The Number of Cylindrical Shells

Given a set P of n points in three dimensions, a cylindrical shell or zone cylinder is formed by two cylindrical cylinders with the same axis such that all points of P are between the two cylinders. We prove that the number of cylindrical shells enclosing P passing through combinatorially different subsets of P has size Omega(n^3) and O(n^4) (previous known bound was O(n^5) )

Effects of fiber and interfacial layer architectures on the thermoplastic response of metal matrix composites

Examined here is the effect of fiber and interfacial layer morphologies on thermal fields in metal matrix composites (MMCs). A micromechanics model based on an arbitrarily layered concentric cylinder configuration is used to calculate thermal stress fields in MMCs subjected to spatially uniform temperature changes. The fiber is modelled as a layered material with isotropic or orthotropic elastic layers, whereas the surrounding matrix, including interfacial layers, is treated as a strain-hardening, elastoplastic, von Mises solid with temperature-dependent parameters. The solution to the boundary-value problem of an arbitrarily layered concentric cylinder under the prescribed thermal loading is obtained using the local/global stiffness matrix formulation originally developed for stress analysis of multilayered elastic media. Examples are provided that illustrate how the morphology of the SCS6 silicon carbide fiber and the use of multiple compliant layers at the fiber/matrix interface affect the evolution of residual stresses in SiC/Ti composites during fabrication cool-down

Circular Cylinders by Four or Five Points in Space

International audienceWe are interested in computing effectively cylinders through 5 points, and in other problems involved in metrology. In particular, we consider the cylinders through 4 points with a fix radius and with extremal radius. For these different problems, we give bounds on the number of solutions and exemples show that these bounds are optimal. Finally, we describe two algebraic methods which can be used here to solve efficiently these problems and some experimentation results

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version

On the number of cylindrical shells

Theme 2 - Genie logiciel et calcul symbolique - Projet PrismeSIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : 14802 E, issue : a.2001 n.4234 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

On The Number Of Cylindrical Shells

Given a set P of n points in three dimensions, a cylindrical shell or zone cylinder is formed by two cylindrical cylinders with the same axis such that all points of P are between the two cylinders. We prove that the number of cylindrical shells enclosing P passing through combinatorially different subsets of P has size\Omega\Gamma ) and O(n ) (previous known bound was O(n^5))

On The Number Of Cylindrical Shells

Given a set P of n points in three dimensions, a cylindrical shell or zone cylinder is formed bytwo cylindrical cylinders with the same axis such that all points of P are between the two cylinders. We prove that the number of cylindrical shells enclosing P passing through combinatorially di#erent subsets of P has size# # and O#n # #previous known bound was O#n ##