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81.
F.J. Martín-Reyes 《Journal of Mathematical Analysis and Applications》2010,368(2):469-481
Let T be a positive invertible linear operator with positive inverse on some Lp(μ), 1?p<∞, where μ is a σ-finite measure. We study the convergence in the Lp(μ)-norm and the almost everywhere convergence of the bilinear operators
82.
A modified Crank-Nicolson scheme based on one-sided difference approximations is proposed for solving time-dependent convection dominated diffusion equations in two-dimensional space. The modified scheme is consistent and unconditionally stable. A priori L2 error estimate for the fully discrete modified scheme is derived. With the use of the incremental unknowns preconditioner at each time step, a comparison among several classical numerical schemes has been made and numerical results confirm stability and efficiency of the modified Crank-Nicolson scheme. 相似文献
83.
The C
1 density conjecture of Palis asserts that diffeomorphisms exhibiting either a homoclinic tangency or a heterodimensional cycle are C
1 dense in the complement of the C
1 closure of hyperbolic systems. In this paper we prove some results towards the conjecture.* Work supported by the National Natural Science Foundation and the Doctoral Education Foundation of China, and the Qiu Shi Science and Technology Foundation of Hong Kong. 相似文献
84.
The problem of extracting space-charge-limited ion beams from spherical emission boundaries is analyzed for simple,two electrode,parallel-plate and spherical sector electrode systems by application of Langmuir-Blodgett theory with account taken for the divergent lens effect caused by the aperture in the extraction electrode.Results derived from simulation studies for the three electrode system,designed for use with the Oak Ridge National Laboratory ECR ion source,complement predictions made from elementary analytical theory with or without magnetic field in the extraction region of the source.Under minimum half- angular divergence(minimum emittance)conditions,the plasma emission boundary has an optimum curvature and the perveance,P,(i.e,current density,j and extraction gap,d),has an optimum value for a given charge- state.From these studies,we find that the optimum perveance for any electrode system can be determined from the Child-Langmuir relation for the parallel-plate electrode system multiplied by a factor,F with value 0.49≤F≤1. 相似文献
85.
86.
许兴业 《数学物理学报(A辑)》2009,29(1):87-93
该文以Schauder-Tychonoff不动点定理为工具,建立了一类Rn上带奇异性的非线性双调和方程 Δ2u=f(|x|, u,| u|)u-β (x ∈ Rn, n ≥ 3, β > 0) 正的径向对称整体解的存在性定理,并给出了解的有关性质,所得的结果丰富和发展了文献[1--5]的结果. 相似文献
87.
AN EQUIVALENT CONTINUUM METHOD OF LATTICE STRUCTURES 总被引:1,自引:0,他引:1
Fan Hualin Yang Wei 《Acta Mechanica Solida Sinica》2006,19(2):103-113
An equivalent continuum method is developed to analyze the effective stiffness of three-dimensional stretching dominated lattice materials. The strength and three-dimensional plastic yield surfaces are calculated for the equivalent continuum. A yielding model is formulated and compared with the results of other models. The bedding-in effect is considered to include the compliance of the lattice joints. The predicted stiffness and strength are in good agreement with the experimental data, validating the present model in the prediction of the mechanical properties of stretching dominated lattice structures. 相似文献
88.
R. Bórquez 《Stochastics An International Journal of Probability and Stochastic Processes》2018,90(2):165-171
The property of countable convexity of the set which contains all dominated martingale laws, for a family of measurable functions with values in a separable Borel space, is proved to be equivalent to the existence of a sufficient statistic. The result is then used to derive a representation of such laws in terms of their extreme points, which are laws of uniformly integrable martingales. Finally, we show that martingales with sufficient statistics converge with probability 1. 相似文献
89.
Principal interval decomposition framework for POD reduced‐order modeling of convective Boussinesq flows 下载免费PDF全文
A principal interval decomposition (PID) approach is presented for the reduced‐order modeling of unsteady Boussinesq equations. The PID method optimizes the lengths of the time windows over which proper orthogonal decomposition (POD) is performed and can be highly effective in building reduced‐order models for convective problems. The performance of these POD models with and without using the PID approach is investigated by applying these methods to the unsteady lock‐exchange flow problem. This benchmark problem exhibits a strong shear flow induced by a temperature jump and results in the Kelvin–Helmholtz instability. This problem is considered a challenging benchmark problem for the development of reduced‐order models. The reference solutions are obtained by direct numerical simulations of the vorticity and temperature transport equations using a compact fourth‐order‐accurate scheme. We compare the accuracy of reduced‐order models developed with different numbers of POD basis functions and different numbers of principal intervals. A linear interpolation model is constructed to obtain basis functions when varying physical parameters. The predictive performance of our models is then analyzed over a wide range of Reynolds numbers. It is shown that the PID approach provides a significant improvement in accuracy over the standard Galerkin POD reduced‐order model. This numerical assessment of the PID shows that it may represent a reliable model reduction tool for convection‐dominated, unsteady‐flow problems. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
90.
In the paper, the existence of positive radially symmetric entire solutions for a class of singular nonlinear polyharmonic equations on
is proved. Some properties are obtained. The results of this paper are generalizations of those in Refs. [Math. Z. 67 (1957) 32; Arch. Math. 9 (1958) 308; Proc. R. Soc. Edinburg 82A (1979) 189; Hiroshima Math. J. 17 (1989) 13]. 相似文献