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Merge trees represent the topology of scalar functions. To assess the topo-logical similarity of functions, one can compare their merge trees. To do so, one needs a notion of a distance between merge trees, which we define. We provide examples of using our merge tree distance and compare this new measure to other ways used to characterize topological… (More)
In this paper are considered existing multi-touch technologies, pointed main problems of the development and observed one of the new existing approaches of fingertip detection and touch detection algorithm is given.
We establish an analog of Faulhaber's theorem for a power sum of binomial coefficients. We study reciprocal power sums of binomial coefficients and Faulhaber coefficients for a power sum of triangular numbers.
We describe the relation between graph decompositions into walks and the normal ordering of differential operators in the n-th Weyl algebra. Under several specifications , we study new types of restricted set partitions, and a generalization of Stirling numbers, which we call the λ-Stirling numbers.