Given a subset K of the unit Euclidean sphere, we estimate the minimal number m = m(K) of hyperplanes that generate a uniform tessellation of K, in the sense that the fraction of the hyperplanes separating any pair x, y ∈ K is nearly proportional to the Euclidean distance between x and y. Random hyperplanes prove to be almost ideal for this problem; they achieve the almost optimal bound m = O(w...

3D shape co-segmentation is an important topic in computer graphics. The idea of co-analysis brings new insights into understanding a collection of shapes. Rather than analysing individual shapes, an entire set is looked at, giving much more information about the class of shape in the set. Existing co-segmentation techniques use both face and segment level descriptors in order to provide enough...

-This paper proposes a grey interval relation TOPSIS method for the decision making in which all of the attribute weights and attribute values are given by the interval grey numbers. In this paper, all of the subjective and objective weights are obtained by interval grey number and decision-making is based on four methods such as the relative approach degree of grey TOPSIS, the relative approac...

The Falconer conjecture says that if a compact planar set has Hausdorff dimension > 1, then the Euclidean distance set ∆(E) = {|x − y| : x, y ∈ E} has positive Lebesgue measure. In this paper we prove, under the same assumptions, that for almost every ellipse K, ∆ K (E) = {||x − y|| K : x, y ∈ E} has positive Lebesgue measure, where || · || K is the norm induced by an ellipse K. Equivalently, w...

This paper studies networks where all nodes are distributed on a unit square A , [− 1 2 , 1 2 ] following a Poisson distribution with known density ρ and a pair of nodes separated by an Euclidean distance x are directly connected with probability grρ(x) , g(x/rρ), independent of the event that any other pair of nodes are directly connected. Here g : [0,∞) → [0, 1] satisfies the conditions of ro...

, for t ∈ R. (1) The line lab is the set of parameterizations of the rotations of R 2 that take a to b. We consider the set of n lines L = {lab : a, b ∈ P}. (2) To prove that P determines Ω(n/ log n) distinct distances, it suffices to prove that the number of pairs of intersecting lines in L is O(n logn). Let Nk denote the number of points in R that are incident to exactly k lines of L, and let...

This paper presents a brief overview of the Speaker recognition process, its trends and applications. Further a simple technique based on the Euclidean distance comparison is proposed. The technique is applied for both text-dependent as well as text independent identification. Text dependent identification gives excellent results whereas text independent identification gives almost 80% matching...

Let f : D → C be an analytic function on the unit disc which is in the Dirichlet class, so the Euclidean area of the image, counting multiplicity, is finite. The Euclidean length of a radial arc of hyperbolic length ρ is then o(ρ). In this note we consider the corresponding results when f maps into the unit disc with the hyperbolic metric or the Riemann sphere with the spherical metric. Similar...

The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comaprisons matrix is based on a logarithmic transformation of a pairwise comparisons matrix into a vector space with the Euclidean metric. Orthogonal basis is introduced in the vector space. The orthogonal projection of the transformed matrix onto the space formed by the images of consistent matrices is ...