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An algorithm for finding roots which retains that prior estimate for which the function value has opposite sign from the function value at the current best estimate of the ...

Let R be a plane region bounded above by a continuous curve y=f(x), below by the x-axis, and on the left and right by x=a and x=b, then the volume of the solid of revolution ...

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 ...

Let f and g be nonnegative and continuous functions on the closed interval [a,b], then the solid of revolution obtained by rotating the curves f(x) and g(x) about the x-axis ...

A nonnegative function g(x,y) describing the "distance" between neighboring points for a given set. A metric satisfies the triangle inequality g(x,y)+g(y,z)>=g(x,z) (1) and ...

The metric dimension beta(G) (Tillquist et al. 2021) or dim(G) (Tomescu and Javid 2007, Ali et al. 2016) of a graph G is the smallest number of nodes required to identify all ...

Given a metric g_(alphabeta), the discriminant is defined by g = det(g_(alphabeta)) (1) = |g_(11) g_(12); g_(21) g_(22)| (2) = g_(11)g_(22)-(g_(12))^2. (3) Let g be the ...

Also known as Kolmogorov entropy, Kolmogorov-Sinai entropy, or KS entropy. The metric entropy is 0 for nonchaotic motion and >0 for chaotic motion.

1. Find a complete system of invariants, or 2. Decide when two metrics differ only by a coordinate transformation. The most common statement of the problem is, "Given metrics ...

The term metric signature refers to the signature of a metric tensor g=g_(ij) on a smooth manifold M, a tool which quantifies the numbers of positive, zero, and negative ...