Let f be a function that is analytic in the unit disc. We give new estimates, and new proofs of existing estimates, of the Euclidean length of the image under f of a radial segment in the unit disc. Our methods are based on the hyperbolic geometry of plane domains, and we address some new questions that follow naturally from this approach.

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consist of an incomplete set of distances and the output is a set of points in Euclidean space realizing those given distances. We survey the theory of Euclidean distance geometry and its most important applications, with special emphasis o...

While the size of multimedia database increases, the demand for efficient search for multimedia data becomes more and more urgent. Most recent works on audio classification and retrieval adopt Euclidean distance as their distance measures. However, Euclidean distance is not a perceptual distance measure for some audio features. The purpose of this work is to derive two new distance measures for...

Graphs are attached to 2r where 2r is the ring with 2 r elements using an analogue of Euclidean distance. M.R. DeDeo (2003) showed that these graphs are non-Ramanujan for r 4. In this paper, we will show that finite Euclidean graphs attached to 2r are non Ramanujan for r 2 except for r = 2 and d = 2, 3. Together with the results in Medrano et al. (1998), this implies that finite Euclidean graph...

We show that the Euclidean distance degree of a real orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustrate how this result can greatly simplify calculations in concrete circumstances.

This pilot study investigates the phonetic realisation of Estonian Swedish long close vowels comparing them with Central Swedish and Finland Swedish counterparts. It appears that in the Rickul variety of Estonian Swedish there is a distinction between only three long close vowels. The analysed vowels of Estonian Swedish are more similar to those of Central Swedish than Finland Swedish, as measu...

The feature of our method different from other fuzzy grey relation method for supermixed multiple attribute group decision-making is that all of the subjective and objective weights are obtained by interval grey number and that the group decisionmaking is performed based on the relative approach degree of grey TOPSIS, the relative approach degree of grey incidence and the relative membership de...

Consider a population of citizens uniformly spread over the entire plane, that faces a problem of locating public facilities to be used by its members. The cost of every facility is financed by its users, who also face an idiosyncratic private access cost to the facility. We assume that the facilities’ cost is independent of location and access costs are linear with respect to the Euclidean dis...

Let n points be arbitrarily placed in B(D), a disk in R having diameter D. Denote by lij the Euclidean distance between point i and j. In this paper, we show n ∑ i=1 ( min j 6=i l ij ) ≤ D 2 0.3972 . We then extend the result to R.