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1.
This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka–Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone identity. 相似文献
2.
In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results. 相似文献
3.
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5.
Bobby Wilson 《偏微分方程通讯》2015,40(8):1521-1542
This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case. 相似文献
6.
An attempt is made to find out the suitable entrainment and exit boundary conditions in laminar flow situations. Streamfunction vorticity formulation of the Navier–Stokes equations are solved by ADI method. Two‐dimensional laminar plane wall jet flow is used to test different forms of the boundary conditions. Results are compared with the experimental and similarity solution and the proper boundary condition is suggested. The Kind 1 boundary condition is recommended. It consists of zero first derivative condition for velocity variable and for streamfunction equation, mixed derivative at the entrainment and exit boundaries. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
7.
M.A. Tawhid 《Journal of Optimization Theory and Applications》2002,113(1):149-164
In this paper, we give some sufficient conditions for the local uniqueness of solutions to nonsmooth variational inequalities where the underlying functions are H-differentiable and the underlying set is a closed convex set/polyhedral set/box/polyhedral cone. We show how the solution of a linearized variational inequality is related to the solution of the variational inequality. These results extend/unify various similar results proved for C
1 and locally Lipschitzian variational inequality problems. When specialized to the nonlinear complementarity problem, our results extend/unify those of C
2 and C
1 nonlinear complementarity problems. 相似文献
8.
We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point. 相似文献
9.
An Improved Gradient Projection-based Decomposition Technique for Support Vector Machines 总被引:2,自引:0,他引:2
Luca Zanni 《Computational Management Science》2006,3(2):131-145
In this paper we propose some improvements to a recent decomposition technique for the large quadratic program arising in
training support vector machines. As standard decomposition approaches, the technique we consider is based on the idea to
optimize, at each iteration, a subset of the variables through the solution of a quadratic programming subproblem. The innovative
features of this approach consist in using a very effective gradient projection method for the inner subproblems and a special
rule for selecting the variables to be optimized at each step. These features allow to obtain promising performance by decomposing
the problem into few large subproblems instead of many small subproblems as usually done by other decomposition schemes. We
improve this technique by introducing a new inner solver and a simple strategy for reducing the computational cost of each
iteration. We evaluate the effectiveness of these improvements by solving large-scale benchmark problems and by comparison
with a widely used decomposition package. 相似文献
10.
Bo Jin Xi Wang Jing Chen Feng Zhang Xinli Cheng Zhijun Chen 《Applied Surface Science》2006,252(16):5627-5631
The oxidation of SiGe film epitaxial grown on top of SOI wafers has been studied. These SiGe/SOI samples were oxidized at 700, 900, 1100 °C. Germanium atoms were rejected from SiGe film to SOI layer. A new Si1−xGex (x is minimal) layer formed at SiGe/Si interface. As the germanium atoms diffused, the new Si1−xGex (x is minimal) layer moved to Si/SiO2 interface. Propagation of threading dislocation in SiGe film to SOI substrate was hindered by the new SiGe/Si interface. Strain in SOI substrate transferred from SiGe film was released through dislocation nucleation and propagation inner. The relaxation of SiGe film could be described as: strain relaxed through strain equalization and transfer process between SiGe film and SOI substrates. Raman spectroscopy was used to characterize the strain of SiGe film. Microstructure of SiGe/SOI was observed by transmission electron microscope (TEM). 相似文献