Existence of positive solutions for multi-point boundary value problems.
A counter-example in singular integral theory
An improvement of a lemma of Calderón and Zygmund involving singular spherical harmonic kernels is obtained and a counter-example is given to show that this result is best possible. In a particular case when the singularity is O(|log r|), let and suppose f vanishes outside of a compact subset of , N ≥ 2. Also, let k(x) be a Calderón-Zygmund kernel of spherical harmonic type. Suppose f(x) = O(|log r|) as r → 0 in the -sense. Set . Then F(x) = O(log²r) as r → 0 in the -sense, 1 < p < ∞....
Algorithm and experiments in testing planar graphs for isomorphism.
Inferring graph grammars by detecting overlap in frequent subgraphs
In this paper we study the inference of node and edge replacement graph grammars. We search for frequent subgraphs and then check for an overlap among the instances of the subgraphs in the input graph. If the subgraphs overlap by one node, we propose a node replacement graph grammar production. If the subgraphs overlap by two nodes or two nodes and an edge, we propose an edge replacement graph grammar production. We can also infer a hierarchy of productions by compressing portions of a graph described...
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