Related papers: Volume difference inequalities
We prove a limit theorem for the the maximal interpoint distance (also called the diameter) for a sample of n i.i.d. points in the unit ball of dimension 2 or more. The exact form of the limit distribution and the required normalisation are…
We establish an inequality comparing the height and the $\chi$-arithmetic volume of toric metrized divisors on $\mathbb{P}^1_{\mathbb{Q}}$. This gives a partial answer to a question of Burgos, Moriwaki, Philippon and Sombra ([5, remark…
The defect of valued field extensions is a major obstacle in open problems in resolution of singularities and in the model theory of valued fields, whenever positive characteristic is involved. We continue the detailed study of defect…
We solve several new sharp inequalities relating three quantities amongst the area, perimeter, inradius, circumradius, diameter, and minimal width of planar convex bodies. As a consequence, we narrow the missing gaps in each of the missing…
We consider a heat equation and a wave equation in a spatial interval over a time interval. This article deals with inverse problems of determining sizes of spatial intervals by extra boundary data of solutions of the governing equations.…
We define the lower and upper mutual dimensions $mdim(x:y)$ and $Mdim(x:y)$ between any two points $x$ and $y$ in Euclidean space. Intuitively these are the lower and upper densities of the algorithmic information shared by $x$ and $y$. We…
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
What distributions arise as the distribution of the distance between two typical points in some measured metric space? This seems to be a surprisingly subtle problem. We conjecture that every distribution with a density function whose…
Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…
This note provides a simple proof for the equality between the normalized volume of a convex polytope with $m$ vertices and the mixed volume of $m$ simplices and thus shows the seemingly restrictive problem of computing mixed volume of…
Several recent studies have been devoted to investigating the limitations that ordinary quantum mechanics and/or quantum gravity might impose on the measurability of space-time observables. These analyses are often confined to the…
The concept of a hyperuniformity disorder length $h$ was recently introduced for analyzing volume fraction fluctuations for a set of measuring windows. This length permits a direct connection to the nature of disorder in the spatial…
In this paper, following the method of Cheng-Li-Yau, we first modify the coefficients in the constant $B_n$ to improve the volume gap. Further, we also enlarge our gap by applying an estimate of Cheng-Yang for eigenvalues of Laplacian.
Some extensions of an inequality from IMO'2001 are proven by means of the Lagrange multiplier criterion.
Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…
We extend a newly developed formal system for the description of astrophysical maps. In this formalism, we consider the difference between maps to be the distance between elements of a pseudometric space (the space of all such maps). This…
We establish the log-concavity of the volume of central sections of dilations of the cross-polytope (the strong B-inequality for the cross-polytope and Lebesgue measure restricted to an arbitrary subspace).
Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to the…
We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of a strictly stationary orthomartingale random field. These inequalities can be used to establish complete convergence of…
In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.