On theL p-bounds for maximal functions associated to convex bodies inR n

1986 ◽  
Vol 54 (3) ◽  
pp. 257-265 ◽  
Author(s):  
J. Bourgain
Keyword(s):  
Convex Bodies ◽  
Maximal Functions

Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle

2005 ◽  
Vol 11 (4) ◽  
pp. 517-525
Author(s):  
Juris Steprāns
Keyword(s):  
Harmonic Analysis ◽  
Set Theory ◽  
Harmonic Functions ◽  
Maximal Functions ◽  
Pigeonhole Principle ◽  
Cardinal Invariants ◽  
Geometric Objects

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.

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
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