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In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.

A smooth curve is a curve which is a smooth function, where the word "curve" is interpreted in the analytic geometry context. In particular, a smooth curve is a continuous ...

A smooth function is a function that has continuous derivatives up to some desired order over some domain. A function can therefore be said to be smooth over a restricted ...

A surface parameterized in variables u and v is called smooth if the tangent vectors in the u and v directions satisfy T_uxT_v!=0, where AxB is a cross product.

A polyhedron with extra triangular faces, given by the Schläfli symbol s{p; q}.

Johnson solid J_(85).

The socle of a group G is the subgroup generated by its minimal normal subgroups. For example, the symmetric group S_4 has two nontrivial normal subgroups: A_4 and ...

Socrates is reported to have stated: "One thing I know is that I know nothing."

Let P(1/x) be a linear functional acting according to the formula <P(1/x),phi> = Pint(phi(x))/xdx (1) = ...

The geometry of the Lie group R semidirect product with R^2, where R acts on R^2 by (t,(x,y))->(e^tx,e^(-t)y).