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981.
刘德金 《纯粹数学与应用数学》2011,27(2):151-157
覆盖方法的应用在粗糙集理论研究中越来越受到重视,其中拓扑空间的子集关于子基的内部和闭包两个概念尤为重要.在由它们导入的关于子基的开集,闭集的基础上,给出了拓扑空间关于子基的紧致性概念,并研究它的性质,得到一般拓扑空间中紧致性的一种推广. 相似文献
982.
林鸿钊 《纯粹数学与应用数学》2011,27(5):650-655
为了进一步研究Banach空间中集合的紧致性,受极限集与极限算子定义的启发,给出了弱极限集与弱极限算子的定义,得到了它们的等价刻画,利用空间结构与算子理想的互动关系证明了弱极限算子全体是Pietsch意义下的闭满射算子理想. 相似文献
983.
In this paper, we consider a non-local PDE model with delay for population dynamics in ℝ
n
. First, we prove the existence and uniqueness of weak solutions under some suitable decayed assumptions on non-local term
at infinity. Then, we obtain the global attractor by proving ω-limit compactness property of the solution operator semigroup. 相似文献
984.
In this paper, the structure of the critical group of the graph K
m
× C
n
is determined, where m, n ≥ 3. 相似文献
985.
Juan Alberto Rodriguez-Velazquez José María Sigarreta Ismael Gonzalez Yero Sergio Bermudo 《数学学报(英文版)》2011,27(3):497-504
A defensive (offensive) k-alliance in Γ = (V,E) is a set S ⊆ V such that every υ in S (in the boundary of S) has at least k more neighbors in S than it has in V / S. A set X ⊆ V is defensive (offensive) k-alliance free, if for all defensive (offensive) k-alliance S, S/X ≠ ∅, i.e., X does not contain any defensive (offensive) k-alliance as a subset. A set Y ⊆ V is a defensive (offensive) k-alliance cover, if for all defensive (offensive) k-alliance S, S ∩ Y ≠ ∅, i.e., Y contains at least one vertex from each defensive (offensive) k-alliance of Γ. In this paper we show several mathematical properties of defensive (offensive) k-alliance free sets and defensive (offensive) k-alliance cover sets, including tight bounds on their cardinality. 相似文献
986.
For the planar Z
2-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions
of the first six Liapunov constants are completely discussed. The necessary and sufficient conditions for the existence of
the bi-center are obtained. All possible first integrals are given. Under small Z
2-equivariant cubic perturbations, the conclusion that there exist at most 12 small-amplitude limit cycles with the scheme
〈6 ∐ 6〉 is proved. 相似文献
987.
In two real Banach spaces, we shall present two conditions, under one of which each nonexpansive mapping must be an isometry. 相似文献
988.
Observations of sampling are often subject to rounding, but are modeled as though they were unrounded. This paper examines
the impact of rounding errors on parameter estimation with multi-layer ranked set sampling. It shows that the rounding errors
seriously distort the behavior of covariance matrix estimate, and lead to inconsistent estimation. Taking this into account,
we present a new approach to implement the estimation for this model, and further establish the strong consistency and asymptotic
normality of the proposed estimators. Simulation experiments show that our estimates based on rounded multi-layer ranked set
sampling are always more efficient than those based on rounded simple random sampling. 相似文献
989.
Bingquan Ji Luming Zhang Xuanxuan Zhou 《Numerical Methods for Partial Differential Equations》2019,35(3):1056-1079
In this article, a compact finite difference method is developed for the periodic initial value problem of the N‐coupled nonlinear Klein–Gordon equations. The present scheme is proved to preserve the total energy in the discrete sense. Due to the difficulty in obtaining the priori estimate from the discrete energy conservation law, the cut‐off function technique is employed to prove the convergence, which shows the new scheme possesses second order accuracy in time and fourth order accuracy in space, respectively. Additionally, several numerical results are reported to confirm our theoretical analysis. Lastly, we apply the reliable method to simulate and study the collisions of solitary waves numerically. 相似文献
990.
In this article, we study the second-order optimality conditions for a class of circular conic optimization problem. First, the explicit expressions of the tangent cone and the second-order tangent set for a given circular cone are derived. Then, we establish the closed-form formulation of critical cone and calculate the “sigma” term of the aforementioned optimization problem. At last, in light of tools of variational analysis, we present the associated no gap second-order optimality conditions. Compared to analogous results in the literature, our approach is intuitive and straightforward, which can be manipulated and verified. An example is illustrated to this end. 相似文献