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F_x[sin(2pik_0x)](k) = int_(-infty)^inftye^(-2piikx)((e^(2piik_0x)-e^(-2piik_0x))/(2i))dx (1) = 1/2iint_(-infty)^infty[-e^(-2pii(k-k_0)x)+e^(-2pii(k+k_0)x)]dx (2) = ...

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 ...

Consider a finite collection of points p=(p_1,...,p_n), p_i in R^d Euclidean space (known as a configuration) and a graph G whose graph vertices correspond to pairs of points ...

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.

The free product G*H of groups G and H is the set of elements of the form g_1h_1g_2h_2...g_rh_r, where g_i in G and h_i in H, with g_1 and h_r possibly equal to e, the ...

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.