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The idea is that this series can now be used to define the exponential of large classes of mathematical objects: complex numbers, matrices, power series, operators?. For the

We argue inductively for a tree node that the graph constructed by processing each of the child nodes of that node contains two root vertices and that these roots are available for

We show that a discrete fixed point theorem of Eilenberg is equivalent to the restriction of the contraction principle to the class of non-Archimedean bounded metric spaces.. We

We use these to show that a segmentation approach to the EIT inverse problem has a unique solution in a suitable space using a fixed point

We can therefore generate F U (n) using a simple modification of the algorithm RootedTrees from Section 3: the canonically ordered tree R that represents a unicentroidal free tree T

In our previous papers, we used the theorems in finite operator calculus to count the number of ballot paths avoiding a given pattern.. From the above example, we see that we have

The main problem upon which most of the geometric topology is based is that of classifying and comparing the various supplementary structures that can be imposed on a

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