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11.
12.
Tohru Nakashima 《Designs, Codes and Cryptography》2010,57(1):107-115
We discuss the properties of algebraic-geometric codes defined by a vector bundle on a curve X over a finite field. We investigate the correction capacities of the codes defined from vector bundles constructed by means
of finite coverings of X. 相似文献
13.
We consider the time-dependent Schrödinger-Hartree equation (1) $$iu_t + \Delta u = \left( {\frac{1}{r}*|u|^2 } \right)u + \lambda \frac{u}{r},(t, x) \in \mathbb{R} \times \mathbb{R}^3 ,$$ (2) $$u(0,x) = \phi (x) \in \Sigma ^{2,2} ,x \in \mathbb{R}^3 ,$$ where λ≧0 and \(\Sigma ^{2,2} = \{ g \in L^2 ;\parallel g\parallel _{\Sigma ^{2,2} }^2 = \sum\limits_{|a| \leqq 2} {\parallel D^a g\parallel _2^2 + \sum\limits_{|\beta | \leqq 2} {\parallel x^\beta g\parallel _2^2< \infty } } \} \) . We show that there exists a unique global solutionu of (1) and (2) such that $$u \in C(\mathbb{R};H^{1,2} ) \cap L^\infty (\mathbb{R};H^{2,2} ) \cap L_{loc}^\infty (\mathbb{R};\Sigma ^{2,2} )$$ with $$u \in L^\infty (\mathbb{R};L^2 ).$$ Furthermore, we show thatu has the following estimates: $$\parallel u(t)\parallel _{2,2} \leqq C,a.c. t \in \mathbb{R},$$ and $$\parallel u(t)\parallel _\infty \leqq C(1 + |t|)^{ - 1/2} ,a.e. t \in \mathbb{R}.$$ 相似文献
14.
Rapid large-scale magnetic-field dissipation is observed in a full kinetic simulation of cross-field current instabilities in a current sheet even when the thickness of the current sheet is at ion scale. The Kelvin-Helmholtz instability caused by the velocity shear between the current-carrying ions and the cold background ions excites the lower-hybrid drift instability at the edges of the undulated current sheet. We show that the nonlinear coupling between these two instabilities is responsible for the observed rapid dissipation. The simulation result presents a new route for magnetic-field dissipation in an ion-scale current sheet and demonstrates the general significance of nonlinear cross-scale coupling in collisionless plasmas. 相似文献
15.
Weighted Strichartz estimates with homogeneous weights with critical exponents are proved for the wave equation without a support restriction on the forcing term. The method of proof is based on expansion by spherical harmonics and on the Sobolev space over the unit sphere, by which the required estimates are reduced to the radial case. As an application of the weighted Strichartz estimates, the existence and uniqueness of self‐similar solutions to nonlinear wave equations are proved on up to five space dimensions. © 2006 Wiley Periodicals, Inc. 相似文献
16.
The energy method in the Fourier space is useful in deriving the decay estimates for problems in the whole space Rn. In this paper, we study half space problems in and develop the energy method in the partial Fourier space obtained by taking the Fourier transform with respect to the tangential variable x′∈Rn−1. For the variable x1∈R+ in the normal direction, we use L2 space or weighted L2 space. We apply this energy method to the half space problem for damped wave equations with a nonlinear convection term and prove the asymptotic stability of planar stationary waves by showing a sharp convergence rate for t→∞. The result obtained in this paper is a refinement of the previous one in Ueda et al. (2008) [13]. 相似文献
17.
We study the global Cauchy problem for the mass critical nonlinear Schrödinger equations. We prove the global existence of analytic solutions in both space and time variables for sufficiently small and exponentially decaying Cauchy data. The method of proof depends on the Leibniz rule for the generator of pseudo-conformal transforms at the L 2 critical level. 相似文献
18.
We introduce the notion of Auslander–Gorenstein resolution and show that a Noetherian ring is an Auslander–Gorenstein ring if it admits an Auslander–Gorenstein resolution over another Auslander–Gorenstein ring. 相似文献
19.
We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite
energy solution converges to the corresponding solution of the nonlinear Schr?dinger equation in the energy space, after the
infinite oscillation in time is removed. We also derive the optimal rate of convergence in .
Received: 13 July 2000 / Published online: 1 February 2002 相似文献
20.
We introduce a notion of Gorenstein algebras of codimension c and demonstrate that Serre duality theory plays an essential role in the theory of derived equivalences for Gorenstein algebras. 相似文献