共查询到20条相似文献,搜索用时 46 毫秒
1.
2.
3.
Let q be a positive integer. Recently, Niu and Liu proved that, if , then the product is not a powerful number. In this note, we prove (1) that, for any odd prime power ? and , the product is not a powerful number, and (2) that, for any positive odd integer ?, there exists an integer such that, for any positive integer , the product is not a powerful number. 相似文献
4.
We investigate the regularity of random attractors for the non-autonomous non-local fractional stochastic reaction–diffusion equations in with . We prove the existence and uniqueness of the tempered random attractor that is compact in and attracts all tempered random subsets of with respect to the norm of . The main difficulty is to show the pullback asymptotic compactness of solutions in due to the noncompactness of Sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the Wiener process. We establish such compactness by the ideas of uniform tail-estimates and the spectral decomposition of solutions in bounded domains. 相似文献
5.
6.
《Journal of Mathematical Analysis and Applications》2014,419(2):783-795
We study restriction estimates for algebraic varieties in d-dimensional vector spaces over finite fields. Unlike the Euclidean case, if the dimension d is even, then it is conjectured that the Stein–Tomas restriction result can be improved to the estimate for both spheres and paraboloids in finite fields. In this paper we show that the conjectured restriction estimate holds in the specific case when test functions under consideration are restricted to d-coordinate functions or homogeneous functions of degree zero. To deduce our result, we use the connection between the restriction phenomena for our varieties in d dimensions and those for homogeneous varieties in dimensions. 相似文献
7.
8.
Daniela Giachetti Pedro J. Martínez-Aparicio François Murat 《Journal of Functional Analysis》2018,274(6):1747-1789
In the present paper we perform the homogenization of the semilinear elliptic problem In this problem is a Carathéodory function such that a.e. for every , with h in some and Γ a function such that and for every . On the other hand the open sets are obtained by removing many small holes from a fixed open set Ω in such a way that a “strange term” appears in the limit equation in the case where the function depends only on x.We already treated this problem in the case of a “mild singularity”, namely in the case where the function satisfies . In this case the solution to the problem belongs to and its definition is a “natural” and rather usual one.In the general case where exhibits a “strong singularity” at , which is the purpose of the present paper, the solution to the problem only belongs to but in general does not belong to anymore, even if vanishes on in some sense. Therefore we introduced a new notion of solution (in the spirit of the solutions defined by transposition) for problems with a strong singularity. This definition allowed us to obtain existence, stability and uniqueness results.In the present paper, using this definition, we perform the homogenization of the above semilinear problem and we prove that in the homogenized problem, the “strange term” still appears in the left-hand side while the source term is not modified in the right-hand side. 相似文献
9.
Douglas P. Hardin Michael C. Northington Alexander M. Powell 《Applied and Computational Harmonic Analysis》2018,44(2):294-311
A sharp version of the Balian–Low theorem is proven for the generators of finitely generated shift-invariant spaces. If generators are translated along a lattice to form a frame or Riesz basis for a shift-invariant space V, and if V has extra invariance by a suitable finer lattice, then one of the generators must satisfy , namely, . Similar results are proven for frames of translates that are not Riesz bases without the assumption of extra lattice invariance. The best previously existing results in the literature give a notably weaker conclusion using the Sobolev space ; our results provide an absolutely sharp improvement with . Our results are sharp in the sense that cannot be replaced by for any . 相似文献
10.
In this paper, we apply the variational method with Structural Prescribed Boundary Conditions (SPBC) to prove the existence of periodic and quasi-periodic solutions for the planar four-body problem with two pairs of equal masses and . A path on satisfies the SPBC if the boundaries and , where A and B are two structural configuration spaces in and they depend on a rotation angle and the mass ratio .We show that there is a region such that there exists at least one local minimizer of the Lagrangian action functional on the path space satisfying the SPBC for any . The corresponding minimizing path of the minimizer can be extended to a non-homographic periodic solution if θ is commensurable with π or a quasi-periodic solution if θ is not commensurable with π. In the variational method with the SPBC, we only impose constraints on the boundary and we do not impose any symmetry constraint on solutions. Instead, we prove that our solutions that are extended from the initial minimizing paths possess certain symmetries.The periodic solutions can be further classified as simple choreographic solutions, double choreographic solutions and non-choreographic solutions. Among the many stable simple choreographic orbits, the most extraordinary one is the stable star pentagon choreographic solution when . Remarkably the unequal-mass variants of the stable star pentagon are just as stable as the equal mass choreographies. 相似文献
11.
We consider the Sobolev spaces and and the Besov spaces , where Ω is a sufficiently regular (see Lemma 2) subdomain of . It is well known that for the values of the two Sobolev spaces coincide, with equivalence of the norms, and that the inclusion holds. The Note is concerned with the explicit analysis of the constants appearing in the continuity bounds for the injections and and of their dependence on the regularity s of the spaces. The analysis is carried out by using the wavelet characterization of the corresponding norms. 相似文献
12.
胡国恩 《数学物理学报(B辑英文版)》2005,25(3):545-554
Lp(Rn) (1<p<∞) boundedness and a weak type endpoint estimate are considered for the commutators of singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness of the singular integral operators implies the Lp(Rn) boundedness (1<p<∞) and the weak type (H1(Rn), L1(Rn))boundedness for the corresponding commutators. A new interpolation theorem is also established. 相似文献
13.
14.
Mamadou Sango 《Comptes Rendus Mathematique》2006,342(8):563-568
We investigate the Neumann problem for a nonlinear elliptic operator of Leray–Lions type in , , where Ω is a domain in , is a closed set located in the neighborhood of a -dimensional manifold Γ lying inside Ω. We study the asymptotic behavior of as , when the set tends to Γ. To cite this article: M. Sango, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
15.
Under the assumption that , we derive necessary and sufficient conditions in terms of spectral data for (non-self-adjoint) Schrödinger operators in with periodic and antiperiodic boundary conditions to possess a Riesz basis of root vectors (i.e., eigenvectors and generalized eigenvectors spanning the range of the Riesz projection associated with the corresponding periodic and antiperiodic eigenvalues).We also discuss the case of a Schauder basis for periodic and antiperiodic Schrödinger operators in , . 相似文献
16.
17.
19.
20.