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41.
Suppose that is the set of connected graphs such that a graph G if and only if G satisfies both (F1) if X is an edge cut of G with |X|3, then there exists a vertex v of degree |X| such that X consists of all the edges incident with v in G, and (F2) for every v of degree 3, v lies in a k-cycle of G, where 2k3.In this paper, we show that if G and (G)3, then for every pair of edges e,fE(G), G has a trail with initial edge e and final edge f which contains all vertices of G. This result extends several former results. 相似文献
42.
Radial basis functions (RBFs) have found important applications in areas such as signal processing, medical imaging, and neural networks since the early 1980s. Several applications require that certain physical properties are satisfied by the interpolant, for example, being divergence-free in case of incompressible data. In this paper we consider a class of customized (e.g., divergence-free) RBFs that are matrix-valued and have compact support; these are matrix-valued analogues of the well-known Wendland functions. We obtain stability estimates for a wide class of interpolants based on matrix-valued RBFs, also taking into account the size of the compact support of the generating RBF. We conclude with an application based on an incompressible Navier–Stokes equation, namely the driven-cavity problem, where we use divergence-free RBFs to solve the underlying partial differential equation numerically. We discuss the impact of the size of the support of the basis function on the stability of the solution.
AMS subject classification 65D05 相似文献
43.
Lev Bukovsky Krzysztof Ciesielski 《Proceedings of the American Mathematical Society》2005,133(2):605-611
A topological space is a -space provided that, for every sequence of continuous functions from to , if the series converges pointwise, then it converges pseudo-normally. We show that every regular Lindelöf -space has the Rothberger property. We also construct, under the continuum hypothesis, a -subset of of cardinality continuum.
44.
Krzysztof Ciesielski Janusz Pawlikowski 《Proceedings of the American Mathematical Society》2002,130(7):2007-2013
We show that the property
- (P)
- for every Darboux function there exists a continuous nowhere constant function such that is Darboux
- (A)
- for every subset of of cardinality there exists a uniformly continuous function such that ,
- (B)
- for an arbitrary function whose image contains a non-trivial interval there exists an of cardinality such that the restriction of to is uniformly continuous,
45.
Hall's theorem for bipartite graphs gives a necessary and sufficientcondition for the existence of a matching in a given bipartitegraph. Aharoni and Ziv have generalized the notion of matchabilityto a pair of possibly infinite matroids on the same set andgiven a condition that is sufficient for the matchability ofa given pair (M, W) of finitary matroids, where the matroidM is SCF (a sum of countably many matroids of finite rank).The condition of Aharoni and Ziv is not necessary for matchability.The paper gives a condition that is necessary for the existenceof a matching for any pair of matroids (not necessarily finitary)and is sufficient for any pair (M, W) of finitary matroids,where the matroid M is SCF. 相似文献
46.
Nash-Williams [6] formulated a condition that is necessary andsufficient for a countable family A=(Ai)iI of sets to have atransversal. In [7] he proved that his criterion applies alsowhen we allow the set I to be arbitrary and require only thatiJAi=Ø for any uncountable JI. In this paper, we formulateanother criterion of a similar nature, and prove that it isequivalent to the criterion of Nash-Williams for any familyu. We also present a self-contained proof that if iJAi=Øfor any uncountable JI, then our condition is necessary andsufficient for the family u to have a transversal. 相似文献
47.
Krzysztof Ciesielski 《Periodica Mathematica Hungarica》1995,31(1):11-20
In the paper we prove that the complex analytic functions are (ordinarily) density continuous. This stays in contrast with the fact that even such a simple function asG:22,G(x,y)=(x,y
3
), is not density continuous [1]. We will also characterize those analytic functions which are strongly density continuous at the given pointa . From this we conclude that a complex analytic functionf is strongly density continuous if and only iff(z)=a+bz, wherea, b andb is either real or imaginary. 相似文献
48.
Tutte introduced the theory of nowhere zero flows and showed that a plane graph G has a face k-coloring if and only if G has a nowhere zero A-flow, for any Abelian group A with |A|≥k. In 1992, Jaeger et al. [9] extended nowhere zero flows to group connectivity of graphs: given an orientation D of a graph G, if for any b:V(G)?A with ∑v∈V(G)b(v)=0, there always exists a map f:E(G)?A−{0}, such that at each v∈V(G), in A, then G is A-connected. Let Z3 denote the cyclic group of order 3. In [9], Jaeger et al. (1992) conjectured that every 5-edge-connected graph is Z3-connected. In this paper, we proved the following.
(i)
Every 5-edge-connected graph is Z3-connected if and only if every 5-edge-connected line graph is Z3-connected. (ii)
Every 6-edge-connected triangular line graph is Z3-connected. (iii)
Every 7-edge-connected triangular claw-free graph is Z3-connected.
49.
Maomao Cai 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(13):4581-4588
An explicit integro-differential equation formulation is derived for surface ocean waves with finite depth. The equation involves only 2D surface variables. For this equation, we establish the stability and existence of solutions, and explain the effect of depth on surface wave properties. 相似文献
50.