scholarly journals A Lipschitz condition for the width function of convex bodies in arbitrary Minkowski spaces

2009 ◽  
Vol 22 (1) ◽  
pp. 142-145
Author(s):  
Horst Martini ◽  
Walter Wenzel
Keyword(s):  
Lipschitz Condition ◽  
Convex Bodies ◽  
Minkowski Spaces ◽  
Width Function

scholarly journals A Class of Star-Shaped Bodies

1959 ◽  
Vol 2 (3) ◽  
pp. 175-180 ◽  
Author(s):  
Z.A. Melzak
Keyword(s):  
Surface Area ◽  
Lipschitz Condition ◽  
Convex Bodies ◽  
Nonempty Interior ◽  
Empty Interior ◽  
Selection Principle ◽  
Positive Functions ◽  
Bounded Sets ◽  
Bounded Convex

The more important properties of the class κ of all bounded convex bodies in E3 with non-empty interior include: uniform approximability by polyhedra, existence of volume and surface area, and Blaschke's selection principle, [l ], [2 ]. In this note we define and consider a class ℋ of star-shaped bodies in E3, which enjoys many properties of κ, among them the above-mentioned ones, and is considerably larger. Roughly speaking, ℋ consists of closed bounded sets in E3 with nonempty interior, whose boundary is completely visible from every point of a set with non-empty interior. It turns out that ℋ is identifiable with the class of all real-valued positive functions on the sphere S3 which satisfy a Lipschitz condition.

Universal points of convex bodies and bisectors in Minkowski spaces

2014 ◽  
Vol 14 (3) ◽  
Author(s):  
I. Bárány ◽  
R. Schneider
Keyword(s):  
Convex Bodies ◽  
Minkowski Spaces

scholarly journals Ball convex bodies in Minkowski spaces

2017 ◽  
Vol 289 (2) ◽  
pp. 287-316 ◽  
Author(s):  
Thomas Jahn ◽  
Horst Martini ◽  
Christian Richter
Keyword(s):  
Convex Bodies ◽  
Minkowski Spaces

Titchmarsh's theorem of Hankel transform

2019 ◽  
pp. 11-24
Author(s):  
Mohamed-Ahmed Boudref
Keyword(s):  
Number Theory ◽  
Data Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Analytic Number Theory ◽  
Hankel Transform ◽  
Partial Differential ◽  
Analytic Number ◽  
Bessel Transform

Hankel transform (or Fourier-Bessel transform) is a fundamental tool in many areas of mathematics and engineering, including analysis, partial differential equations, probability, analytic number theory, data analysis, etc. In this article, we prove an analog of Titchmarsh's theorem for the Hankel transform of functions satisfying the Hankel-Lipschitz condition.

Excess entropy of the systems of molecules differing in size and shape

1983 ◽  
Vol 48 (1) ◽  
pp. 192-198 ◽  
Author(s):  
Tomáš Boublík
Keyword(s):  
Equation Of State ◽  
Hard Spheres ◽  
Excess Entropy ◽  
Convex Bodies ◽  
Pure Substance ◽  
Liquid Equilibrium ◽  
Simple Rules ◽  
Different Shapes ◽  
The Mean

The excess entropy of mixing of mixtures of hard spheres and spherocylinders is determined from an equation of state of hard convex bodies. The obtained dependence of excess entropy on composition was used to find the accuracy of determining ΔSE from relations employed for the correlation and prediction of vapour-liquid equilibrium. Simple rules were proposed for establishing the mean parameter of nonsphericity for mixtures of hard bodies of different shapes allowing to describe the P-V-T behaviour of solutions in terms of the equation of state fo pure substance. The determination of ΔSE by means of these rules is discussed.

scholarly journals Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

2020 ◽  
Vol 26 (1) ◽  
pp. 67-77 ◽  
Author(s):  
Silvestru Sever Dragomir
Keyword(s):  
Euclidean Space ◽  
Convex Functions ◽  
Convex Bodies ◽  
Integral Inequalities ◽  
Divergence Theorem ◽  
Several Variables ◽  
Type Integral ◽  
Bounded Convex

AbstractIn this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space {\mathbb{R}^{n}} for any {n\geq 2}.

Masslessness and light-cone propagation in 3+2 de Sitter and 2+1 Minkowski spaces

1986 ◽  
Vol 33 (2) ◽  
pp. 415-420 ◽  
Author(s):  
M. Flato ◽  
C. Fronsdal ◽  
J. P. Gazeau
Keyword(s):  
Light Cone ◽  
De Sitter ◽  
Minkowski Spaces
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