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1.
2.
J. Bourgain 《Israel Journal of Mathematics》1986,54(3):257-265
The dimension-freeL
2-maximal inequality for convex symmetric bodies obtained in [2] is extended forp>3/2. 相似文献
3.
J. Bourgain 《Israel Journal of Mathematics》1989,67(3):291-311
This paper is a follow up of [B1]. It is shown that the sequence of squares {n
2|n=1, 2, ...} contains Λ(p)-subsets of “maximal density”, for any givenp>4. The proof is based on the probabilistic method developed in [B1] and a precise estimate of the Λ(p)-constant for the sequence of squares itself. Analogues of this phenomenon are obtained for other arithmetic sets, such as
the sequence ofkth powers {n
k |n=1, 2, ...} or the sequence of prime numbers. Sections 2 and 3 of the paper are of independent interest to orthogonal system
theory. 相似文献
4.
We establish new estimates for the Laplacian, the div–curl system, and more general Hodge systems in arbitrary dimension, with an application to minimizers of the Ginzburg–Landau energy. To cite this article: J. Bourgain, H. Brezis, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
5.
Jean Bourgain 《Communications in Mathematical Physics》1996,176(2):421-445
Consider the2D defocusing cubic NLSiu
t+u–u|u|2=0 with Hamiltonian
. It is shown that the Gibbs measure constructed from the Wick ordered Hamiltonian, i.e. replacing ||4 by ||4 :, is an invariant measure for the appropriately modified equationiu
t
+ u‒ [u|u
2–2(|u|2
dx)u]=0. There is a well defined flow on thesupport of the measure. In fact, it is shown that for almost all data the solutionu, u(0)=, satisfiesu(t)–e
it C
Hs
(), for somes>0. First a result local in time is established and next measure invariance considerations are used to extend the local result to a global one (cf. [B2]). 相似文献
6.
We studied the adsorption behaviour at the liquid/air and liquid/solid interface of a new anionic surfactant derived from sugar, the sodium decyl galacturonate. The surface tension of aqueous solutions, measured in equilibrium and as a function of time, is particularly affected by the presence of decanol, synthesis residue, which amount ranges between about 0 and 13%. The surface tension lowering is accelerated in presence of decanol, owing to its rapid diffusion to the interface or/and because it affects the mobility and adsorption process of the anionic surfactant molecules. The wetting power of surfactant solutions were also investigated in relation with textile treatment applications. We measured the kinetics of absorption of surfactant solutions in a piece of standard cotton and compared it to the absorption of pure decanol, a completely wetting liquid and to the absorption of an alkylpolyglucoside. The time at which the fabric piece is saturated appears to be related to the adsorption of surface-active molecules on the fibers at the advancing liquid front/fabric contact line. Decanol was found to promote absorption and micellar life-time seem to reflect the differences observed at high concentration. This study shows the importance of controlling the amount of surface-active residues which may alter the kinetics of surfactant adsorption, particularly in industrial processes where equilibrium conditions are not reached. 相似文献
7.
In this paper we consider an isotropic variant of the BMO‐type norm recently introduced (Bourgain, Brezis, and Mironescu, 2015). We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.© 2016 Wiley Periodicals, Inc. 相似文献
8.
9.
J. Bourgain 《Journal d'Analyse Mathématique》2012,118(1):221-249
It is shown that any primitive integral Apollonian circle packing captures a fraction of the prime numbers. Basically, the method consists of applying the circle method and considering the curvatures produced by a well-chosen family of binary quadratic forms. 相似文献
10.
Jean Bourgain 《Comptes Rendus Mathematique》2002,335(6):529-531
We consider quasi-periodic Schrödinger operators H on of the form H=Hλ,x,ω=λv(x+nω)δn,n′+Δ where v is a non-constant real analytic function on the d-torus and Δ denotes the discrete lattice Laplacian on . Denote by Lω(E) the Lyapounov exponent, considered as function of the energy E and the rotation vector . It is shown that for |λ|>λ0(v), there is the uniform minoration for all E and ω. For all λ and ω, Lω(E) is a continuous function of E. Moreover, Lω(E) is jointly continuous in (ω,E), at any point such that k·ω0≠0 for all . To cite this article: J. Bourgain, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 529–531. 相似文献