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931.
A fundamental research is carried out into convergence and stability properties of IMEX (implicit–explicit) Runge–Kutta schemes applied to reaction–diffusion equations. It is shown that a fully discrete scheme converges if it satisfies certain conditions using a technique of the B-convergence analysis, developed by Burrage, Hundsdorfer and Verwer in 1986. Stability of the schemes is also examined on the basis of a scalar test equation, proposed by Frank, Hundsdorfer and Verwer in 1997. 相似文献
932.
We prove existence of small amplitude periodic solutions of completely resonant wave equations with frequencies in a Cantor set of asymptotically full measure, via a variational principle. A Lyapunov-Schmidt decomposition reduces the problem to a finite dimensional bifurcation equation—variational in nature—defined on a Cantor set of non-resonant parameters. The Cantor gaps are due to “small divisors” phenomena. To solve the bifurcation equation we develop a suitable variational method. In particular, we do not require the typical “Arnold non-degeneracy condition” of the known theory on the nonlinear terms. As a consequence our existence results hold for new generic sets of nonlinearities. 相似文献
933.
This paper deals with the critical curve of the non-Newtonian polytropic filtration equation coupled via nonlinear boundary flux. The critical global existence curve is obtained by constructing various self-similar supersolutions and subsolutions. Furthermore, we get some new results on the critical Fujita curve. 相似文献
934.
For a supersonic Euler flow past a straight-sided wedge whose vertex angle is less than the extreme angle, there exists a shock-front emanating from the wedge vertex, and the shock-front is usually strong especially when the vertex angle of the wedge is large. In this paper, we establish the L1 well-posedness for two-dimensional steady supersonic Euler flows past a Lipschitz wedge whose boundary slope function has small total variation, when the total variation of the incoming flow is small. In this case, the Lipschitz wedge perturbs the flow, and the waves reflect after interacting with the strong shock-front and the wedge boundary. We first obtain the existence of solutions in BV when the incoming flow has small total variation by the wave front tracking method and then establish the L1 stability of the solutions with respect to the incoming flows. In particular, we incorporate the nonlinear waves generated from the wedge boundary to develop a Lyapunov functional between two solutions containing strong shock-fronts, which is equivalent to the L1 norm, and prove that the functional decreases in the flow direction. Then the L1 stability is established, so is the uniqueness of the solutions by the wave front tracking method. Finally, the uniqueness of solutions in a broader class, the class of viscosity solutions, is also obtained. 相似文献
935.
The pebbling threshold of the square of cliques 总被引:1,自引:0,他引:1
A. Bekmetjev 《Discrete Mathematics》2008,308(19):4306-4314
Given an initial configuration of pebbles on a graph, one can move pebbles in pairs along edges, at the cost of one of the pebbles moved, with the objective of reaching a specified target vertex. The pebbling number of a graph is the minimum number of pebbles so that every configuration of that many pebbles can reach any chosen target. The pebbling threshold of a sequence of graphs is roughly the number of pebbles so that almost every (resp. almost no) configuration of asymptotically more (resp. fewer) pebbles can reach any chosen target. In this paper we find the pebbling threshold of the sequence of squares of cliques, improving upon an earlier result of Boyle and verifying an important instance of a probabilistic version of Graham's product conjecture. 相似文献
936.
937.
Per Salberger 《Mathematische Zeitschrift》2008,258(4):805-826
We give upper bounds for the number of rational points of bounded height on the complement of the lines on projective surfaces. 相似文献
938.
The main purpose of this paper is to show, in the two-dimensional torus, a necessary and sufficient condition in order to certain perturbations of zero order of a system of constant real vector fields to be globally s-solvable. We are also interested in studying its global s-hypoellipticity. We present connections between these global concepts and a priori estimates. We also present two applications of our results for systems of operators with variable coefficients. 相似文献
939.
We introduce two new types of inversive generators for pseudorandom numbers. These new methods offer several advantages over
the conventional inversive generator. For instance, we establish good correlation properties of our generators that cannot
be obtained for the conventional inversive generator with current methods. A new bound on character sums for finite fields
is the essential technical tool for this work.
Authors’ addresses: Harald Niederreiter, Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore
117543, Republic of Singapore; Jo?l Rivat, Institut de Mathématiques de Luminy, Université de la Méditerranée, CNRS-UMR 6206,
163 avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France 相似文献
940.
Here expounded is a kind of symbolic operator method that can be used to construct many transformation formulas and summation formulas for various types of power series including some old ones and more new ones. 相似文献