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A variational problem for axisymmetric shapes is stated where the shapes with extreme average mean curvature and extreme average cur- vature deviator at relevant constraints are
Corollary 24 In a P Q-tree which represents a given hypergraph, a cluster that has an ancestor which is an ancestor-P -node and spans all its vertices, has at most C vertices for
Solutions of integral equa- tions are expressed by the inverse operators of auxiliary exterior and interior boundary value problems, i.e., theorems on the solvability of
We denote by Rec(Σ, S) (and budRec(Σ, S)) the class of tree series over Σ and S which are recognized by weighted tree automata (respectively, by bottom- up deterministic weighted
The paper is organized as follows: in Section 2 is presented the necessary back- ground on fragmentation processes and real trees, culminating with Proposition 2.7, which gives a
The operators considered in this work will satisfy the hypotheses of The- orem 2.2, and henceforth the domain of L will be extended so that L is self adjoint. Results similar to
We will show that either the set of nodes with L (w) = 0 or those nodes together with the root form a minimum distance-k dominating set. Dominators are pushed beginning at the leaves
A nonempty binary tree can also be regarded as a rooted directed tree graph (arborescence) where the outgoing arcs of each node are labeled by distinct labels from the set { L, R