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Let R(x) be the ramp function, then the Fourier transform of R(x) is given by F_x[R(x)](k) = int_(-infty)^inftye^(-2piikx)R(x)dx (1) = i/(4pi)delta^'(k)-1/(4pi^2k^2), (2) ...

The solution to the differential equation [D^(2v)+alphaD^v+betaD^0]y(t)=0 (1) is y(t)={e_alpha(t)-e_beta(t) for alpha!=beta; ...

An early name for calculus of variations. The term is also sometimes used in place of predicate calculus.

A functional differential equation is a differential equation in which the derivative y^'(t) of an unknown function y has a value at t that is related to y as a function of ...

On a Riemannian manifold, there is a unique connection which is torsion-free and compatible with the metric. This connection is called the Levi-Civita connection.

The circles on the polygon diagonals of a complete quadrilateral as diameters are coaxal. Furthermore, the orthocenters of the four triangles of a complete quadrilateral are ...

The class of all regular sequences of particularly well-behaved functions equivalent to a given regular sequence. A distribution is sometimes also called a "generalized ...

The Goldberg graphs are a family of graphs discovered by Goldberg (1981) which are snarks for n=5, 7, 9, .... Precomputed properties of Goldberg graphs are implemented in the ...

Two numbers are heterogeneous if their prime factors are distinct. For example, 6=2·3 and 24=2^3·3 are not heterogeneous since their factors are each (2, 3).

The indefinite summation operator Delta^(-1) for discrete variables, is the equivalent of integration for continuous variables. If DeltaY(x)=y(x), then Delta^(-1)y(x)=Y(x).