Let S be a set of n points and let w be a function that assigns non-negative weights to points in S. The additive weighted distance dw(p, q) between two points p, q ∈ S is defined as w(p) + d(p, q) + w(q) if p 6= q and it is zero if p = q. Here, d(p, q) denotes the (geodesic) Euclidean distance between p and q. A graph G(S,E) is called a t-spanner for the additive weighted set S of points if fo...

A recent approach to signal segmentation in additive noise [1, 2] uses features of small spectrogram sub-units accrued over the full spectrogram. The original work considered chirp signals in additive white Gaussian noise. This paper extends this work first by considering similar signals at different signal-to-noise ratios and then in the context of speech recognition. For the chirp case, a cos...

Egoroff’s theorem is established for set-valued measures, which take values in the family of all non-void, closed subsets of a real normed space using Hausdorff metric by several authors. In this paper, we prove Egoroff’s theorem remains valid for non-additive measures, which take values in a family of sets of topological vector spaces using two types of convergency of set sequences.

Topological measures and quasi-linear functionals generalize linear functionals. We define study deficient topological on locally compact spaces. A measure a space is set function open closed sets which finitely additive sets, inner regular outer sets. Deficient measures. First we investigate positive, negative, total variation of signed that only assumed to be These variations turn out Then ex...