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An ideal I of a partial order P is a subset of the elements of P which satisfy the property that if y in I and x<y, then x in I. For k disjoint chains in which the ith chain ...

In a normal n×n Latin square, the entries in each row and column are chosen from a "global" set of n objects. Like a Latin square, a partial Latin square has no two rows or ...

A rational function P(x)/Q(x) can be rewritten using what is known as partial fraction decomposition. This procedure often allows integration to be performed on each term ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the parabolas of parabolic cylindrical coordinates about the x-axis, ...

A quadratic surface given by the equation x^2+2rz=0.

The scale factors are h_u=h_v=sqrt(u^2+v^2), h_theta=uv and the separation functions are f_1(u)=u, f_2(v)=v, f_3(theta)=1, given a Stäckel determinant of S=u^2+v^2. The ...

A cyclide formed by inversion of a standard torus when inversion sphere is tangent to the torus.

A point p on a regular surface M in R^3 is said to be parabolic if the Gaussian curvature K(p)=0 but S(p)!=0 (where S is the shape operator), or equivalently, exactly one of ...

The map x^' = x+1 (1) y^' = 2x+y+1, (2) which leaves the parabola x^('2)-y^'=(x+1)^2-(2x+y+1)=x^2-y (3) invariant.

The arc length of the parabolic segment y=h(1-(x^2)/(a^2)) (1) illustrated above is given by s = int_(-a)^asqrt(1+y^('2))dx (2) = 2int_0^asqrt(1+y^('2))dx (3) = ...