An extremal property of the generalized arcsine distribution

Metrika ◽  
2012 ◽  
Vol 76 (3) ◽  
pp. 347-355 ◽  
Author(s):  
Karl Michael Schmidt ◽  
Anatoly Zhigljavsky
Keyword(s):  
Extremal Property ◽  
Arcsine Distribution

An extremal property of the hypersphere

1951 ◽  
Vol 47 (1) ◽  
pp. 245-247 ◽  
Author(s):  
A. M. Macbeath
Keyword(s):  
Convex Body ◽  
Extremal Property ◽  
Plane Case ◽  
Simple Application ◽  
Plane Convex ◽  
Plane Convex Body

It was shown by Sas (1) that, if K is a plane convex body, then it is possible to inscribe in K a convex n-gon occupying no less a fraction of its area than the regular n-gon occupies in its circumscribing circle. It is the object of this note to establish the n-dimensional analogue of Sas's result, giving incidentally an independent proof of the plane case. The proof is a simple application of the Steiner method of symmetrization.

Some Properties of the Arcsine Distribution

1980 ◽  
Vol 75 (369) ◽  
pp. 173-175 ◽  
Author(s):  
Barry C. Arnold ◽  
Richard A. Groeneveld
Keyword(s):  
Arcsine Distribution

INTERPOLATION OF CHEBYSHEV POLYNOMIALS AND INTERACTING FOCK SPACES

2006 ◽  
Vol 09 (03) ◽  
pp. 361-371 ◽  
Author(s):  
IZUMI KUBO ◽  
HUI-HSIUNG KUO ◽  
SUAT NAMLI
Keyword(s):  
Orthogonal Polynomials ◽  
Anderson Model ◽  
Chebyshev Polynomials ◽  
Field Operator ◽  
Parameter Family ◽  
Probability Measures ◽  
Fock Spaces ◽  
Arcsine Distribution ◽  
Multiplicative Renormalization ◽  
Renormalization Method

We discover a family of probability measures μa, 0 < a ≤ 1, [Formula: see text] which contains the arcsine distribution (a = 1) and semi-circle distribution (a = 1/2). We show that the multiplicative renormalization method can be used to produce orthogonal polynomials, called Chebyshev polynomials with one parameter a, which reduce to Chebyshev polynomials of the first and second kinds when a = 1 and 1/2 respectively. Moreover, we derive the associated Jacobi–Szegö parameters. This one-parameter family of probability measures coincides with the vacuum distribution of the field operator of the interacting Fock spaces related to the Anderson model.

On Twisted Odd Graphs

2000 ◽  
Vol 9 (3) ◽  
pp. 227-240
Author(s):  
M. A. FIOL ◽  
E. GARRIGA ◽  
J. L. A. YEBRA
Keyword(s):  
Automorphism Group ◽  
Extremal Property ◽  
Involutive Automorphism ◽  
Basic Properties

The twisted odd graphs are obtained from the well-known odd graphs through an involutive automorphism. As expected, the twisted odd graphs share some of the interesting properties of the odd graphs but, in general, they seem to have a more involved structure. Here we study some of their basic properties, such as their automorphism group, diameter, and spectrum. They turn out to be examples of the so-called boundary graphs, which are graphs satisfying an extremal property that arises from a bound for the diameter of a graph in terms of its distinct eigenvalues.

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