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One of a set of numbers defined in terms of an invariant generated by the finite cyclic covering spaces of a knot complement. The torsion numbers for knots up to 9 crossings ...

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 mathematical structure A is said to be closed under an operation + if, whenever a and b are both elements of A, then so is a+b. A mathematical object taken together with ...

Given a group with elements A and X, there must be an element B which is a similarity transformation of A,B=X^(-1)AX so A and B are conjugate with respect to X. Conjugate ...

Let G be a group with normal series (A_0, A_1, ..., A_r). A normal factor of G is a quotient group A_(k+1)/A_k for some index k<r. G is a solvable group iff all normal ...

A point lattice is a regularly spaced array of points. In the plane, point lattices can be constructed having unit cells in the shape of a square, rectangle, hexagon, etc. ...

Let L be an extension field of K, denoted L/K, and let G be the set of automorphisms of L/K, that is, the set of automorphisms sigma of L such that sigma(x)=x for every x in ...

A group G is said to act on a set X when there is a map phi:G×X->X such that the following conditions hold for all elements x in X. 1. phi(e,x)=x where e is the identity ...