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1.
We study the singularity formation for the cubic focusing L 2-critical nonlinear Schrödinger equation on \({\mathbb{R}^{2}}\) . In a series of recent works, Merle and Raphaël have completely described the so called log–log blowup regime and proven its stability in the energy space H 1. Our aim in this paper is to investigate the stability of this blowup regime under rough perturbations in the direction of developing a theory at the level of the critical space L 2. By blending the Merle, Raphaël techniques with the quantitative I-method developed by Colliander, Keel, Staffilani, Takaoka and Tao for the study of the Cauchy problem for rough data, we obtain the stability of the log–log regime in H s for all s > 0. 相似文献
2.
Robert J. Taggart 《Mathematische Zeitschrift》2009,261(4):933-949
Suppose that {T
t
: t ≥ 0} is a symmetric diffusion semigroup on L
2(X) and denote by its tensor product extension to the Bochner space , where belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the Hopf–Dunford–Schwartz ergodic theorem
and show that this extends to a maximal theorem for analytic continuations of on . As an application, we show that such continuations exhibit pointwise convergence. 相似文献
3.
We consider the mixed problem,
in a class of Lipschitz graph domains in two dimensions with Lipschitz constant at most 1. We suppose the Dirichlet data,
f
D
, has one derivative in L
p
(D) of the boundary and the Neumann data, f
N
, is in L
p
(N). We find a p
0 > 1 so that for p in an interval (1, p
0), we may find a unique solution to the mixed problem and the gradient of the solution lies in L
p
.
L. Lanzani, L. Capogna and R. M. Brown were supported, in part, by the U.S. National Science Foundation. 相似文献
4.
In this paper we investigate the spectral exponent, i.e. logarithm of the spectral radius of operators having the form
and acting in spaces Lp(X, μ), where X is a compact topological space, φk∈C(X), φ = (φk)k=1N∈C(X)N, and
are linear positive operators (Ukf≥ 0 for f≥ 0). We consider the spectral exponent ln r(Aφ) as a functional depending on vector-function φ. We prove that ln r(Aφ) is continuous and on a certain subspace
of C(X)N is also convex. This yields that the spectral exponent is the Fenchel-Legendre transform of a convex functional
defined on a set
of continuous linear positive and normalized functionals on the subspace
of coefficients φ that is
相似文献
5.
6.
N. Fusco G. Moscariello C. Sbordone 《Calculus of Variations and Partial Differential Equations》2008,33(3):377-390
We show that the limit f of a weakly convergent sequence of W
1,1 homeomorphisms f
j
with finite distortion has finite distortion as well, provided that it is a homeomorphism. Moreover, the lower semicontinuity
of the distortions is deduced both in case of outer and inner distortion. 相似文献
7.
Christine Bessenrodt 《Archiv der Mathematik》2007,89(1):1-9
Starting from the question when all irreducible p-Brauer characters for a symmetric or an alternating group are of p-power degree, we classify the p-modular irreducible representations of p-power dimension in some families of representations for these groups. In particular, this then allows to confirm a conjecture
by W. Willems for the alternating groups.
Received: 14 June 2006 相似文献
8.
Massimo Giulietti 《Combinatorica》2009,29(1):19-25
All sets of lines providing a partition of the set of internal points to a conic C in PG(2,q), q odd, are determined. There exist only three such linesets up to projectivities, namely the set of all non-tangent lines to
C through an external point to C, the set of all non-tangent lines to C through a point in C, and, for square q, the set of all non-tangent lines to C belonging to a Baer subplane PG(2,√q) with √q+1 common points with C. This classification theorem is the analogous of a classical result by Segre and Korchmáros [9] characterizing
the pencil of lines through an internal point to C as the unique set of lines, up to projectivities, which provides a partition
of the set of all non-internal points to C. However, the proof is not analogous, since it does not rely on the famous Lemma
of Tangents of Segre which was the main ingredient in [9]. The main tools in the present paper are certain partitions in conics
of the set of all internal points to C, together with some recent combinatorial characterizations of blocking sets of non-secant
lines, see [2], and of blocking sets of external lines, see [1]. 相似文献
9.
Kaushal Verma 《Mathematische Annalen》2009,344(3):645-701
Let D be a bounded domain in C
2 with a non-compact group of holomorphic automorphisms. Model domains for D are obtained under the hypotheses that at least one orbit accumulates at a boundary point near which the boundary is smooth,
real analytic and of finite type.
The author was supported by DST (India) Grant No.: SR/S4/MS-283/05 and in part by a grant from UGC under DSA-SAP, Phase IV. 相似文献
10.
Anna de Mier 《Combinatorica》2007,27(6):699-720
We give a correspondence between graphs with a given degree sequence and fillings of Ferrers diagrams by nonnegative integers
with prescribed row and column sums. In this setting, k-crossings and k-nestings of the graph become occurrences of the identity and the antiidentity matrices in the filling. We use this to show
the equality of the numbers of k-noncrossing and k-nonnesting graphs with a given degree sequence. This generalizes the analogous result for matchings and partition graphs
of Chen, Deng, Du, Stanley, and Yan, and extends results of Klazar to k > 2. Moreover, this correspondence reinforces the links recently discovered by Krattenthaler between fillings of diagrams
and the results of Chen et al. 相似文献
11.
<Emphasis Type="Italic">L</Emphasis>-functions of symmetric products of the Kloosterman sheaf over Z
The classical n-variable Kloosterman sums over the finite field F
p
give rise to a lisse -sheaf Kl
n+1 on , which we call the Kloosterman sheaf. Let L
p
(G
m, F
p
, Sym
k
Kl
n+1, s) be the L-function of the k-fold symmetric product of Kl
n+1. We construct an explicit virtual scheme X of finite type over Spec Z such that the p-Euler factor of the zeta function of X coincides with L
p
(G
m, F
p
, Sym
k
Kl
n+1, s). We also prove similar results for and .
The research of L. Fu is supported by the NSFC (10525107). 相似文献
12.
Benny Sudakov 《Combinatorica》2007,27(4):509-518
We show that every K
4-free graph G with n vertices can be made bipartite by deleting at most n
2/9 edges. Moreover, the only extremal graph which requires deletion of that many edges is a complete 3-partite graph with
parts of size n/3. This proves an old conjecture of P. Erdős.
Research supported in part by NSF CAREER award DMS-0546523, NSF grant DMS-0355497, USA-Israeli BSF grant, and by an Alfred
P. Sloan fellowship. 相似文献
13.
Kamal Boussaf 《Rendiconti del Circolo Matematico di Palermo》2007,56(3):381-390
We study sets of range uniqueness (SRU’s) in a complete, ultrametric, algebraically closed fieldK for analytic elements. We find monotonic distances sequences which appear to be SRU’s completely different from those known in ©. On the other hand, most of open closed sets cannot be SRU’s. 相似文献
14.
Consider the set of all proper edge-colourings of a graph G with n colours. Among all such colourings, the minimum length of a longest two-coloured cycle is denoted L(n, G). The problem of understanding L(n, G) was posed by Häggkvist in 1978 and, specifically, L(n, K n,n ) has received recent attention. Here we construct, for each prime power q ≥ 8, an edge-colouring of K n,n with n colours having all two-coloured cycles of length ≤ 2q 2, for integers n in a set of density 1 ? 3/(q ? 1). One consequence is that L(n, K n,n ) is bounded above by a polylogarithmic function of n, whereas the best known general upper bound was previously 2n ? 4. 相似文献
15.
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for
BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞. 相似文献
16.
We study extensions of p-local finite groups where the kernel is a p-group. In particular, we construct examples of saturated fusion systems which do not come from finite groups, but which have normal p-subgroups such that is the fusion system of a finite group. One of the tools used to do this is the concept of a “transporter system”, which
is modelled on the transporter category of a finite group, and is more general than a linking system.
B. Oliver is partially supported by UMR 7539 of the CNRS.
J. Ventura is partially supported by FCT/POCTI/FEDER and grant PDCT/MAT/58497/2004. 相似文献
17.
We introduce a notion ofq-analogue of the perfect numbers. We also define a new zeta function which we call a zeta function ofq-perfect numbers. In this paper, the properties of theq-perfect numbers and the zeta functions are studied. Especially, we determine theq-perfect numbers whenq is a root of unity. 相似文献
18.
Takashi Noiri 《Rendiconti del Circolo Matematico di Palermo》2007,56(2):171-184
We introduce a new set calledmg-closed which is defined on a family of sets satisfying some minimal conditions. This set enables us to unify certain kind
of modifications of generalized closed sets due to Levine [17]. 相似文献
19.
Jean-François Babadjian Vincent Millot 《Calculus of Variations and Partial Differential Equations》2009,36(1):7-47
This paper extends the result of Babadjian and Millot (preprint, 2008) on the homogenization of integral functionals with
linear growth defined for Sobolev maps taking values in a given manifold. Through a Γ-convergence analysis, we identify the
homogenized energy in the space of functions of bounded variation. It turns out to be finite for BV-maps with values in the manifold. The bulk and Cantor parts of the energy involve the tangential homogenized density introduced
in Babadjian and Millot (preprint, 2008), while the jump part involves an homogenized surface density given by a geodesic
type problem on the manifold. 相似文献
20.
Ye Li 《Journal of Geometric Analysis》2007,17(3):495-511
We obtain a local volume growth for complete, noncompact Riemannian manifolds with small integral bounds and with Bach tensor
having finite L2 norm in dimension 4. 相似文献