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1.
在局部凸空间已有的中点局部kk-一致凸性和中点局部k-一致光滑性这一对对偶概念的基础上,证明了中点局部kk-一致凸性与中点局部(k+1)-一致凸性的关系,给出了在P-自反的条件下它们之间的等价对偶定理. 相似文献
2.
Toll convexity is a variation of the so-called interval convexity. A tolled walk between two non-adjacent vertices and in a graph is a walk, in which is adjacent only to the second vertex of and is adjacent only to the second-to-last vertex of . A toll interval between is a set . A set is toll convex, if for all . A toll closure of a set is the union of toll intervals between all pairs of vertices from . The size of a smallest set whose toll closure is the whole vertex set is called a toll number of a graph , . The first part of the paper reinvestigates the characterization of convex sets in the Cartesian product of two graphs. It is proved that the toll number of the Cartesian product of two graphs equals 2. In the second part, the toll number of the lexicographic product of two graphs is studied. It is shown that if is not isomorphic to a complete graph, . We give some necessary and sufficient conditions for . Moreover, if has at least two extreme vertices, a complete characterization is given. Furthermore, graphs with are characterized. Finally, the formula for is given — it is described in terms of the so-called toll-dominating triples or, if is complete, toll-dominating pairs. 相似文献
3.
《Mathematische Nachrichten》2017,290(17-18):3020-3028
Let X be a measurable space, let be a family of measurable subsets of it, and let be a subspace of complex measures on X that is also closed under restrictions of measures. In this paper we introduce the ‐convergence topology and the ‐strict topology on . Among other results, we find necessary and sufficient conditions for Hausdorff‐ness and coincide‐ness of these topologies. Applications to Lebesgue spaces, and also examples in Hausdorff topological spaces and locally compact groups are given. 相似文献
4.
Xiao-Bing Li Zhi Lin Qi-Lin Wang Jia-Wei Chen 《Numerical Functional Analysis & Optimization》2017,38(11):1410-1425
This paper is concerned with Hölder continuity of the solution to a saddle point problem. Some new su?cient conditions for the uniqueness and Hölder continuity of the solution for a perturbed saddle point problem are established. Applications of the result on Hölder continuity of the solution for perturbed constrained optimization problems are presented under mild conditions. Examples are given to illustrate the obtained results. 相似文献
5.
6.
José Rául Quintero 《Journal of Dynamics and Differential Equations》2003,15(1):125-142
We study nonlinear orbital stability and instability of the set of ground state solitary wave solutions of a one-dimensional Boussinesq equation or one-dimensional Benney–Luke equation. It is shown that a solitary wave (traveling wave with finite energy) may be orbitally stable or unstable depending on the range of the wave's speed of propagation. 相似文献
7.
郭兴明 《应用数学和力学(英文版)》1996,17(5):445-450
CHARACTERISTICSOFSUBDIFFERENTIALSOFFUNCTIONS(郭兴明)CHARACTERISTICSOFSUBDIFFERENTIALSOFFUNCTIONS¥GuoXingming(ReceivedJune16,1995... 相似文献
8.
We show that a planar BV homeomorphism can be approximated in the area strict sense, together with its inverse, with smooth or piecewise affine homeomorphisms. 相似文献
9.
Ljiljana Petrović 《Stochastics An International Journal of Probability and Stochastic Processes》2018,90(2):200-213
The paper considers a statistical concept of causality in continuous time in the filtered probability spaces which is based on the Granger’s definition of causality. The given causality concept is then applied to the solution of the martingale problem (associated with the stochastic differential equation driven with semimartingales). More precisely, we show that the given causality concept is closely connected to the concept of extremality of measures for the solutions of the martingale problem, for the stopped martingale problem and for the local martingale problem. We also show the equivalence between some models of causality and local uniqueness (for the solutions of the martingale problem). 相似文献
10.
In this paper we investigate spectral matrices, i.e., matrices with equal spectral and numerical radii. Various characterizations and properties of these matrices are given. 相似文献