MIXED CHORD-INTEGRALS OF STAR BODIES

Star integrals and unbiased estimators

We review in brief the development and implementation of the Star integral, a tool yielding measurements of correlations much superior to conventional methods. A version for use in pion interferometry is explained. We also show how effects of nonpoissonian overall multiplicity distributions may be eliminated if desired and quote results eliminating statistical biases arising in correlation meas...

On Mixed Brightness-integrals

We establish the greatest upper bound for the product of the i-th brightness-integrals of a convex body and its polar dual. Further, the greatest upper bound for the product of the brightness-integrals of order p of a convex body and its polar dual is also given.

Detecting Symmetry in Star Bodies

Let K be a convex body in R, i.e. a compact convex set with a non-empty interior. We say that K is origin-symmetric if K = −K. The presence of origin-symmetry is an essential assumption in various problems. Many results that hold for origin-symmetric convex bodies fail in the absence of the symmetry condition. For example, origin-symmetric convex bodies are uniquely determined by the volumes of...

New inequalities for star bodies

Mixed Integrals and Related Inequalities

In this paper we define an addition operation on the class of quasiconcave functions. While the new operation is similar to the well-known supconvolution, it has the property that it polarizes the Lebesgue integral. This allows us to define mixed integrals, which are the functional analogs of the classic mixed volumes. We extend various classic inequalities, such as the Brunn-Minkowski and the ...