17 trang
45 lượt xem
5 lượt tải
Science reports
Đề tài " Convergence versus integrability in Birkhoff normal form " We show that any analytically integrable Hamiltonian system near an equilibrium point admits a convergent Birkhoff normalization. The proof is based on a new, geometric approach to the topic. 1. Introduction Among the fundamental problems concerning analytic (real or complex) Hamiltonian systems near an equilibrium point, one may mention the following two: 1) Convergent Birkhoff. In this paper, by “convergent Birkhoff” we mean a normalization, i.e., a local analytic symplectic system of coordinates in which the Hamiltonian function will Poisson commute with the semisimple part of its quadratic part. ...
Đề tài "The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schr¨odinger equation "
The blow-up dynamic and upper bound on the blow-up rate for critical nonlinear Schr¨dinger equation o
By Frank Merle and Pierre Raphael
Abstract We consider the critical nonlinear Schr¨dinger equation iut = −∆u−|u| N u o with initial condition u(0, x) = u0 in dimension N = 1. For u0 ∈ H 1 , local existence in the time of solutions on an interval [0, T ) is known, and there exist finite time blow-up solutions, that is, u0 such that limt↑
67 trang
41 lượt xem
7 lượt tải
Đề tài " A cornucopia of isospectral pairs of metrics on spheres with different local geometries " This article concludes the comprehensive study started in [Sz5], where the first nontrivial isospectral pairs of metrics are constructed on balls and spheres. These investigations incorporate four different cases since these balls and spheres are considered both on 2-step nilpotent Lie groups and on their solvable extensions. In [Sz5] the considerations are completely concluded in the ball-case and in the nilpotent-case. The other cases were mostly outlined. In this paper the isospectrality theorems are completely established on spheres. ...
54 trang
63 lượt xem
6 lượt tải
Đề tài " On the distribution of matrix elements for the quantum cat map " For many classically chaotic systems it is believed that the quantum wave functions become uniformly distributed, that is the matrix elements of smooth observables tend to the phase space average of the observable. In this paper we study the fluctuations of the matrix elements for the desymmetrized quantum cat map. We present a conjecture for the distribution of the normalized matrix elements, namely that their distribution is that of a certain weighted sum of traces of independent matrices in SU(2). This is in contrast to generic chaotic systems where the distribution is expected to be Gaussian. ...
20 trang
66 lượt xem
6 lượt tải
Đề tài " The uniqueness of the helicoid "
In this paper we will discuss the geometry of finite topology properly embedded minimal surfaces M in R3 . M of finite topology means M is homeomorphic to a compact surface M (of genus k and empty boundary) minus a finite number of points p1 , ..., pj ∈ M , called the punctures. A closed neighborhood E of a puncture in M is called an end of M . We will choose the ends sufficiently small so they are topologically S 1 × [0, 1) and hence, annular. We remark that M is orientable since M is properly...
33 trang
67 lượt xem
6 lượt tải
Đề tài " Roth’s theorem in the primes " We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a restriction theorem for the primes. 1. Introduction Arguably the second most famous result of Klaus Roth is his 1953 upper bound [21] on r3 (N ), defined 17 years...
29 trang
61 lượt xem
7 lượt tải
Đề tài " Geometrization of 3dimensional orbifolds " This paper is devoted to the proof of the orbifold theorem: If O is a compact connected orientable irreducible and topologically atoroidal 3-orbifold with nonempty ramification locus, then O is geometric (i.e. has a metric of constant curvature or is Seifert fibred). As a corollary, any smooth orientationpreserving nonfree finite group action on S 3 is conjugate to an orthogonal action. Contents 1. Introduction 2. 3-dimensional orbifolds 2.1. Basic definitions 2.2. Spherical and toric decompositions 2.3. Finite group actions on spheres with fixed points 2.4. Proof of the orbifold theorem from the main theorem 3. ...
97 trang
54 lượt xem
7 lượt tải
Đề tài " On fusion categories " Using a variety of methods developed in the literature (in particular, the theory of weak Hopf algebras), we prove a number of general results about fusion categories in characteristic zero. We show that the global dimension of a fusion category is always positive, and that the S-matrix of any (not necessarily hermitian) modular category is unitary. We also show that the category of module functors between two module categories over a fusion category is semisimple, and that fusion categories and tensor functors between them are undeformable (generalized Ocneanu rigidity). In particular the number of such categories (functors) realizing a...
63 trang
53 lượt xem
6 lượt tải
Đề tài " A resolution of the K(2)-local sphere at the prime 3 " We develop a framework for displaying the stable homotopy theory of the sphere, at least after localization at the second Morava K-theory K(2). At the prime 3, we write the spectrum LK(2) S 0 as the inverse limit of a tower of hF fibrations with four layers. The successive fibers are of the form E2 where F is a finite subgroup of the Morava stabilizer group and E2 is the second Morava or Lubin-Tate homology theory. We give explicit calculation of the homotopy groups of these fibers.
47 trang
56 lượt xem
6 lượt tải
Đề tài " The classification of torsion endo-trivial modules " This paper settles a problem raised at the end of the seventies by J.L. Alperin [Al1], E.C. Dade [Da] and J.F. Carlson [Ca1], namely the classification of torsion endo-trivial modules for a finite p-group over a field of characteristic p. Our results also imply, at least when p is odd, the complete classification of torsion endo-permutation modules. We refer to [CaTh] and [BoTh] for an overview of the problem and its importance in the representation theory of finite groups.
62 trang
49 lượt xem
6 lượt tải
Đề tài " Discreteness of spectrum and positivity criteria for Schr¨odinger operators " We provide a class of necessary and sufficient conditions for the discreteness of spectrum of Schr¨dinger operators with scalar potentials which o are semibounded below. The classical discreteness of spectrum criterion by A. M. Molchanov (1953) uses a notion of negligible set in a cube as a set whose Wiener capacity is less than a small constant times the capacity of the cube. We prove that this constant can be taken arbitrarily between 0 and 1. This solves a problem formulated by I. M. Gelfand in 1953. Moreover, we extend the notion of negligibility by allowing the constant to...
25 trang
47 lượt xem
7 lượt tải
Đề tài " The density of discriminants of quartic rings and fields "Steiner symmetrization, one of the simplest and most powerful symmetrization
processes ever introduced in analysis, is a classical and very well-known
device, which has seen a number of remarkable applications to problems of
geometric and functional nature. Its importance stems from the fact that,
besides preserving Lebesgue measure, it acts monotonically on several geometric
and analytic quantities associated with subsets of Rn. Among these,
perimeter certainly holds a prominent position. Actually, the proof of the
isoperimetric property of the ball was the original motivation for Steiner to
introduce his symmetrization in...
34 trang
44 lượt xem
7 lượt tải
Đề tài " Formation of singularities for a transport equation with nonlocal velocity " We study a 1D transport equation with nonlocal velocity and show the formation of singularities in finite time for a generic family of initial data. By adding a diffusion term the finite time singularity is prevented and the solutions exist globally in time. 1. Introduction In this paper we study the nature of the solutions to the following class of equations (1.1)
14 trang
59 lượt xem
6 lượt tải
Đề tài " Finite and infinite arithmetic progressions in sumsets " We prove that if A is a subset of at least cn1/2 elements of {1, . . . , n}, where c is a sufficiently large constant, then the collection of subset sums of A contains an arithmetic progression of length n. As an application, we confirm a long standing conjecture of Erd˝s and Folkman on complete sequences. o
36 trang
53 lượt xem
6 lượt tải
Đề tài " The number of extensions of a number field with fixed degree and bounded discriminant " We give an upper bound on the number of extensions of a fixed number field of prescribed degree and discriminant ≤ X; these bounds improve on work of Schmidt. We also prove various related results, such as lower bounds for the number of extensions and upper bounds for Galois extensions.
20 trang
62 lượt xem
7 lượt tải
Đề tài " Classical and modular approaches to exponential Diophantine equations I. Fibonacci and Lucas perfect powers "Annals of Mathematics
This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat’s Last Theorem. In this paper we give new improved bounds for linear forms in three logarithms. We also apply a combination of classical techniques with the modular approach to show that the only perfect powers in the Fibonacci sequence are 0, 1, 8 and 144 and the only perfect powers in the Lucas sequence are 1...
51 trang
50 lượt xem
8 lượt tải
Đề tài " An abelianization of SU(2) WZW model " The purpose of this paper is to carry out the abelianization program proposed by Atiyah [1] and Hitchin [9] for the geometric quantization of SU(2) Wess-Zumino-Witten model. Let C be a Riemann surface of genus g. Let Mg be the moduli space of semi-stable rank 2 holomorphic vector bundles on C with trivial determinant. For a positive integer k, let Γ(Mg , Lk ) be the space of holomorphic sections of the k-th tensor product of the determinant line bundle L on Mg . An element of Γ(Mg , Lk ) is called a rank 2 theta function...
50 trang
68 lượt xem
9 lượt tải
Đề tài " A geometric LittlewoodRichardson rule " We describe a geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties into the union of Schubert varieties. There are no restrictions on the base field, and all multiplicities arising are 1; this is important for applications. This rule should be seen as a generalization of Pieri’s rule to arbitrary Schubert classes, by way of explicit homotopies. It has straightforward bijections to other Littlewood-Richardson rules, such as tableaux, and Knutson and Tao’s puzzles. This gives the first geometric proof and interpretation of the Littlewood-Richardson rule. Geometric consequences are described here and in [V2], [KV1], [KV2],...
53 trang
47 lượt xem
7 lượt tải
Đề tài " Reducibility or nonuniform hyperbolicity for quasiperiodic Schr¨odinger cocycles " We show that for almost every frequency α ∈ R\Q, for every C ω potential v : R/Z → R, and for almost every energy E the corresponding quasiperiodic Schr¨dinger cocycle is either reducible or nonuniformly hyperbolic. This result o gives very good control on the absolutely continuous part of the spectrum of the corresponding quasiperiodic Schr¨dinger operator, and allows us to complete o the proof of the Aubry-Andr´ conjecture on the measure of the spectrum of e the Almost Mathieu Operator. ...
31 trang
38 lượt xem
7 lượt tải
Đề tài "Bounds for polynomials with a unit discrete norm " Let E be the set of N equidistant points in (−1, 1) and Pn (E) be the set of all polynomials P of degree ≤ n with max{|P (ζ)|, ζ ∈ E} ≤ 1. We prove that π Kn,N (x) = max |P (x)| ≤ C log , √ N P ∈Pn (E) arctan n r2 − x2 |x| ≤ r := 1 − n2 /N 2
where n
35 trang
49 lượt xem
7 lượt tải
Chịu trách nhiệm nội dung: Nguyễn Công Hà. ©2025 Công ty TNHH Tài Liệu trực tuyến Vi Na.
Địa chỉ: 54A Nơ Trang Long, P. Bình Thạnh, TP.HCM - Điện thoại: 0283 5102 888 - Email: info@tailieu.vn
Giấy phép Mạng Xã Hội số: 670/GP-BTTTT cấp ngày 30/11/2015