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 .

he epidemiological study of burned patients in   west azarbalian (1382)   m. khoshkalam [1] ,m.s. jamirzadeh [2] , m.s .     abstract     introduction: bum injuries still produce a significant morbidity and mortality in iran. this study was carried out to show the epidemiology, mortality, and etiological factors of burned patients in province of west azarbaijan.   methods & materials: this stud...

The renin-angiotensin system (RAS) has emerged as one of the essential links in the pathophysiology of vascular disease. Angiotensin (Ang) II, the main peptide of the RAS, was considered as a vasoactive hormone, but in the past years, this view has been modified to a growth factor that regulates cell proliferation/apoptosis and fibrosis. Recently, this view has been enlarged with a novel concep...

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...

Vacuum.-By creating a vacuum the process of decalcification can be characterized as follows: Insoluble calciurn-salts+acid o-soluble calciumsalts+CO2. The carbon dioxide, rapidly extracted, will disturb the balance of the chemical equilibrium, and, according to Le Chatelier, result in an acceleration of the reaction. Waerhaug (1949), however, points out that there will be a more intensive conta...

TheMinkowski sum of two setsA,B ∈ IR, denotedA⊕B, is defined as {a+ b | a ∈ A, b ∈ B}. We describe an efficient and robust implementation for the construction of Minkowski sums of polygons in IR using the convolution of the polygon boundaries. This method allows for faster computation of the sum of non-convex polygons in comparison to the widely-used methods for Minkowski-sum computation that d...

This paper presents a new algorithm for computing the hit point and normal of a ray and a general convex object. The algorithm is loosely based on the the Gilbert-Johnson-Keerthi algorithm for computing the distance between convex objects in the sense that it is applicable to the same family of convex objects and uses the same subalgorithm for computing the closest point of a simplex. Since thi...