On critical sets of convex polyhedra

Dziechcińska-Halamoda, Z.; Szwiec, W.

doi:10.1007/bf01229330

Cited by 6 publications

(2 citation statements)

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“…The measures of asymmetry for convex bodies, which in principle can be traced back to an early paper by Minkowski [1897], have been studied for a long time [Asplund et al 1962;Besicovitch 1948;Chakerian and Stein 1964;Eggleston 1952;Klee 1953;Rogers and Shephard 1958;Stein 1956]. In particular, after B. Grünbaum formulated in his well-known paper [1963] a general definition of measures of (central) asymmetry (or symmetry), many mathematicians have contributed their efforts to this topic: studying the properties/applications of those known measures of asymmetry [Böröczky 2010;Dziechcińska-Halamoda and Szwiec 1985;Ekström 2000;Gluskin and Litvak 2008;Groemer 2000;Groemer and Wallen 2001;Guo 2005;Guo and Kaijser 1999;Hug and Schneider 2007;Kaiser 1996;Petitjean 2003;Schneider 2009;Soltan 2005;Mizushima 2000;Toth 2009; 2008], looking for new ones or studying other types of measure of asymmetry [Tuzikov et al 2000;Tuzikov et al 1997;Zouaki 2003]. Several such measures, most of which are related to extremal problems, are proposed and investigated.…”

Section: Some Open Problemsmentioning

confidence: 99%

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2015

Pacific J. Math.

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Denote by J the operator of coefficient stripping. We show that for any free convolution semigroup f t W t 0g with finite variance, applying a single stripping produces semicircular evolution with nonzero initial condition, J OE t D ť ; , where ˇ; is the semicircular distribution with meanˇand variance . For more general freely infinitely divisible distributions , expressions of the form Q t arise from stripping Q t , where f. Q t ; t / W t 0g forms a semigroup under the operation of two-state free convolution. The converse to this statement holds in the algebraic setting. Numerous examples illustrating these constructions are computed. Additional results include the formula for generators of such semigroups.

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Section: Some Open Problemsmentioning

confidence: 99%

Untitled

2015

Pacific J. Math.

View full text Add to dashboard Cite

show abstract

“…The measures of asymmetry for convex bodies, which in principle can be traced back to an early paper by Minkowski [1897], have been studied for a long time [Asplund et al 1962;Besicovitch 1948;Chakerian and Stein 1964;Eggleston 1952;Klee 1953;Rogers and Shephard 1958;Stein 1956]. In particular, after B. Grünbaum formulated in his well-known paper [1963] a general definition of measures of (central) asymmetry (or symmetry), many mathematicians have contributed their efforts to this topic: studying the properties/applications of those known measures of asymmetry [Böröczky 2010;Dziechcińska-Halamoda and Szwiec 1985;Ekström 2000;Gluskin and Litvak 2008;Groemer 2000;Groemer and Wallen 2001;Guo 2005;Guo and Kaijser 1999;2002;Hug and Schneider 2007;Kaiser 1996;Petitjean 2003;Schneider 2009;Soltan 2005;Mizushima 2000;Toth 2009;2008], looking for new ones or studying other types of measure of asymmetry [Tuzikov et al 2000;Tuzikov et al 1997;Zouaki 2003]. Several such measures, most of which are related to extremal problems, are proposed and investigated.…”

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confidence: 99%