We prove that the reciprocal of the volume of the polar bodies, about the Santaló point, of a shadow system of convex bodies Kt, is a convex function of t. Thus extending to the non-symmetric case a… (More)

We give a description of an affine mapping T involving contact pairs of two general convex bodies K and L, when T (K) is in a position of maximal volume in L. This extends the classical John’s… (More)

Grünbaum introduced measures of symmetry for convex bodies that measure how far a given convex body is from a centrally symmetric one. Here, we introduce new measures of symmetry that measure how far… (More)

We establish new functional versions of the Blaschke-Santaló inequality on the volume product of a convex body which generalize to the non-symmetric setting an inequality of K. Ball [2] and we give a… (More)

The MAGIC telescope observed the region around the distant blazar 3C 66A for 54.2 hr in 2007 August–December. The observations resulted in the discovery of a γ-ray source centered at celestial… (More)

We answer in the negative a question by Grünbaum who asked if there exists a finite basis of affine invariant points. We give a positive answer to another question by Grünbaum about the “size” of the… (More)

Marked lipid deposits selectively localized in the grooves of so-called aortic functional structures were found in a 5-month-old infant who died of rapidly progressing crescentic glomerulonephritis.… (More)

We find properties that a class € of closed bounded convex subsets of a Banach space E and a mapping p : £ —► R+ should satisfy in order to obtain the following result: Theorem. Let <£ and p:i-»E+… (More)

Mots clés : cGVHD / kératoacanthome / laser Abstract – Introduction: The oral mucosa is involved in 80% of patients with chronic Graft Versus Host Disease (cGVHD). Oral mucous keratoacanthoma (KA)… (More)