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Author : Gérard Iooss
Publisher : American Mathematical Society(RI)
Page : 144 pages
File Size : 40,7 Mb
Release : 2014-09-11
Category : TECHNOLOGY & ENGINEERING
ISBN : 1470405547
Author : Gérard Iooss,Pavel I. Plotnikov
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 51,9 Mb
Release : 2009-01-01
Category : Science
ISBN : 9780821866818
Author : Grard Iooss,Pavel I. Plotnikov
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 54,5 Mb
Release : 2009-06-05
Category : Science
ISBN : 9780821843826
The authors consider doubly-periodic travelling waves at the surface of an infinitely deep perfect fluid, only subjected to gravity $g$ and resulting from the nonlinear interaction of two simply periodic travelling waves making an angle $2\theta$ between them. Denoting by $\mu =gL/c^{2}$ the dimensionless bifurcation parameter ( $L$ is the wave length along the direction of the travelling wave and $c$ is the velocity of the wave), bifurcation occurs for $\mu = \cos \theta$. For non-resonant cases, we first give a large family of formal three-dimensional gravity travelling waves, in the form of an expansion in powers of the amplitudes of two basic travelling waves. ``Diamond waves'' are a particular case of such waves, when they are symmetric with respect to the direction of propagation. The main object of the paper is the proof of existence of such symmetric waves having the above mentioned asymptotic expansion. Due to the occurence of small divisors, the main difficulty is the inversion of the linearized operator at a non trivial point, for applying the Nash Moser theorem. This operator is the sum of a second order differentiation along a certain direction, and an integro-differential operator of first order, both depending periodically of coordinates. It is shown that for almost all angles $\theta$, the 3-dimensional travelling waves bifurcate for a set of ``good'' values of the bifurcation parameter having asymptotically a full measure near the bifurcation curve in the parameter plane $(\theta,\mu ).$
Author : Massimiliano Berti,Riccardo Montalto
Publisher : American Mathematical Soc.
Page : 171 pages
File Size : 49,6 Mb
Release : 2020-04-03
Category : Education
ISBN : 9781470440695
The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
Author : Massimiliano Berti,Jean-Marc Delort
Publisher : Springer
Page : 269 pages
File Size : 48,7 Mb
Release : 2018-11-02
Category : Mathematics
ISBN : 9783319994864
The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure. In contrast to the many results known for these equations on the real line, with decaying Cauchy data, one cannot make use of dispersive properties of the linear flow. Instead, a normal forms-based procedure is used, eliminating those contributions to the Sobolev energy that are of lower degree of homogeneity in the solution. Since the water waves equations form a quasi-linear system, the usual normal forms approaches would face the well-known problem of losses of derivatives in the unbounded transformations. To overcome this, after a paralinearization of the capillary-gravity water waves equations, we perform several paradifferential reductions to obtain a diagonal system with constant coefficient symbols, up to smoothing remainders. Then we start with a normal form procedure where the small divisors are compensated by the previous paradifferential regularization. The reversible structure of the water waves equations, and the fact that we seek solutions even in space, guarantees a key cancellation which prevents the growth of the Sobolev norms of the solutions.
Author : Albert Ai
Publisher : Springer Nature
Page : 373 pages
File Size : 44,8 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9783031604522
Author : Makoto Sakai
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 52,8 Mb
Release : 2010
Category : Fluid mechanics
ISBN : 9780821848104
For a given plane domain, the author adds a constant multiple of the Dirac measure at a point in the domain and makes a new domain called a quadrature domain. The quadrature domain is characterized as a domain such that the integral of a harmonic and integrable function over the domain equals the integral of the function over the given domain plus the integral of the function with respect to the added measure. The family of quadrature domains can be modeled as the Hele-Shaw flow with a free-boundary problem. The given domain is regarded as the initial domain and the support point of the Dirac measure as the injection point of the flow.
Author : Dillon Mayhew,Gordon Royle,Geoff Whittle
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 45,5 Mb
Release : 2010
Category : Combinatorial designs and configurations
ISBN : 9780821848265
The authors give a characterization of the internally $4$-connected binary matroids that have no minor isomorphic to $M(K_{3,3})$. Any such matroid is either cographic, or is isomorphic to a particular single-element extension of the bond matroid of a cubic or quartic Mobius ladder, or is isomorphic to one of eighteen sporadic matroids.
Author : Gelu Popescu
Publisher : American Mathematical Soc.
Page : 105 pages
File Size : 52,6 Mb
Release : 2009-06-05
Category : Mathematics
ISBN : 9780821843963
This paper concerns unitary invariants for $n$-tuples $T:=(T_1,\ldots, T_n)$ of (not necessarily commuting) bounded linear operators on Hilbert spaces. The author introduces a notion of joint numerical radius and works out its basic properties. Multivariable versions of Berger's dilation theorem, Berger-Kato-Stampfli mapping theorem, and Schwarz's lemma from complex analysis are obtained. The author studies the joint (spatial) numerical range of $T$ in connection with several unitary invariants for $n$-tuples of operators such as: right joint spectrum, joint numerical radius, euclidean operator radius, and joint spectral radius. He also proves an analogue of Toeplitz-Hausdorff theorem on the convexity of the spatial numerical range of an operator on a Hilbert space, for the joint numerical range of operators in the noncommutative analytic Toeplitz algebra $F_n^\infty$.
Author : Dirk Kussin
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 48,5 Mb
Release : 2009-08-07
Category : Mathematics
ISBN : 9780821844007
In these notes the author investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. As a main result he shows that each such curve $\mathbb{X}$ admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain $R$ in the sense of Chatters and Jordan. Moreover, there is a natural bijection between the points of $\mathbb{X}$ and the homogeneous prime ideals of height one in $R$, and these prime ideals are principal in a strong sense.
Author : Mark D. Hamilton
Publisher : American Mathematical Soc.
Page : 73 pages
File Size : 40,5 Mb
Release : 2010
Category : Geometric quantization
ISBN : 9780821847145
"Volume 207, number 971 (first of 5 numbers)."
Author : Irina D. Suprunenko
Publisher : American Mathematical Soc.
Page : 168 pages
File Size : 52,7 Mb
Release : 2009-06-05
Category : Mathematics
ISBN : 9780821843697
The minimal polynomials of the images of unipotent elements in irreducible rational representations of the classical algebraic groups over fields of odd characteristic are found. These polynomials have the form $(t-1)^d$ and hence are completely determined by their degrees. In positive characteristic the degree of such polynomial cannot exceed the order of a relevant element. It occurs that for each unipotent element the degree of its minimal polynomial in an irreducible representation is equal to the order of this element provided the highest weight of the representation is large enough with respect to the ground field characteristic. On the other hand, classes of unipotent elements for which in every nontrivial representation the degree of the minimal polynomial is equal to the order of the element are indicated. In the general case the problem of computing the minimal polynomial of the image of a given element of order $p^s$ in a fixed irreducible representation of a classical group over a field of characteristic $p>2$ can be reduced to a similar problem for certain $s$ unipotent elements and a certain irreducible representation of some semisimple group over the field of complex numbers. For the latter problem an explicit algorithm is given. Results of explicit computations for groups of small ranks are contained in Tables I-XII. The article may be regarded as a contribution to the programme of extending the fundamental results of Hall and Higman (1956) on the minimal polynomials from $p$-solvable linear groups to semisimple groups.
Author : Istvan Berkes,Michel Weber
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 49,7 Mb
Release : 2009
Category : Convergence
ISBN : 9780821843246
Presents a general study of the convergence problem and intends to prove several fresh results and improve a number of old results in the field. This title studies the case when the nk are random and investigates the discrepancy the sequence (nkx) mod 1.
Author : Drew Armstrong
Publisher : American Mathematical Soc.
Page : 176 pages
File Size : 51,6 Mb
Release : 2009-10-08
Category : Mathematics
ISBN : 9780821844908
This memoir is a refinement of the author's PhD thesis -- written at Cornell University (2006). It is primarily a desription of new research but also includes a substantial amount of background material. At the heart of the memoir the author introduces and studies a poset $NC^{(k)}(W)$ for each finite Coxeter group $W$ and each positive integer $k$. When $k=1$, his definition coincides with the generalized noncrossing partitions introduced by Brady and Watt in $K(\pi, 1)$'s for Artin groups of finite type and Bessis in The dual braid monoid. When $W$ is the symmetric group, the author obtains the poset of classical $k$-divisible noncrossing partitions, first studied by Edelman in Chain enumeration and non-crossing partitions.
Author : Pascal Lefèvre
Publisher : American Mathematical Soc.
Page : 87 pages
File Size : 54,8 Mb
Release : 2010
Category : Composition operators
ISBN : 9780821846377
"The authors investigate composition operators on Hardy-Orlicz spaces when the Orlicz function Psi grows rapidly: compactness, weak compactness, to be p-summing, order bounded, ... , and show how these notions behave according to the growth of Psi. They introduce an adapted version of Carleson measure. They construct various examples showing that their results are essentially sharp. In the last part, they study the case of Bergman-Orlicz spaces."--Publisher's description.