We show that for every n ≥ 4, 0 ≤ k ≤ n − 3, p ∈ (0, 3] and every origin-symmetric convex body K in Rn, the function ‖x‖−k 2 ‖x‖ −n+k+p K represents a positive definite distribution on Rn, where ‖·‖2 is the Euclidean norm and ‖·‖K is the Minkowski functional of K. We apply this fact to prove a result of Busemann-Petty type that the inequalities for the derivatives of order (n−4) at zero of X-ra...

and that the same holds if any n— 1 of the signs are replaced by strict inequality. Those unimodular lattices, such as Z , which have only the origin in common with the open cube shall be called critical, as shall the corresponding matrices. Minkowski conjectured, and Hajos [ l ] proved in 1938, that a critical lattice must contain one of the points (5»i, • • • , 5,-»), i = 1, • • • , n. If A i...

We begin the study of billiard dynamics in Finsler geometry. We deduce the Finsler billiard reflection law from the “least action principle”, and extend the basic properties of Riemannian and Euclidean billiards to the Finsler and Minkowski settings, respectively. We prove that the Finsler billiard map is a symplectomorphism, and compute the mean free path of the Finsler billiard ball. For the ...

In this paper we discuss a possible discrete approximation of non-metrical Minkowski distances. The existing approaches for Minkowski metrics considering distance functions based on local neighborhoods are not suitable for this task in their present form. We can overcome this difficulty with considering the minimum of such distance functions. In this way we can take full advantage of the former...

In this paper we will introduce a new method for approximating non-metrical Minkowski distances. The existing approaches for Minkowski metrics considering distance functions based on local neighborhoods are not suitable for this task in their present form. In our approach we can overcome this difficulty with considering the minimum of such distance functions. In this way we can take full advant...

In this paper, we study the C1 Hermite interpolation problem using Minkowski Pythagorean Hodograph (MPH) quartics in R2,1. As a preliminary step, we characterize MPH curves in R2,1 by the roots of the hodographs of their complexified spine curves. We present two schemes for this interpolation problem: one is a subdivision scheme using direct C1 interpolation and the other is a two step scheme u...

Automatic prediction of visual discomfort for stereoscopic videos is important to address the viewing safety issues in stereoscopic displays. In literature, disparity and motion characteristics have been known as major factors of visual discomfort caused by stereoscopic content. For developing an algorithm to accurately predict visual discomfort in stereoscopic videos, this study investigates h...

We consider a deformation of N=1 four dimensional Minkowski superspace where odd coordinates θ do not anticommute. We define supersymmetric and associative star product and show how the remaining (anti)commutation relations among the superspace coordinates are modified. In particular, the even coordinates do not commute as well. We also study chiral and vector superfields and their interactions...

In this work, we used two types of impairments in a psychophysical experiment to measure the overall annoyance and individual strength of three impairment features (fuzzy, blocky, and blurry). The impairments were generated by compressing the original videos with MPEG-2 at two different bitrates: 1.0 and 7.5 Mbps. The heavily compressed videos presented blurry and blocky impairments, while the ...

Abstract. The aim of this paper is to study properties of sections of convex bodies with respect to different types of measures. We present a formula connecting the Minkowski functional of a convex symmetric body K with the measure of its sections. We apply this formula to study properties of general measures most of which were known before only in the case of the standard Lebesgue measure. We ...