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For the Helmholtz differential equation to be separable in a coordinate system, the scale factors h_i in the Laplacian del ...

If pi on V and pi^' on V^' are irreducible representations and E:V|->V^' is a linear map such that pi^'(g)E=Epi(g) for all g in and group G, then E=0 or E is invertible. ...

Separation of variables is a method of solving ordinary and partial differential equations. For an ordinary differential equation (dy)/(dx)=g(x)f(y), (1) where f(y)is nonzero ...

The distance a point moves due to shear divided by the perpendicular distance of a point from the invariant line.

Let f_1(z), ..., f_m(z) for m>=1 be a set of E-functions that (1) form a solution of the system of differential equations y_k^'=q_(k0)+sum_(j=1)^mq_(kj)y_j for q_(kj) in C(z) ...

Consider (1) If the probability distribution is governed by a Markov process, then P_3(y_1,t_1;y_2,t_2|y_3,t_3) = P_2(y_2,t_2|y_3,t_3) (2) = P_2(y_2|y_3,t_3-t_2). (3) ...

A square grid is a grid formed by tiling the plane regularly with squares.

Strong convergence is the type of convergence usually associated with convergence of a sequence. More formally, a sequence {x_n} of vectors in a normed space (and, in ...

A number of attractive 20-compounds of the regular tetrahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...

Tetrahedron picking is the process of picking tetrahedra at random within a given shape in 3 or higher dimensions. The most natural definition of a random tetrahedron is one ...