Related papers: Volume difference inequalities
Comparison of $1$-dimensional distance functions is a basic tool in Alexandrov geometry and it is used to characterize spaces with curvature bounded above or below. For the zero curvature bound there is a differential inequality which…
The main objective of the paper is to establish explicit estimates on some applicable inequalities in two variables on time scales which can be used in the study of certain qualitative properties of dynamical equations on time scales.
We obtain estimates of all components of the velocity of a 3D rigid body moving in a viscous incompressible fluid without any symmetry restriction on the shape of the rigid body or the container. The estimates are in terms of suitable norms…
In this paper we deal with problems concerning the volume of the convex hull of two "connecting" bodies. After a historical background we collect some results, methods and open problems, respectively.
In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex bodies. The original inequalities provide an optimal relation between the volume of a convex body and the volume of…
Formulae for the line-of-sight and transverse comoving distances, proper motion distance, angular diameter distance, luminosity distance, k-correction, distance modulus, comoving volume, lookback time, age, and object intersection…
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…
We study the class of (locally) anti-blocking bodies as well as some associated classes of convex bodies. For these bodies, we prove geometric inequalities regarding volumes and mixed volumes, including Godberson's conjecture, near-optimal…
We present a family of Bell inequalities for three parties and arbitrarily many outcomes, which can be seen as a natural generalization of the Mermin Bell inequality. For a small number of outcomes, we verify that our inequalities define…
This paper is devoted to the study of a discrepancy-type characteristic -- the fixed volume discrepancy -- of the Korobov point sets in the unit cube. It was observed recently that this new characteristic allows us to obtain optimal rate of…
Motivated by conjectures of Mahler and Makai Jr., we study bounds on the volume of a convex body in terms of the successive minima of its polar body.
Available algorithms for the initialization of volume fractions typically utilize exact functions to model fluid interfaces, or they rely on computationally costly intersections between volume meshes. Here, a new algorithm is proposed that…
Distances play important roles in cosmological observations, especially in gravitational lens systems, but there is a problem in determining distances because they are defined in terms of light propagation, which is influenced…
Using the translation method of Tartar, Murat, Lurie, and Cherkaev bounds are derived on the volume occupied by an inclusion in a three-dimensional conducting body. They assume electrical impedance tomography measurements have been made for…
In this paper, we prove that two different observers don't equally measure the distance between two points A and B. For this, we introduce some postulates and obtain a new formula to show distance between A and B. In this formula, radius of…
We prove various inequalities measuring how far from an isometry a local map from a manifold of high curvature to a manifold of low curvature must be. We consider the cases of volume-preserving, conformal and quasi-conformal maps. The…
We use the theory of calibrations to write the equation of a minimal volume vector field on a given Riemann surface.
We prove that a bounded open set U in Euclidean n-space has k-width less than C(n) Volume(U)^{k/n}. Using this estimate, we give lower bounds for the k-dilation of degree 1 maps between certain domains in Euclidean space. In particular, we…
In the calculation of the formation enthalpy of a defect, a stress term accompanying the formation volume of the defect appears. This formation volume is conventionally interpreted as the difference in volume between crystals with and…
The isoperimetric problem asks for the maximum area of a region of given perimeter. It is natural to consider other measurements of a region, such as the diameter and width, and ask for the extreme value of one when another is fixed. The…