On the number of cylindrical shells
نویسنده
چکیده
Given a set P of n points in three dimensions, a cylindrical shell (or zone cylinder) is formed by two circular 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 Ω(n) and O(n) (the previously known bound was O(n)). As a consequence, the minimum enclosing shell can be found in O(n) time.
منابع مشابه
Buckling of Stiffened Thin-Walled Cylindrical Shells under Axial Compression with Symmetrical Imperfections
This study aimed to investigate the effects of stiffeners on buckling of thin cylindrical shells under uniform axial compression. To this end, more than 300 finite element models of stiffened cylindrical shells were prepared. The variables considered are shell thickness, number, dimension and the location of the vertical and horizontal stiffeners as well as circular symmetrical imperfections. R...
متن کاملEffect of shell axial deformation on flutter of cantilevered cylindrical shells under follower forces
Axial vibration effect of shell particles on dynamic stability of a cantilevered cylindrical shell under an axial follower force was addressed. In spite of free-ended shells, the reduced axial force under this effect cannot be derived analytically. Instead, an approximate method was proposed based on the fact that the static (and harmonic) axial deformation under an axial load in a free-ended b...
متن کاملMiniband formation engineering in GaN/AlN constant total effective radius multi-shells quantum dots and rings with on-center hydrogenic donor impurities
In this work, we have studied the miniband and minigaps of GaN/AlN constant total effective radius multi-shells quantum dots (CTER-MSQDs) and Rings (CTERMSQRs).We have investigated effects of the Hydrogenic donor impurities, quantum dots and rings radii, and the number of wells on miniband formation by sub-band energy calculations. We show that in these systems, minigaps can be created and then...
متن کاملPredicting the buckling Capacity of Steel Cylindrical Shells with Rectangular Stringers under Axial Loading by using Artificial Neural Networks
A parametric study was carried out in order to investigate the buckling capacity of the vertically stiffened cylindrical shells. To this end ANSYS software was used. Cylindrical steel shells with different yield stresses, diameter-to-thickness ratios (D/t) and number of stiffeners were modeled and their buckling capacities were calculated by displacement control nonlinear static analysis. Radi...
متن کاملCalculation of Natural Frequencies of Bi-Layered Rotating Functionally Graded Cylindrical Shells
In this paper, an exact analytical solution for free vibration of rotating bi-layered cylindrical shell composed of two independent functionally graded layers was presented. The thicknesses of the shell layers were assumed to be equal and constant. The material properties of the constituents of bi-layered FGM cylindrical shell were graded in the thickness direction of the layers of the shell ac...
متن کاملDiscrepancies Between Free Vibration of FML and Composite Cylindrical Shells Reinforced by CNTs
In this study, discrepancies between the free vibration of fiber-metal laminate (FML) and composite cylindrical shells reinforced by carbon nanotubes (CNTs) based on Love’s first approximation shell theory have been considered by beam modal function model. The representative volume elements consist of three and four phases for composite and FML structures, respectively, which include fiber, CNT...
متن کامل