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121.
Junyong Zhang 《偏微分方程通讯》2015,40(6):995-1028
In this paper, we study some modified linear restriction estimates of the dynamics generated by Schrödinger operator on metric cone M, where the metric cone M is of the form M = (0, ∞) r × Σ, with the cross section Σ being a compact (n ? 1)-dimensional Riemannian manifold (Σ, h) and the equipped metric being g = dr 2 + r 2 h. Assuming the initial data possesses additional regularity in angular variable θ ∈ Σ, we show some linear restriction estimates for the solutions. In terms of their applications, we obtain global-in-time Strichartz estimates for radial initial data and show small initial data scattering theory for the mass-critical nonlinear Schrödinger equation on two-dimensional metric cones. 相似文献
122.
Nobu Kishimoto 《Journal of Differential Equations》2009,247(5):1397-856
In this article we establish the bilinear estimates corresponding to the 1D and 2D NLS with a quadratic nonlinearity , which imply the local well-posedness of the Cauchy problem in Hs for s?−1 in the 1D case and for s>−1 in the 2D case. This is a continuation of our study [N. Kishimoto, Local well-posedness for the Cauchy problem of the quadratic Schrödinger equation with nonlinearity , Commun. Pure Appl. Anal. 7 (2008) 1123-1143] on the 1D NLS with nonlinearity . Previous papers by Kenig, Ponce and Vega, and Colliander, Delort, Kenig and Staffilani established local well-posedness for s>−3/4 in 1D and in 2D, respectively, and when the nonlinearity is restricted to cu2, papers by Bejenaru and Tao, and Bejenaru and De Silva improved these results to s?−1 in 1D and s>−1 in 2D. The bilinear estimate for 2D also yields an improvement on the growth rate of Sobolev norms of finite energy global-in-time solutions to the 2D cubic NLS. 相似文献
123.
124.
Primitive normal polynomials with a prescribed coefficient 总被引:1,自引:0,他引:1
In this paper, we established the existence of a primitive normal polynomial over any finite field with any specified coefficient arbitrarily prescribed. Let n15 be a positive integer and q a prime power. We prove that for any aFq and any 1m<n, there exists a primitive normal polynomial f(x)=xn−σ1xn−1++(−1)n−1σn−1x+(−1)nσn such that σm=a, with the only exceptions σ1≠0. The theory can be extended to polynomials of smaller degree too. 相似文献
125.
Sanghyuk Lee 《Transactions of the American Mathematical Society》2006,358(8):3511-3533
Recently, the sharp -bilinear (adjoint) restriction estimates for the cone and the paraboloid were established by Wolff and Tao, respectively. Their results rely on the fact that for the cone and the paraboloid, the nonzero principal curvatures have the same sign. We generalize those bilinear restriction estimates to surfaces with curvatures of different signs.
126.
Kamal Aziziheris 《代数通讯》2018,46(8):3351-3355
127.
Masaharu Morimoto 《Transactions of the American Mathematical Society》2003,355(6):2341-2384
Let be a finite group. It is well known that a Mackey functor is a module over the Burnside ring functor , where ranges over the set of all subgroups of . For a fixed homomorphism , the Wall group functor is not a Mackey functor if is nontrivial. In this paper, we show that the Wall group functor is a module over the Burnside ring functor as well as over the Grothendieck-Witt ring functor . In fact, we prove a more general result, that the functor assigning the equivariant surgery obstruction group on manifolds with middle-dimensional singular sets to each subgroup of is a module over the Burnside ring functor as well as over the special Grothendieck-Witt ring functor. As an application, we obtain a computable property of the functor described with an element in the Burnside ring.
128.
Let be a domain of the Euclidean space R
m
sent onto itself by a finite group G of congruences. In this paper we first define M
elementary restriction matrices related to the group G and to a system of irreducible matrix representations of G. We then describe a general procedure to generate M
restriction matrices for any finite-dimensional space V() of real functions defined on , when V() is invariant with respect to G. The number M depends only on the group G. Restriction matrices for the space V() have a block structure and all blocks can be obtained as from an elementary restriction matrix. Restriction matrices related to V() define a decomposition of V() as the sum of M subspaces. Finally, owing to restriction matrices, we propose a result of decomposition for linear systems. Several examples are presented.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
129.
We establish the upper bound
with a prime and any positive integer, the sum being over all nonprincipal multiplicative characters .
130.
The influence of the volume restriction effect on phase separation in colloidal dispersions consisting of a nonadsorbing polymer has been studied using statistical mechanical cell models and perturbation theories in combination with Monte Carlo experiments. The attractive interparticle potential proposed by Asakura and Oosawa is used to represent the effect of polymer depletion between the particles. The equilibrium properties are determined using the cell model for the solid-like phase (with Monte Carlo simulations for the structure of the solid phase) and a perturbation theory for the liquid-like phase. Both aqueous and nonaqueous dispersions are considered, and the phase separation behavior predicted is compared with available experimental and theoretical results. 相似文献