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A conservative vector field (for which the curl del xF=0) may be assigned a scalar potential where int_CF·ds is a line integral.

A function A such that B=del xA. The most common use of a vector potential is the representation of a magnetic field. If a vector field has zero divergence, it may be ...

The parameter r (sometimes also denoted mu) in the logistic equation x_(n+1)=rx_n(1-x_n).

The Kähler potential is a real-valued function f on a Kähler manifold for which the Kähler form omega can be written as omega=ipartialpartial^_f. Here, the operators ...

The following conditions are equivalent for a conservative vector field on a particular domain D: 1. For any oriented simple closed curve C, the line integral ∮_CF·ds=0. 2. ...

An algorithm for finding the nearest local minimum of a function which presupposes that the gradient of the function can be computed. The method of steepest descent, also ...

Lagrange multipliers, also called Lagrangian multipliers (e.g., Arfken 1985, p. 945), can be used to find the extrema of a multivariate function f(x_1,x_2,...,x_n) subject to ...

If del xF=0 (i.e., F(x) is an irrotational field) in a simply connected neighborhood U(x) of a point x, then in this neighborhood, F is the gradient of a scalar field phi(x), ...

A method of stochastic optimization including techniques such as gradient search or Robbins-Monro stochastic approximation.

For a smooth harmonic map u:M->N, where del is the gradient, Ric is the Ricci curvature tensor, and Riem is the Riemann tensor.