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The level set of a differentiable function f:R^n->R corresponding to a real value c is the set of points {(x_1,...,x_n) in R^n:f(x_1,...,x_n)=c}. For example, the level set ...

The maximum and minimum of the normal curvature kappa_1 and kappa_2 at a given point on a surface are called the principal curvatures. The principal curvatures measure the ...

The torsion of a space curve, sometimes also called the "second curvature" (Kreyszig 1991, p. 47), is the rate of change of the curve's osculating plane. The torsion tau is ...

The term "total curvature" is used in two different ways in differential geometry. The total curvature, also called the third curvature, of a space curve with line elements ...

The spherical harmonics can be generalized to vector spherical harmonics by looking for a scalar function psi and a constant vector c such that M = del x(cpsi) (1) = psi(del ...

The treewidth is a measure of the count of original graph vertices mapped onto any tree vertex in an optimal tree decomposition. Determining the treewidth of an arbitrary ...

Let f(x,y) be a homogeneous function of order n so that f(tx,ty)=t^nf(x,y). (1) Then define x^'=xt and y^'=yt. Then nt^(n-1)f(x,y) = ...

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 ...

States that for a nondissipative Hamiltonian system, phase space density (the area between phase space contours) is constant. This requires that, given a small time increment ...

In general, "a" calculus is an abstract theory developed in a purely formal way. "The" calculus, more properly called analysis (or real analysis or, in older literature, ...