Related papers: An Explicit Formula of the Intrinsic Metric on the…
We present the numbers of ice model and eight-vertex model configurations (with Boltzmann factors equal to one), I(n) and E(n) respectively, on the two-dimensional Sierpinski gasket SG(n) at stage $n$. For the eight-vertex model, the number…
This work studies the entropic regularization formulation of the 2-Wasserstein distance on an infinite-dimensional Hilbert space, in particular for the Gaussian setting. We first present the Minimum Mutual Information property, namely the…
Riemann surfaces are among the simplest and most basic geometric objects. They appear as key players in many branches of physics, mathematics, and other sciences. Despite their widespread significance, how to compute distances between pairs…
We introduce several new functions that measure the distance between two points $x$ and $y$ in a domain $G\subsetneq\mathbb{R}^n$ by using the arithmetic or the logarithmic mean of the Euclidean distances from the points $x$ and $y$ to the…
We introduce a concept of distance for a space-time where the notion of point is replaced by the notion of physical states e.g. probability distributions. We apply ideas of information theory and compute the Fisher information matrix on…
We confirm, in a more general framework, a part of the conjecture posed by R. Bell, C.-W. Ho, and R. S. Strichartz [Energy measures of harmonic functions on the Sierpi\'nski gasket, Indiana Univ. Math. J. 63 (2014), 831--868] on the…
In 2005, Liu et al. calculated the dimensionality of the intersection of Sierpinski carpet and a straight line with rational slope in the sense of Lebesgue measure.Sierpinski carpet is a self-similar set in two-dimensional planes obtained…
We give formulas for calculating the interleaving distance between rectangle persistence modules that depend solely on the geometry of the underlying rectangles. Moreover, we extend our results to calculate the bottleneck distance for…
A method of induction the distances with Hilbert structure is proposed. Some properties of the method are studied. Typical examples of corresponding metric spaces are discussed. Key words: Hilbert spaces; metric spaces; isometric embedding…
The aim of this paper is to demonstrate relations between Gromov-Hausdorff distance properties and the Borsuk Conjecture. The Borsuk number of a given bounded metric space $X$ is the infimum of cardinal numbers $n$ such that $X$ can be…
We give explicit bounds on the intersection number between any curve on a tight multigeodesic and the two ending curves. We use this to construct all tight multigeodesics and so conclude that distances in the curve graph are computable. The…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
Under certain continuity conditions, we estimate upper and lower box dimension of graph of a function defined on the Sierpinski gasket. We also give an upper bound for Hausdorff dimension and box dimension of graph of function having finite…
The inner product provides a conceptually and algorithmically simple method for calculating the comoving distance between two cosmological objects given their redshifts, right ascension and declination, and arbitrary constant curvature. The…
Computing intrinsic distances on discrete surfaces is at the heart of many minimization problems in geometry processing and beyond. Solving these problems is extremely challenging as it demands the computation of on-surface distances along…
In this paper motivated from subspace coding we introduce subspace-metric codes and subset-metric codes. These are coordinate-position independent pseudometrics and suitable for the folded codes. The half-Singleton upper bounds for linear…
We calculate the exact Casimir interaction energy between two perfectly conducting, very long, eccentric cylindrical shells using a mode summation technique. Several limiting cases of the exact formula for the Casimir energy corresponding…
We present a new method for embedding a causal set into an interval of Minkowski spacetime. The method uses spacetime volumes for causally related elements to define causal set analogs of Minkowski inner products. These are used to…
In this article, formulas for the calculation of force and torque between two circular filaments arbitrarily oriented in space were derived by using Kalantarov-Zeitlin's method. Formulas are presented in an analytical form through integral…
Recently, Le Donne and the author introduce a notion of intrinsically Lipschitz graphs in metric spaces. The idea of this paper is to investigate about the properties of the intrinsically Lipschitz constants. More precisely, we give the…