Related papers: Quadratic metric comparisons
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…
In this paper we give some relationship between G-metric spaces, partial metric spaces and GP-metric spaces.
Computing the Fr\'echet distance between two polygonal curves takes roughly quadratic time. In this paper, we show that for a special class of curves the Fr\'echet distance computations become easier. Let $P$ and $Q$ be two polygonal curves…
In this paper we study two different weighted isoperimetric inequalities. In the first part of the paper we prove a sharp stability result for the isoperimetric inequality with a log-convex weight. In the second part we analize the behavior…
Given strong local Dirichlet forms and $\mathbb{R}^N$-valued functions on a metrizable space, we introduce the concepts of geodesic distance and intrinsic distance on the basis of these objects. They are defined in a geometric and an…
In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as…
We study metric properties of symmetric divergences on Hermitian positive definite matrices. In particular, we prove that the square root of these divergences is a distance metric. As a corollary we obtain a proof of the metric property for…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
We review the relations between distance matrices and isometric embeddings and give simple proofs that distance matrices defined on euclidean and spherical spaces have all eigenvalues except one non-negative. Several generalizations are…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
In contrast to the spatial Bell's inequalities, which probe entanglement between spatially-separated systems, the Leggett-Garg inequalities test the correlations of a single system measured at different times. Violation of a genuine…
The interplay among the spectrum, geometry and magnetic field in tubular neighbourhoods of curves in Euclidean spaces is investigated in the limit when the cross section shrinks to a point. Proving a norm resolvent convergence, we derive…
This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.
We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.
Quantum mechanics presents peculiar properties that, on the one hand, have been the subject of several theoretical and experimental studies about its very foundations and, on the other hand, provide tools for developing new technologies,…
In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…
We review the literature concerning the Hardy inequality for regions in Euclidean space and in manifolds, concentrating on the best constants. We also give applications of these inequalities to boundary decay and spectral approximation.
We discuss the use of inequalities to obtain the solution of certain variational problems on time scales.
Given two sets of basis vectors in n-dimensional space, there exists a relation between their lengths and mutual angles, expressed as relations between the two metric matrices and the mixed matrix. In this paper these relations are given,…
Two measures of entanglement, negativity and concurrence are studied for two arbitrary qudits. We obtain negativity as an expectation value of an operator. The differences of the squares of negativity and concurrence are invariants of…