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Axisymmetric Viscous Fluid Motions Around Conical Surfaces
SIAM Journal on Applied Mathematics, 1966Abstract : The introduction of complex Navier-Stokes equations shows that steady axisymmetric motions of viscous incompressible fluids around conical surfaces can be expressed in terms of the corresponding general solution of the Stokes equations of slow motions.
Schwiderski, E. W. +2 more
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Uniformizing Surfaces with Conical Singularities
2015We consider a class of singular equations, motivated by the problem of prescribing the Gaussian curvature, as well as from some models in theoretical physics such as self-dual Chern–Simons theory or Electroweak theory: our goal is to prove existence results by attacking the problem variationally, using suitable improvements of the Moser–Trudinger ...
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Conic Constant and Paraxial Radius of Curvature Measurements, for Conic Surfaces.
Optical Fabrication and Testing Workshop, 1985A technique was developed1 to find the profile of a conic surface, along one diameter. In this method it is necessary to - determine a set of values of the longitudinal aberration2, X, - and the corresponding angles, θ. For this method one assumes - that the values of the paraxial radius of curvature, r, and the conic constant, k, are known, and they ...
R. Díaz-Uribe +3 more
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Conic-like subdivision curves on surfaces
The Visual Computer, 2012In this paper, we introduce a novel nonlinear curve subdivision scheme, suitable for designing curves on surfaces. The scheme is based on the concept of geodesic conic Bezier curves, which represents a natural extension of geodesic Bezier curves for the rational quadratic case.
Jorge Estrada Sarlabous +4 more
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Aberrations of a Conic Surface
20116.1 Introduction So far, we have considered the aberrations of spherical surfaces, which are conic surfaces of zero eccentricity. In this chapter, we discuss the aberrations of a conic surface with an arbitrary value of eccentricity. Our starting point is imaging by and aberrations of a spherical surface discussed in Sections 1.8 and 4.2.
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Lagrange interpolation on the conical surface
SCIENTIA SINICA Mathematica, 2015Summary: In this paper, we apply the superposition interpolation process and the factorization methods to discuss the well-posedness of Lagrange interpolation on the conical surface. Several ways to construct the properly posed set of nodes for Lagrange interpolation on the conical surface are proposed by choosing proper points along generatrices ...
Liang, Xuezhang, Li, Qiang, Liu, Chang
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Surface Sag and Conic Sections
2018During the process of optical system design and layout, it is often necessary to determine the depth, or sag, of an optical surface at some specific height (aperture radius). For example, consider the configuration of a simple lens cell, as shown in Figure G.1(a).
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