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The solution to the differential equation [D^(2v)+alphaD^v+betaD^0]y(t)=0 (1) is y(t)={e_alpha(t)-e_beta(t) for alpha!=beta; ...

A closed curve associated with a knot which is displaced along the normal by a small amount. For a knot K parameterized as x^mu(s) for 0<=s<=L along the length of the knot by ...

If F is a group, then the extensions G of F of order o with G/phi(G)=F, where phi(G) is the Frattini subgroup, are called Frattini extensions.

A group given by G/phi(G), where phi(G) is the Frattini subgroup of a given group G.

The intersection phi(G) of all maximal subgroups of a given group G.

A semigroup with a noncommutative product in which no product can ever be expressed more simply in terms of other elements.

Two closed simply connected 4-manifolds are homeomorphic iff they have the same bilinear form beta and the same Kirby-Siebenmann invariant kappa. Any beta can be realized by ...

A group acts freely if there are no group fixed points. A point which is fixed by every group element would not be free to move.

Pick any point P on a conic section, and draw a series of right angles having this point as their vertices. Then the line segments connecting the rays of the right angles ...

The French metro metric is an example for disproving apparently intuitive but false properties of metric spaces. The metric consists of a distance function on the plane such ...