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991.
Hiroyuki Chihara 《Mathematische Annalen》1999,315(4):529-567
We discuss local existence and gain of regularity for semilinear Schr?dinger equations which generally cause loss of derivatives.
We prove our results by advanced energy estimates. More precisely, block diagonalization and Doi's transformation, together
with symbol smoothing for pseudodifferential operators with nonsmooth coefficients, apply to systems of Schr?dinger-type equations.
In particular, the sharp G?rding inequality for pseudodifferential operators whose coefficients are twice continuously differentiable,
plays a crucial role in our proof.
Received: 14 December 1998 相似文献
992.
Aurélie Fischer 《Journal of multivariate analysis》2010,101(9):2207-2221
This paper deals with the problem of quantization of a random variable X taking values in a separable and reflexive Banach space, and with the related question of clustering independent random observations distributed as X. To this end, we use a quantization scheme with a class of distortion measures called Bregman divergences, and provide conditions ensuring the existence of an optimal quantizer and an empirically optimal quantizer. Rates of convergence are also discussed. 相似文献
993.
Byungchul Cha 《Journal of Number Theory》2010,130(4):1048-1055
We derive a formula for the density of positive integers satisfying a certain system of inequality, often referred as prime number races, in the case of the polynomial rings over finite fields. This is a function field analog of the work of Feuerverger and Martin, who established such formula in the number field case, building up on the fundamental work of Rubinstein and Sarnak. 相似文献
994.
K.L. Kozlov 《Topology and its Applications》2010,157(4):698-707
The approach to the problem of the distribution of the functors of the Stone-?ech compactification, the Hewitt realcompactification or the Dieudonné completion with the operation of taking products is discussed using uniform structures on products. In particular, the role of different rectangular conditions is shown. Relative analogues of this question and new examples of (strongly) rectangular products are presented. Characterizations of bounded rectangular subsets of the product are given. 相似文献
995.
Marion Scheepers 《Topology and its Applications》2010,157(9):1651-557
We obtain from the consistency of the existence of a measurable cardinal the consistency of “small” upper bounds on the cardinality of a large class of Lindelöf spaces whose singletons are Gδ sets. 相似文献
996.
Veronika Kornecká-Kurková 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1663-1669
For a continuous map of the interval, there are more than 50 conditions characterizing zero topological entropy. Some are applicable to the class of triangular maps (x,y)?(f(x),gx(y)) of the square, but only a few of them are equivalent in this more general setting. In 1989, A.N. Sharkovsky posed the problem of proving or disproving all possible implications between them. During last 20 years, 32 conditions were considered, and most of the work was done. Only 45 relations out of 992 remained not clear. In this paper we give a survey of known results, provide two new examples disproving another 26 possible implications, and spell out the remaining 19 open problems; all but one concern distributional chaos. 相似文献
997.
Tuomas Airaksinen Sanna Mönkölä 《Journal of Computational and Applied Mathematics》2010,234(6):1796-1802
Processes that can be modelled with numerical calculations of acoustic pressure fields include medical and industrial ultrasound, echo sounding, and environmental noise. We present two methods for making these calculations based on Helmholtz equation. The first method is based directly on the complex-valued Helmholtz equation and an algebraic multigrid approximation of the discretized shifted-Laplacian operator; i.e. the damped Helmholtz operator as a preconditioner. The second approach returns to a transient wave equation, and finds the time-periodic solution using a controllability technique. We concentrate on acoustic problems, but our methods can be used for other types of Helmholtz problems as well. Numerical experiments show that the control method takes more CPU time, whereas the shifted-Laplacian method has larger memory requirement. 相似文献
998.
D.K.R. Babajee M.T. Darvishi 《Journal of Computational and Applied Mathematics》2010,233(8):2002-2943
In this paper, two Chebyshev-like third order methods free from second derivatives are considered and analyzed for systems of nonlinear equations. The methods can be obtained by having different approximations to the second derivatives present in the Chebyshev method. We study the local and third order convergence of the methods using the point of attraction theory. The computational aspects of the methods are also studied using some numerical experiments including an application to the Chandrasekhar integral equations in Radiative Transfer. 相似文献
999.
Marta Grzanek Anna Michalak Andrzej Rogowski 《Nonlinear Analysis: Theory, Methods & Applications》2008
The problem of Lyapunov stability for systems of ODE’s of Caratheodory type is considered. It is proved that without the necessity of calculating Dini or Clarke generalized gradients, the locally Lipschitz Lyapunov function can follow different kinds of stability. 相似文献
1000.
P.E. Kloeden 《Journal of Differential Equations》2008,244(8):2062-2090
The existence and uniqueness of a variational solution satisfying energy equality is proved for a semilinear heat equation in a non-cylindrical domain with homogeneous Dirichlet boundary condition, under the assumption that the spatial domains are bounded and increase with time. In addition, the non-autonomous dynamical system generated by this class of solutions is shown to have a global pullback attractor. 相似文献