Let SH denote the homothety class generated by a convex set S ⊂ R: SH = {a + λS | a ∈ R, λ > 0}. We determine conditions for the Minkowski sum BH + CH or the Minkowski difference BH ∼ CH of homothety classes BH and CH generated by closed convex sets B,C ⊂ R to lie in a homothety class generated by a closed convex set (more generally, in the union of countably many homothety classes generated by...

Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact that does not need the smoothness assumption on P .

Under the extra assumption that the boundary is of class C this was proven by S. Nakajima (= A. Matsumura) in 1926 Theorem 1 solves this problem. For convex bodies with C boundaries and positive curvature Nakajima’s result was generalized by Chakerian [?] in 1967 to “relative geometry” where the width and brightness are measured with with respect to some convex body K0 symmetric about the origi...

Abstract This Graphical Review provides an overview of amide bond activation achieved by selective oxidative addition the N–C(O) acyl to transition metals and nucleophilic addition, resulting in decarbonylative coupling, together with key mechanistic details pertaining distortion underlying this reactivity manifold.

Interest in the toxicological aspects of oxidative stress has grown in recent years, and research has become increasingly focused on the mechanistic aspects of oxidative damage and cellular responses in biological systems. Toxic consequences of oxidative stress at the subcellular level include lipid peroxidation and oxidative damage to DNA and proteins. These effects are often used as end point...

Background: Recent studies have suggested the importance of oxidant/antioxidant status in initiation and progression of breast cancer. The aim of this study was to evaluate oxidative stress markers in breast cancer patients before and after 3 cycles of chemotherapy with adriamycin and cytoxan (AC). Also, in this study the effect of age and the stage of disease on oxidative stress markers were c...