scholarly journals Kotrbatý’s theorem on valuations and geometric inequalities for convex bodies

2021 ◽  
Author(s):  
Semyon Alesker
Keyword(s):  
Convex Bodies ◽  
Geometric Inequalities

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}.

ON THE VOLUME RATIO OF TWO CONVEX BODIES

2002 ◽  
Vol 34 (06) ◽  
pp. 703-707 ◽  
Author(s):  
A. GIANNOPOULOS ◽  
M. HARTZOULAKI
Keyword(s):  
Convex Bodies ◽  
Volume Ratio

Double normals of convex bodies

1964 ◽  
Vol 2 (2) ◽  
pp. 71-80 ◽  
Author(s):  
Nicolaas H. Kuiper
Keyword(s):  
Convex Bodies
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