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Convex cone. A convex cone (light blue). Inside of it, the light red convex cone consists of all points αx + βy with α, β > 0, for the depicted x and y. The curves on the upper right symbolize that the regions are infinite in extent. In linear algebra, a cone —sometimes called a linear cone for distinguishing it from other sorts of cones ...
Recession cone. In mathematics, especially convex analysis, the recession cone of a set is a cone containing all vectors such that recedes in that direction. That is, the set extends outward in all the directions given by the recession cone. [ 1]
NLGI consistency numbers. Common greases are in the range 1 through 3. Those with a NLGI No. of 000 to 1 are used in low viscosity applications. Examples include enclosed gear drives operating at low speeds and open gearing. Grades 0, 1 and 2 are used in highly loaded gearing. Grades 1 through 4 are often used in rolling contact bearings.
Roller cone bit. A roller-cone bit is a drill bit used for drilling through rock that features 2 or 3 abrasive, spinning cones that break up rock and sediment as they grind against it. Roller-cone bits are typically used when drilling for oil and gas. [ 1] A water jet flowing through the bit washes out the rock in a slurry.
Degenerate conic. In geometry, a degenerate conic is a conic (a second-degree plane curve, defined by a polynomial equation of degree two) that fails to be an irreducible curve. This means that the defining equation is factorable over the complex numbers (or more generally over an algebraically closed field) as the product of two linear ...
This means that the cone and the sphere together, if all their material were moved to x = 1, would balance a cylinder of base radius 1 and length 2 on the other side. As x ranges from 0 to 2, the cylinder will have a center of gravity a distance 1 from the fulcrum, so all the weight of the cylinder can be considered to be at position 1. The ...
Cone (algebraic geometry) In algebraic geometry, a cone is a generalization of a vector bundle. Specifically, given a scheme X, the relative Spec. of a quasi-coherent graded OX -algebra R is called the cone or affine cone of R. Similarly, the relative Proj. is called the projective cone of C or R . Note: The cone comes with the -action due to ...
In homological algebra, the mapping cone is a construction on a map of chain complexes inspired by the analogous construction in topology.In the theory of triangulated categories it is a kind of combined kernel and cokernel: if the chain complexes take their terms in an abelian category, so that we can talk about cohomology, then the cone of a map f being acyclic means that the map is a quasi ...