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An ordered pair (a,b) of nonnegative integers such that there is some set of a points and b edges whose removal disconnects the graph and there is no set of a-1 nodes and b ...

The apodization function A(x)=cos((pix)/(2a)). Its full width at half maximum is 4a/3. Its instrument function is I(k)=(4acos(2piak))/(pi(1-16a^2k^2)), which has a maximum of ...

The numbers lambda_(nun) in the Gaussian quadrature formula Q_n(f)=sum_(nu=1)^nlambda_(nun)f(x_(nun)).

If P=p:q:r and U=u:v:w are distinct trilinear points, neither lying on a sideline of the reference triangle DeltaABC, then the crosssum of P and U is the point ...

A cube 13-compound can be constructed as the dual of the octahedron 13-compound. It will be implemented in a future version of the Wolfram Language as ...

A cube 35-compound can be constructed as the dual of the octahedron 35-compound. It will be implemented in a future version of the Wolfram Language as ...

An equation of the form y=ax^3+bx^2+cx+d where only one root is real.

The cumulative count of property P for a sequence S_n={a_1,a_2,...,a_n} is a sequence of counts of the numbers of elements a_i with i<=k that satisfy P for k=1, 2, ..., n. ...

Series expansions of the parabolic cylinder functions U(a,x) and W(a,x). The formulas can be found in Abramowitz and Stegun (1972).

Qualitatively, a deep theorem is a theorem whose proof is long, complicated, difficult, or appears to involve branches of mathematics which are not obviously related to the ...