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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.

An occurrence of a variable in a logic formula which is not inside the scope of a quantifier.

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 ...