocity field is not necessarily Lipschitz. Moreover, for two-dimensional waves, the authors consider solutions such that the curvature of the initial free surface does not belong to L2. The proof is entirely based on the Eulerian formulation of the water waves equations, using microlocal analysis to obtain sharp Sobolev and Hölder estimates. The authors first prove tame estimates in Sobolev spaces depending linearly on Hölder norms and then use the dispersive properties of the water-waves system, namely Strichartz estimates, to control these Hölder norms.
Book Synopsis Bellman Function for Extremal Problems in BMO II: Evolution by : Paata Ivanisvili
Download or read book Bellman Function for Extremal Problems in BMO II: Evolution written by Paata Ivanisvili and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a previous study, the authors built the Bellman function for integral functionals on the space. The present paper provides a development of the subject. They abandon the majority of unwanted restrictions on the function that generates the functional. It is the new evolutional approach that allows the authors to treat the problem in its natural setting. What is more, these new considerations lighten dynamical aspects of the Bellman function, in particular, the evolution of its picture.
Book Synopsis Measure and Capacity of Wandering Domains in Gevrey Near-Integrable Exact Symplectic Systems by : Laurent Lazzarini
Download or read book Measure and Capacity of Wandering Domains in Gevrey Near-Integrable Exact Symplectic Systems written by Laurent Lazzarini and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wandering domain for a diffeomorphism of is an open connected set such that for all . The authors endow with its usual exact symplectic structure. An integrable diffeomorphism, i.e., the time-one map of a Hamiltonian which depends only on the action variables, has no nonempty wandering domains. The aim of this paper is to estimate the size (measure and Gromov capacity) of wandering domains in the case of an exact symplectic perturbation of , in the analytic or Gevrey category. Upper estimates are related to Nekhoroshev theory; lower estimates are related to examples of Arnold diffusion. This is a contribution to the “quantitative Hamiltonian perturbation theory” initiated in previous works on the optimality of long term stability estimates and diffusion times; the emphasis here is on discrete systems because this is the natural setting to study wandering domains.
Book Synopsis On Fusion Systems of Component Type by : Michael Aschbacher
Download or read book On Fusion Systems of Component Type written by Michael Aschbacher and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memoir begins a program to classify a large subclass of the class of simple saturated 2-fusion systems of component type. Such a classification would be of great interest in its own right, but in addition it should lead to a significant simplification of the proof of the theorem classifying the finite simple groups. Why should such a simplification be possible? Part of the answer lies in the fact that there are advantages to be gained by working with fusion systems rather than groups. In particular one can hope to avoid a proof of the B-Conjecture, a important but difficult result in finite group theory, established only with great effort.
Book Synopsis Fusion of Defects by : Arthur Bartels
Download or read book Fusion of Defects written by Arthur Bartels and published by American Mathematical Soc.. This book was released on 2019-04-10 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal nets provide a mathematical model for conformal field theory. The authors define a notion of defect between conformal nets, formalizing the idea of an interaction between two conformal field theories. They introduce an operation of fusion of defects, and prove that the fusion of two defects is again a defect, provided the fusion occurs over a conformal net of finite index. There is a notion of sector (or bimodule) between two defects, and operations of horizontal and vertical fusion of such sectors. The authors' most difficult technical result is that the horizontal fusion of the vacuum sectors of two defects is isomorphic to the vacuum sector of the fused defect. Equipped with this isomorphism, they construct the basic interchange isomorphism between the horizontal fusion of two vertical fusions and the vertical fusion of two horizontal fusions of sectors.
Book Synopsis Crossed Products of Operator Algebras by : Elias G. Katsoulis
Download or read book Crossed Products of Operator Algebras written by Elias G. Katsoulis and published by American Mathematical Soc.. This book was released on 2019-04-10 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study crossed products of arbitrary operator algebras by locally compact groups of completely isometric automorphisms. They develop an abstract theory that allows for generalizations of many of the fundamental results from the selfadjoint theory to our context. They complement their generic results with the detailed study of many important special cases. In particular they study crossed products of tensor algebras, triangular AF algebras and various associated C -algebras. They make contributions to the study of C -envelopes, semisimplicity, the semi-Dirichlet property, Takai duality and the Hao-Ng isomorphism problem. They also answer questions from the pertinent literature.
Book Synopsis Time Changes of the Brownian Motion: Poincaré Inequality, Heat Kernel Estimate and Protodistance by : Jun Kigami
Download or read book Time Changes of the Brownian Motion: Poincaré Inequality, Heat Kernel Estimate and Protodistance written by Jun Kigami and published by American Mathematical Soc.. This book was released on 2019-06-10 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including n-dimensional cube [0,1]n are studied. Intuitively time change corresponds to alteration to density of the medium where the heat flows. In case of the Brownian motion on [0,1]n, density of the medium is homogeneous and represented by the Lebesgue measure. The author's study includes densities which are singular to the homogeneous one. He establishes a rich class of measures called measures having weak exponential decay. This class contains measures which are singular to the homogeneous one such as Liouville measures on [0,1]2 and self-similar measures. The author shows the existence of time changed process and associated jointly continuous heat kernel for this class of measures. Furthermore, he obtains diagonal lower and upper estimates of the heat kernel as time tends to 0. In particular, to express the principal part of the lower diagonal heat kernel estimate, he introduces “protodistance” associated with the density as a substitute of ordinary metric. If the density has the volume doubling property with respect to the Euclidean metric, the protodistance is shown to produce metrics under which upper off-diagonal sub-Gaussian heat kernel estimate and lower near diagonal heat kernel estimate will be shown.
Book Synopsis Generalized Mercer Kernels and Reproducing Kernel Banach Spaces by : Yuesheng Xu
Download or read book Generalized Mercer Kernels and Reproducing Kernel Banach Spaces written by Yuesheng Xu and published by American Mathematical Soc.. This book was released on 2019-04-10 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is to endow Banach spaces with reproducing kernels such that machine learning in RKBSs can be well-posed and of easy implementation. First the authors verify many advanced properties of the general RKBSs such as density, continuity, separability, implicit representation, imbedding, compactness, representer theorem for learning methods, oracle inequality, and universal approximation. Then, they develop a new concept of generalized Mercer kernels to construct p-norm RKBSs for 1≤p≤∞ .
Book Synopsis Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc by : Jim Agler
Download or read book Geodesics, Retracts, and the Norm-Preserving Extension Property in the Symmetrized Bidisc written by Jim Agler and published by American Mathematical Soc.. This book was released on 2019-04-10 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: A set V in a domain U in Cn has the norm-preserving extension property if every bounded holomorphic function on V has a holomorphic extension to U with the same supremum norm. We prove that an algebraic subset of the symmetrized bidisc
Book Synopsis On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2 by : Werner Hoffmann
Download or read book On the Geometric Side of the Arthur Trace Formula for the Symplectic Group of Rank 2 written by Werner Hoffmann and published by American Mathematical Soc.. This book was released on 2018-10-03 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors study the non-semisimple terms in the geometric side of the Arthur trace formula for the split symplectic similitude group and the split symplectic group of rank over any algebraic number field. In particular, they express the global coefficients of unipotent orbital integrals in terms of Dedekind zeta functions, Hecke -functions, and the Shintani zeta function for the space of binary quadratic forms.
Book Synopsis Global Regularity for 2D Water Waves with Surface Tension by : Alexandru D. Ionescu
Download or read book Global Regularity for 2D Water Waves with Surface Tension written by Alexandru D. Ionescu and published by American Mathematical Soc.. This book was released on 2019-01-08 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of the authors' analysis is to develop a sufficiently robust method (the “quasilinear I-method”) which allows the authors to deal with strong singularities arising from time resonances in the applications of the normal form method (the so-called “division problem”). As a result, they are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of the authors' analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is of independent interest. As a consequence, the results in this paper are self-contained.
Book Synopsis Interpolation for Normal Bundles of General Curves by : Atanas Atanasov
Download or read book Interpolation for Normal Bundles of General Curves written by Atanas Atanasov and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given n general points p1,p2,…,pn∈Pr, it is natural to ask when there exists a curve C⊂Pr, of degree d and genus g, passing through p1,p2,…,pn. In this paper, the authors give a complete answer to this question for curves C with nonspecial hyperplane section. This result is a consequence of our main theorem, which states that the normal bundle NC of a general nonspecial curve of degree d and genus g in Pr (with d≥g+r) has the property of interpolation (i.e. that for a general effective divisor D of any degree on C, either H0(NC(−D))=0 or H1(NC(−D))=0), with exactly three exceptions.
