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An n-dimensional (convex) polytope is said to have few vertices if their number does not exceed n + 3. Similarly, a simplicial n-sphere with few vertices would not contain more than n + 4 of them. We want to show that all such spheres are realizable as boundary complexes of polytopes.
The Doyen vaginal retractor and the Babcock forceps have been modified so as to facilitate exposure of the abdominal esophagus and identification of the diaphragmatic crura. The use of these two instruments in the transabdominal repair of hiatus hernia is described.
In this paper, we study simplicial complexes as higher-dimensional graphs in order to produce algebraic statements about their facet ideals. We introduce a large class of square-free monomial ideals with Cohen–Macaulay quotients, and a criterion for the Cohen–Macaulayness *Air Max 2014 Mens* of facet ideals of simplicial trees. Along the way, we generalize several concepts from graph theory to simplicial *Nike Air Force Canada Edition* complexes.
A non-linear analysis for finite strain and stress has been developed and applied to symmetrical deformations around cylindrical and spherical cavities in rock. The material non-linearity which is involved may result from either elastic or plastic properties. A drastic analytical simplification reduces the problem to the solution of a first order differential equation. Fracture is analyzed.