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Given a general quadratic curve Ax^2+Bxy+Cy^2+Dx+Ey+F=0, (1) the quantity X is known as the discriminant, where X=B^2-4AC, (2) and is invariant under rotation. Using the ...

Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not explicitly derive equations for such surfaces. Beauville ...

A multiway system that generates causal networks which are all isomorphic as acyclic digraphs is said to exhibit causal invariance, and the causal network itself is also said ...

A polyhedron dissection (or decomposition) is a dissection of one or more polyhedra into other shapes. Two polyhedra can be dissected into each other iff they have equal Dehn ...

A transformation T (a.k.a., map, function) over a domain D takes the elements X in D to elements Y in T(D), where the range (a.k.a., image) of T is defined as ...

A transformation which has only trivial invariant subsets is said to be ergodic.

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.

An m-ary n-ic polynomial (i.e., a homogeneous polynomial with constant coefficients of degree n in m independent variables).

Theta(G;A)=<theta(a):a in A-1> is an A-invariant solvable p^'-subgroup of G.

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...