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51.
Pentti Haukkanen 《Linear and Multilinear Algebra》2013,61(3):301-309
Considering lower closed sets as closed sets on a preposet (P, ≤), we obtain an Alexandroff topology on P. Then order preserving functions are continuous functions. In this article we investigate order preserving properties (and thus continuity properties) of integer-valued arithmetical functions under the usual divisibility relation of integers and power GCD matrices under the divisibility relation of integer matrices. 相似文献
52.
《偏微分方程通讯》2013,38(11-12):1697-1744
Abstract In this paper, we consider the thin film equation u t + div(|u| n ?Δu) = 0 in the multi-dimensional setting and solve the Cauchy problem in the parameter regime n ∈ [2, 3). New interpolation inequalities applied to the energy estimate enable us to control third order derivatives of appropriate powers of solutions. In such a way, a natural solution concept – reminiscent of that one used by Bernis and Friedman [Bernis, F., Friedman, A., (1990). Higher order nonlinear degenerate parabolic equations. J. Differential Equations 83:179–206] in space dimension N = 1 ? becomes available for the first time in the multi-dimensional setting. In addition, we provide the key integral estimate to establish results on the qualitative behavior of solutions like finite speed of propagation or occurrence of a waiting time phenomenon. 相似文献
53.
Andrey Y. Biyanov 《Proceedings of the American Mathematical Society》1997,125(9):2571-2579
The duals of and with respect to disjointness preserving groups are characterized. A. Plessner's result (1929) about the translation group is extended. A Wiener-Young type theorem for disjointness preserving groups is obtained.
54.
A. Jiménez-Vargas 《Journal of Mathematical Analysis and Applications》2008,337(2):984-993
Given a real number α∈(0,1) and a metric space (X,d), let Lipα(X) be the algebra of all scalar-valued bounded functions f on X such that
55.
A new two‐phase structure‐preserving doubling algorithm for critically singular M‐matrix algebraic Riccati equations
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Tsung‐Ming Huang Wei‐Qiang Huang Ren‐Cang Li Wen‐Wei Lin 《Numerical Linear Algebra with Applications》2016,23(2):291-313
Among numerous iterative methods for solving the minimal nonnegative solution of an M‐matrix algebraic Riccati equation, the structure‐preserving doubling algorithm (SDA) stands out owing to its overall efficiency as well as accuracy. SDA is globally convergent and its convergence is quadratic, except for the critical case for which it converges linearly with the linear rate 1/2. In this paper, we first undertake a delineatory convergence analysis that reveals that the approximations by SDA can be decomposed into two components: the stable component that converges quadratically and the rank‐one component that converges linearly with the linear rate 1/2. Our analysis also shows that as soon as the stable component is fully converged, the rank‐one component can be accurately recovered. We then propose an efficient hybrid method, called the two‐phase SDA, for which the SDA iteration is stopped as soon as it is determined that the stable component is fully converged. Therefore, this two‐phase SDA saves those SDA iterative steps that previously have to have for the rank‐one component to be computed accurately, and thus essentially, it can be regarded as a quadratically convergent method. Numerical results confirm our analysis and demonstrate the efficiency of the new two‐phase SDA. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
56.
An energy‐preserving Crank–Nicolson Galerkin method for Hamiltonian partial differential equations
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Haochen Li Yushun Wang Qin Sheng 《Numerical Methods for Partial Differential Equations》2016,32(5):1485-1504
A semidiscretization based method for solving Hamiltonian partial differential equations is proposed in this article. Our key idea consists of two approaches. First, the underlying equation is discretized in space via a selected finite element method and the Hamiltonian PDE can thus be casted to Hamiltonian ODEs based on the weak formulation of the system. Second, the resulting ordinary differential system is solved by an energy‐preserving integrator. The relay leads to a fully discretized and energy‐preserved scheme. This strategy is fully realized for solving a nonlinear Schrödinger equation through a combination of the Galerkin discretization in space and a Crank–Nicolson scheme in time. The order of convergence of our new method is if the discrete L2‐norm is employed. An error estimate is acquired and analyzed without grid ratio restrictions. Numerical examples are given to further illustrate the conservation and convergence of the energy‐preserving scheme constructed.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1485–1504, 2016 相似文献
57.
Let I be a finite interval, s ∈ ℕ0, and r,ν,n ∈ ℕ. Given a set M, of functions defined on I, denote by
M the subset of all functions y ∈ M such that the s-difference is nonnegative on I, ∀τ > 0. Further, denote by the Sobolev class of functions x on I with the seminorm . Also denote by Σ
ν,n
, the manifold of all piecewise polynomials of order ν and with n – 1 knots in I. If ν ≥ max {r,s}, 1 ≤ p,q ≤ ∞, and (r,p,q) ≠ (1,1,∞), then we give exact orders of the best unconstrained approximation and of the best s-monotonicity preserving approximation .
Part of this work was done while the first author visited Tel Aviv University in May 2003 and in March 2004. 相似文献
58.
The second moment numerical method (SMM) of Egan and Mahoney [Numerical modeling of advection and diffusion of urban area source pollutant. Journal of Applied Meteorology 1972; 11 : 312–322] is adapted to solve for the pure advection transport equation in a variety of flow fields. SMM eliminates numerical diffusion by employing a procedure that takes into account the first and second moments of mass distribution in each grid element. For pure translational flow fields, the method is conservative, positive definite and shape‐preserving. In rotational and/or shear flows, the accuracy of SMM is significantly reduced. Two improvements are presented to make the SMM applicable to a wider range of flow problems. It is shown that the improved SMM (ISMM) is less diffusive and more shape‐preserving than the SMM in rotational and/or deformational flows. The ISMM can also be used to solve for a color function in compressible flow fields. The computational efficiency of this method is compared with that of other methods and, for a given accuracy, it is shown that ISMM is a cost‐effective, non‐diffusive and shape‐preserving method. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
59.
Numerical Methods to Solve the Complex Symmetric Stabilizing Solution of the Complex Matrix Equation $X+A^TX^{−1}A=Q$
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Yao Yao & Xiao-Xia Guo 《数学研究》2015,48(1):53-65
When the matrices $A$ and $Q$ have special structure, the structure-preserving
algorithm was used to compute the stabilizing solution of the complex matrix equation $X+A^TX^{-1}A=Q.$ In this paper, we study the numerical methods to solve the complex
symmetric stabilizing solution of the general matrix equation $X+A^TX^{-1}A=Q.$ We
not only establish the global convergence for the methods under an assumption, but
also show the feasibility and effectiveness of them by numerical experiments. 相似文献
60.
Let T be a compact disjointness preserving linear operator from C0(X) into C0(Y), where X and Y are locally compact Hausdorff spaces. We show that T can be represented as a norm convergent countable sum of disjoint rank one operators. More precisely, T = Σn δ ?hn for a (possibly finite) sequence {xn }n of distinct points in X and a norm null sequence {hn }n of mutually disjoint functions in C0(Y). Moreover, we develop a graph theoretic method to describe the spectrum of such an operator (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献