共查询到20条相似文献,搜索用时 75 毫秒
1.
Chien-Hong 《高等学校计算数学学报(英文版)》2010,3(4)
<正>We consider a finite difference scheme for a nonlinear wave equation,whose solutions may lose their smoothness in finite time,i.e.,blow up in finite time.In order to numerically reproduce blow-up solutions,we propose a rule for a time-stepping, which is a variant of what was successfully used in the case of nonlinear parabolic equations.A numerical blow-up time is defined and is proved to converge,under a certain hypothesis,to the real blow-up time as the grid size tends to zero. 相似文献
2.
Massimiliano Berti 《分析论及其应用》2019,35(3):235-267
In the last years much progress has been achieved in KAM theory concerning bifurcation of quasi-periodic solutions of Hamiltonian or reversible partial differential equations.We provide an overview of the state of the art in this field. 相似文献
3.
Elena 《高等学校计算数学学报(英文版)》2010,3(4)
<正>In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging,scientific computing,reverse engineering and geometric modelling.The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation(PDE)-based diffusion model derived by a minimal volume-like variational formulation.The evolution is driven both by the distance from the data set and by the curvature analytically computed by it.The distance function is computed by implicit local interpolants defined in terms of radial basis functions.Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale.The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology, without the need of user-interaction.Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions.Moreover,we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets. 相似文献
4.
傅种孙先生在北京师大附中 总被引:1,自引:0,他引:1
1 傅种孙先生简介 1.1 傅先生基本情况介绍 傅种孙先生(1898~1962)1898年2月27日生于江西省高安县.1920年在北京高等师范学校数理部毕业,留母校附中(即现北京师大附中)任教;1921年任母校数理部的讲师;1928年任教授:抗日战争以前,曾先后兼任北京女子师范大学,北平大学女子文理学院,北京大学,辅仁大学教授;1933年当选北平(北京)市数学会理事长秘书;1935年当选中国数学会评议委员兼<数学杂志>编辑;1945年11月至1946年8月在牛津大学、1946年9月至1947年11月在剑桥大学考察;1947~1962年任北京师范大学数学系教授,1956年前曾兼系主任;在1949~1957年间,曾任北京师范大学教务长(3年)及副校长(5年);1952~1957年任北京市人民代表大会代表,中国数学会及其北京市分会常务理事,<中国数学杂志>及其后身<数学通报>总编辑;1962年1月18日病逝于北京. 相似文献
5.
Local Unstable Entropy and Local Unstable Pressure for Partially Hyperbolic Endomorphisms* 下载免费PDF全文
Xinsheng WANG 《数学年刊B辑(英文版)》2022,43(1):137-160
In this paper, local unstable metric entropy, local unstable topological entropy and local unstable pressure for partially hyperbolic endomorphisms are introduced and investigated. Specially, two variational principles concerning relationships among the above mentioned numbers are formulated. 相似文献
6.
In this paper,nonconforming finite element methods(FEMs)are proposed for the constrained optimal control problems(OCPs)governed by the nonsmooth elliptic equations,in which the popular EQr1 ot element is employed to approximate the state and adjoint state,and the piecewise constant element is used to approximate the control.Firstly,the convergence and superconvergence properties for the nonsmooth elliptic equation are obtained by introducing an auxiliary problem.Secondly,the goal-oriented error estimates are obtained for the objective function through establishing the negative norm error estimate.Lastly,the methods are extended to some other well-known nonconforming elements. 相似文献
7.
We give the direct method of moving planes for solutions to the conformally invariant fractional power sub Laplace equation on the Heisenberg group.The method is based on four maximum principles derived here.Then symmetry and nonexistence of positive cylindrical solutions are proved. 相似文献
8.
Generalizing wavelets by adding desired redundancy and flexibility,framelets(i.e.,wavelet frames)are of interest and importance in many applications such as image processing and numerical algorithms.Several key properties of framelets are high vanishing moments for sparse multiscale representation,fast framelet transforms for numerical efficiency,and redundancy for robustness.However,it is a challenging problem to study and construct multivariate nonseparable framelets,mainly due to their intrinsic connections to factorization and syzygy modules of multivariate polynomial matrices.Moreover,all the known multivariate tight framelets derived from spline refinable scalar functions have only one vanishing moment,and framelets derived from refinable vector functions are barely studied yet in the literature.In this paper,we circumvent the above difficulties through the approach of quasi-tight framelets,which behave almost identically to tight framelets.Employing the popular oblique extension principle(OEP),from an arbitrary compactly supported M-refinable vector functionφwith multiplicity greater than one,we prove that we can always derive fromφa compactly supported multivariate quasi-tight framelet such that:(i)all the framelet generators have the highest possible order of vanishing moments;(ii)its associated fast framelet transform has the highest balancing order and is compact.For a refinable scalar functionφ(i.e.,its multiplicity is one),the above item(ii)often cannot be achieved intrinsically but we show that we can always construct a compactly supported OEP-based multivariate quasi-tight framelet derived fromφsatisfying item(i).We point out that constructing OEP-based quasi-tight framelets is closely related to the generalized spectral factorization of Hermitian trigonometric polynomial matrices.Our proof is critically built on a newly developed result on the normal form of a matrix-valued filter,which is of interest and importance in itself for greatly facilitating the study of refinable vector functions and multiwavelets/multiframelets.This paper provides a comprehensive investigation on OEP-based multivariate quasi-tight multiframelets and their associated framelet transforms with high balancing orders.This deepens our theoretical understanding of multivariate quasi-tight multiframelets and their associated fast multiframelet transforms. 相似文献
9.
Ahmad AL-SALMAN 《Frontiers of Mathematics in China》2021,16(1):13-28
We introduce a class of singular integral operators on product domains along twisted surfaces.We prove that the operators are bounded on Lp provided that the kernels satisfy weak conditions. 相似文献
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11.
In this paper, approximations of attraction domains of the asymptotically stable equilibrium points of some typical Cohen-Grossberg neural networks are achieved. Most Cohen-Grossberg neural networks are highly nonlinear systems which makes it difficult to approximate their attraction domain. Under some weak assumptions, we are allowed to employ the optimal Lyapunov method to obtain a Lyapunov function for asymptotically stable equilibrium points of a given Cohen-Grossberg neural network. With the help of this Lyapunov function, we approximate the corresponding attraction domain by the iterative expansion approach. Numerical simulations also illustrate that the approximation obtained is really part of the attraction domain. 相似文献
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13.
In this paper, new discrete analogue of high-order Cohen-Grossberg neural networks with varying delay is obtained by analysis and approximation techniques. The existence of periodic solution for discrete high-order Cohen-Grossberg neural networks with varying delay is studied by continuation theorem of coincidence degree theory, and sufficient condition is given to guarantee global exponential stability of periodic solution. Finally, an example is given to show the effectiveness of the results in this paper. 相似文献
14.
本文讨论了含混合时滞和脉冲的Cohen-Grossberg神经网络的稳定性.通过应用M矩阵理论和不等式技巧,得到了含混合时滞的Cohen-Grossberg神经网络平衡态的全局指数稳定性的充分条件.相比以前同类文献,本文减弱了部分条件,推广了部分结论,并在文末给出了两个示例.本文结论对于设计和应用神经网络有一定实用价值. 相似文献
15.
R. Sakthivel A. ArunkumarK. Mathiyalagan S. Marshal Anthoni 《Applied mathematics and computation》2011,218(7):3799-3809
This paper is concerned with the problem of passivity analysis for a class of Cohen-Grossberg fuzzy bidirectional associative memory (BAM) neural networks with time varying delay. By employing the delay fractioning technique and linear matrix inequality optimization approach, delay dependent passivity criteria are established that guarantees the passivity of fuzzy Cohen-Grossberg BAM neural networks with uncertainties. The passivity condition is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, a numerical example is given to illustrate the effectiveness of the proposed result. 相似文献
16.
对具有分布时滞的非自治Cohen-Grossberg神经网络进行了研究.通过构造适当的Lyapunov函数,利用不等式分析方法,引入多参数,得到了一系列解的一致有界性且最终有界性和全局指数稳定性的判别准则. 相似文献
17.
考虑一类具有时滞的Cohen-Grossberg神经网络,利用Lyapunov方法和微分不等式理论,得到了其全局指数稳定性的判别准则.该准则引入了更多的参数,更便于系统的设计与分析. 相似文献
18.
In this paper, we study Cohen-Grossberg neural networks (CGNN) with time-varying delay. Based on Halanay inequality and continuation theorem of the coincidence degree, we obtain some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of periodic solution. Our results complement previously known results. 相似文献
19.
本文主要考虑了一类带脉冲的Cohen—Grossberg时滞神经网络模型的全局指数稳定性,通过构造Liapunov函数,应用M矩阵理论和一些不等式的技巧,给出了模型的平凡解全局指数稳定的充分条件。 相似文献
20.
By using the continuation theorem of Mawhin’s coincidence degree theory and the Liapunov func tional method, some sufficient conditions are obtained to ensure the existence, uniqueness and the global exponential stability of the periodic solution to the BAM-type Cohen-Grossberg neural networks involving timevarying delays. 相似文献