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Graph smoothing, also known as smoothing away or smoothing out, is the process of replacing edges e^'=v_iv_j and e^('')=v_jv_k incident at a vertex v_j of vertex degree 2 by ...

The gyrate rhombicosidodecahedron is a convex equilateral solid obtained by rotating one of the pentagonal cupolas of a small rhombicosidodecahedron by 1/10 of a turn. It is ...

Any locally compact Hausdorff topological group has a unique (up to scalars) nonzero left invariant measure which is finite on compact sets. If the group is Abelian or ...

The equations defined by q^. = (partialH)/(partialp) (1) p^. = -(partialH)/(partialq), (2) where p^.=dp/dt and q^.=dq/dt is fluxion notation and H is the so-called ...

The Hankel functions of the first kind are defined as H_n^((1))(z)=J_n(z)+iY_n(z), (1) where J_n(z) is a Bessel function of the first kind and Y_n(z) is a Bessel function of ...

Given collinear points W, X, Y, and Z, Y and Z are harmonic conjugates with respect to W and X if (|WY|)/(|YX|)=(|WZ|)/(|XZ|). (1) W and X are also harmonic conjugates with ...

A harmonic series is a continued fraction-like series [n;a,b,c,...] defined by x=n+1/2(a+1/3(b+1/4(c+...))) (Havil 2003, p. 99). Examples are given in the following table. c ...

Let a straight line AB be divided internally at C and externally at D in the same ratio, so that (AC)/(CB)=-(AD)/(DB). Then AB is said to be divided harmonically at C and D ...

A Hasse diagram is a graphical rendering of a partially ordered set displayed via the cover relation of the partially ordered set with an implied upward orientation. A point ...

The hat is a caret-shaped symbol commonly placed on top of variables to give them special meaning. The symbol x^^ is voiced "x-hat" (or sometimes as "x-roof") in mathematics, ...