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A point at which the flux is outgoing has positive divergence, and is often called a "source" of the field. A point at which the flux is directed inward has negative divergence, and is often called a "sink" of the field. The greater the flux of field through a small surface enclosing a given point, the greater the value of divergence at that point.
This means that the rank at the critical point is lower than the rank at some neighbour point. In other words, let k be the maximal dimension of the open balls contained in the image of f; then a point is critical if all minors of rank k of f are zero. In the case where m = n = k, a point is critical if the Jacobian determinant is zero.
Named after economists Orris C. Herfindahl and Albert O. Hirschman, it is an economic concept widely applied in competition law, antitrust regulation, [1] and technology management. [2] HHI has continued to be used by antitrust authorities, primarily to evaluate and understand how mergers will affect their associated markets. [3]
where Φ 1 and Φ 2 are the flux out of surfaces S 1 and S 2, Φ 31 is the flux through S 3 out of volume 1, and Φ 32 is the flux through S 3 out of volume 2. The point is that surface S 3 is part of the surface of both volumes. The "outward" direction of the normal vector ^ is opposite for each volume, so the flux out of one through S 3 is ...
In mathematics the division polynomials provide a way to calculate multiples of points on elliptic curves and to study the fields generated by torsion points. They play a central role in the study of counting points on elliptic curves in Schoof's algorithm .
In mathematics, divided differences is an algorithm, historically used for computing tables of logarithms and trigonometric functions. [citation needed] Charles Babbage's difference engine, an early mechanical calculator, was designed to use this algorithm in its operation.
In coordinate geometry, the Section formula is a formula used to find the ratio in which a line segment is divided by a point internally or externally. [1] It is used to find out the centroid, incenter and excenters of a triangle. In physics, it is used to find the center of mass of systems, equilibrium points, etc. [2] [3] [4] [5]
An illustration of the five-point stencil in one and two dimensions (top, and bottom, respectively). In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors".