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For P and Q polynomials in n variables, |P·Q|_2^2=sum_(i_1,...,i_n>=0)(|P^((i_1,...,i_n))(D_1,...,D_n)Q(x_1,...,x_n)|_2^2)/(i_1!...i_n!), where D_i=partial/partialx_i, |X|_2 ...

The signed deviation is defined by Deltau_i=(u_i-u^_), so the average deviation is Deltau^_=u_i-u^_^_=u_i^_-u^_=0.

The south pole is the point on a sphere with minimum z-coordinate for a given coordinate system. For a rotating sphere like the Earth, the natural coordinate system is ...

The tangent indicatrix of a curve of constant precession is a spherical helix. The equation of a spherical helix on a sphere with radius r making an angle theta with the ...

A catastrophe which can occur for three control factors and one behavior axis. The swallowtail catastrophe is the universal unfolding of singularity f(x)=x^5 with codimension ...

The point of concurrence K of the symmedians, sometimes also called the Lemoine point (in England and France) or the Grebe point (in Germany). Equivalently, the symmedian ...

A trace form on an arbitrary algebra A is a symmetric bilinear form (x,y) such that (xy,z)=(x,yz) for all x,y,z in A (Schafer 1996, p. 24).

An undecahedron is a polyhedron having 11 faces. Examples include those illustrated above and summarized in the following table. F E V name 11 8 17 biaugmented triangular ...

The unit upper half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]>0}.

There is only one point in front of a perspective drawing where its three mutually perpendicular vanishing points appear in mutually perpendicular directions, but such a ...