共查询到20条相似文献,搜索用时 12 毫秒
1.
Pierre Germain 《Comptes Rendus Mathematique》2005,340(7):547-550
We study in this Note the solutions of the 2D Navier–Stokes equations with initial data in ?BMO. For in the closure of the Schwartz class, we obtain the existence and uniqueness of a global solution, and besides an estimate on its norm in ?BMO. To cite this article: P. Germain, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
2.
Philippe Rigollet 《Comptes Rendus Mathematique》2005,340(1):59-62
We study the problem of the nonparametric estimation of a probability density in . Expressing the mean integrated squared error in the Fourier domain, we show that it is close to the mean squared error in the Gaussian sequence model. Then, applying a modified version of Stein's blockwise method, we obtain a linear monotone oracle inequality and a kernel oracle inequality. As a consequence, the proposed estimator is sharp minimax adaptive (i.e. up to a constant) on a scale of Sobolev classes of densities. To cite this article: Ph. Rigollet, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
3.
Stéphane Fischler 《Comptes Rendus Mathematique》2004,339(10):679-682
Let be the exponent that measures how a non-quadratic real number ξ and its square can be simultaneously approximated by rational numbers with the same denominator. Davenport and Schmidt have proved that is always between the golden ratio γ and 2. Roy, and after him Bugeaud and Laurent, have constructed numbers ξ such that . Their method involves infinite words with many palindrome prefixes. In this text, we define new exponents of approximation that allow us to obtain, to some extent, a characterization of the values obtained by these authors. To cite this article: S. Fischler, C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
4.
Sana Hadj Amor 《Comptes Rendus Mathematique》2006,343(6):423-426
We prove two results on the density of states of the discrete one dimensional quasi-periodic Schrödinger equation with an analytic potential and Diophantine frequencies in the perturbed regime. On the one hand, we prove that this function has the behavior of a Hölder- function. On the other, we show that the length of the gaps has a sub-exponential estimate which depends on its label given by the gap-labeling theorem. To cite this article: S. Hadj Amor, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
5.
Gérard Bourdaud 《Comptes Rendus Mathematique》2005,340(3):221-224
Let us assume that , , and . If f and g are functions in the Besov space , such that g is real valued and such that , then the composed function belongs to . To cite this article: G. Bourdaud, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
6.
Jean-Pierre Marco 《Comptes Rendus Mathematique》2005,340(11):839-842
Let m be an integer ?3, set for , and consider a badly approximable vector . Fix , and . We construct a sequence of Hamiltonian functions of , which converges to ? when , such that for each N the system generated by possesses a -dimensional hyperbolic invariant torus with fixed frequency vector , which admits a homoclinic point with splitting matrix of the form , with , where and . To cite this article: J.-P. Marco, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
7.
Guillaume Duval 《Comptes Rendus Mathematique》2004,339(11):763-768
Let be a differential field extension with differential Galois group . For the natural action of G on the Riemann–Zariski variety of the field extension , we study the invariant valuations when they do exist. We show close relations between these invariant valuations and the elements of F holonomic over K. Next, we study the continuity of the derivation ? with respect to these ν-adic topologies. We give a geometric structure property of G-invariant valuation inspired by Zariski. Finally, we give an answer for the existence problem of invariant valuations in the context of Picard–Vessiot extension. To cite this article: G. Duval, C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
8.
William Alexandre 《Comptes Rendus Mathematique》2004,338(5):365-368
Let q=1,…,n?1 and D be a bounded convex domain in of finite type m. We construct two integral operators Tq and such that for all are continuous, and for all (0,q)-forms h continuous on bD with continuous on bD too, with the additional hypothesis when q=n?1 that ∫bDh∧φ=0 for all φ∈C∞n,0(bD) -fermée, we show . For this construction, we use the Diederich–Fornæss support function of Alexandre (Publ. IRMA Lille 54 (III) (2001)). To prove the continuity of Tq, we integrate by parts and take care of the tangential derivatives. The normal component in z of the kernel of will have a bad behaviour, so, in order to find a good representative of its equivalence class, we isolate the tangential component of the kernel and then integrate by parts again. To cite this article: W. Alexandre, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
9.
Alain Bachelot 《Comptes Rendus Mathematique》2004,339(5):345-350
We develop the scattering theory for the charged Klein–Gordon equation on , when the electrostatic potential has different asymptotics as . In this case, the conserved energy is not positive definite (Klein Paradox). We construct the spectral representation for the harmonic equation, and we establish the existence of a Scattering Operator the symbol of which has a norm strictly larger than 1, for the frequencies in . These results can be applied to the DeSitter–Reissner–Nordstrøm metric, to justify the notion of superradiance of the charged black-holes. To cite this article: A. Bachelot, C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
10.
Wassim Nasserddine 《Comptes Rendus Mathematique》2017,355(5):543-548
Let G be a separable locally compact group with type-I left regular representation, its dual and its Fourier algebra. We prove an analogue of Parseval's theorem and that the mapping is an isometric isomorphism of Banach spaces from onto . 相似文献
11.
Saïd Asserda 《Comptes Rendus Mathematique》2006,342(6):393-398
Let be a complete Riemannian manifold without boundary of dimension n and V be a vector field on M such that is bounded. Suppose that outside a compact set of M, where denotes the upper eigenvalue of ?V and are non-negative decreasing functions such that . There exists positive numbers and which depend only on n and such that if h is a function defined on M with and , where , where is a sequence of M such that , then the equation has no positive solution on M. To cite this article: S. Asserda, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
12.
Gérard Bourdaud 《Comptes Rendus Mathematique》2006,342(4):243-246
We prove an almost sharp Superposition Theorem for a wide class of Besov spaces. Indeed any function which belongs locally to , and vanishes at 0, acts by left composition in . The conditions on the parameters are the following: , and . To cite this article: G. Bourdaud, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
13.
This note aims to present the history of the main researches carried out to represent an ellipse by means of an eight-centered oval and to complete them by giving a geometrical demonstration of the formulas expressing the coordinates of the centers, the radii and the central angles of these arcs of circles making up this oval. These formulas will make it possible to determine its perimeter and thus to approximate the value of that of the ellipse. This result could be useful for archaeologists, who will test the hypothesis according to which some Roman amphitheatres, such as the Coliseum, were built from eight-centered ovals. 相似文献
14.
Anne de Roton 《Comptes Rendus Mathematique》2005,340(3):191-194
We generalise the Beurling–Nyman criterion, already known for the Riemann ζ function, to a larger class of Dirichlet series. We link the density of some subspace of functions in and the localization of the zeros of a Dirichlet series. To do so, we use the structure of the Hardy space of the half-plane. To cite this article: A. de Roton, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献
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16.
Arnaud Münch 《Comptes Rendus Mathematique》2004,339(10):733-738
We present a parameterized family of finite difference schemes for the exact controllability of the 1-D wave equation. These schemes differ from the usual centered ones by additional terms of order to , where h denotes the discretization step in space. Using a discrete version of Ingham's inequality for nonharmonic Fourier series, the spectral properties and dispersion diagrams of the schemes, we determine the parameters leading to a uniform controllability property with respect to h and an optimal stability CFL condition. To cite this article: A. Münch, C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
17.
Dimce Ivanovski 《Comptes Rendus Mathematique》2006,343(6):407-410
Let f be a polynomial map of two variables and let l be a linear form. The affine polar curve of f, for the direction l, is the singular locus of the map . We introduce two resolutions at infinity: the small resolution Π and the total resolution . Let be the line at infinity. The task of this Note is to determine the intersection locus of the strict transform of the polar curve with and . To cite this article: D. Ivanovski, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
18.
Arnaud Münch 《Comptes Rendus Mathematique》2006,343(3):213-218
We consider the wave equation defined on and . We designate by the distributed control of minimal norm obtained with the Hilbert Uniqueness Method which stabilizes the system at time . This Note addresses the question of the optimal position of ω in order to minimize . Assuming , we express the shape derivative of J as a curvilinear integral on ?ω (independently of any adjoint solution) leading to a descent algorithm. A numerical application is given. To cite this article: A. Münch, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
19.
We prove the existence of self-similar solutions for the critical dissipative quasi-geostrophic equation by using the formalism of mild solutions in a space close to . To cite this article: F. Marchand, P.G. Lemarié-Rieusset, C. R. Acad. Sci. Paris, Ser. I 341 (2005). 相似文献
20.
We construct an associative product on the symmetric module of any pre-Lie algebra L. It turns into a Hopf algebra which is isomorphic to the envelopping algebra of . Then we prove that in the case of rooted trees our construction is dual to that of Connes and Kreimer. We also show that symmetric brace algebras and pre-Lie algebras are the same. Finally, we give a similar interpretation of the Hopf algebra of planar rooted trees. To cite this article: J.-M. Oudom, D. Guin, C. R. Acad. Sci. Paris, Ser. I 340 (2005). 相似文献