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  1. Vor 4 Tagen · We derive a generalised asymptotic model for the flow of a thin fluid film over an arbitrarily-parameterised non-axisymmetric curved substrate surface based on the lubrication approximation. In addition to surface tension, gravity, and centrifugal force, our model incorporates the effects of the Coriolis force and disjoining pressure, together with a non-uniform initial condition, which have ...

  2. Vor 5 Tagen · The reloadable Leitz film canisters, which were common in the 1940s, may be marginally taller than modern commercial 35mm film canisters. Even if the film were perfectly flat (which never happens in any 35mm camera), the Summitar has field curvature, so the best focus curves towards you at the sides of the frame.

  3. Vor 3 Tagen · The evolution equation with curvature regularization that models the motion of a two-dimensional thin film by evaporation-condensation on a rigid substrate is considered. The film is strained due ...

  4. Vor 2 Tagen · hide. (Top) History. Overview. Regular surfaces in Euclidean space. Examples. Local metric structure. Geodesic curves on a surface. Geodesic polar coordinates. Gauss–Bonnet theorem. Surfaces of constant curvature. Riemannian connection and parallel transport. Global differential geometry of surfaces. Reading guide. See also. Notes. References.

  5. en.wikipedia.org › wiki › ParabolaParabola - Wikipedia

    Vor 4 Tagen · The radius of curvature at the origin, which is the vertex of the parabola, is twice the focal length. Corollary A concave mirror that is a small segment of a sphere behaves approximately like a parabolic mirror, focusing parallel light to a point midway between the centre and the surface of the sphere.

  6. Vor 6 Tagen · The quantity κ is a measure of how the tangent vector is changing in the plane, and τ is a measure of how much the curve is twisting out of the osculating plane. Curvature is sometimes written as κ=1/ρ, where ρ is the radius of a circle in the osculating plane whose tangent and curvature exactly match that of the curve at the point.

  7. Vor 5 Tagen · Local Curvature Descent: Squeezing More Curvature out of Standard and Polyak Gradient Descent. We contribute to the growing body of knowledge on more powerful and adaptive stepsizes for convex optimization, empowered by local curvature information.