Blaschke Valuations

Valuations on Log-Concave Functions

A classification of SL(n) and translation covariant Minkowski valuations on log-concave functions is established. The moment vector and the recently introduced level set body of log-concave functions are characterized. Furthermore, analogs of the Euler characteristic and volume are characterized as SL(n) and translation invariant valuations on log-concave functions. 2000 AMS subject classificat...

Intersection Bodies and Valuations

All GL (n) covariant star-body-valued valuations on convex polytopes are completely classified. It is shown that there is a unique nontrivial such valuation. This valuation turns out to be the so-called “intersection operator”—an operator that played a critical role in the solution of the Busemann-Petty problem. Introduction. A function Z defined on the set K of convex bodies (that is, of conve...

Quotient BCI-algebras induced by pseudo-valuations

In this paper, we study pseudo-valuations on a BCI-algebra and obtain some related results. The relation between pseudo-valuations and ideals is investigated. We use a pseudo-metric induced by a pseudovaluation to introduce a congruence relation on a BCI-algebra. We define the quotient algebra induced by this relation and prove that it is also a BCI-algebra and study its properties.

Realization of a Certain Class of Semi-Groups as Value Semi-Groups of Valuations

α Valuations of Special Classes of Quadratic Graphs