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The socle of a group G is the subgroup generated by its minimal normal subgroups. For example, the symmetric group S_4 has two nontrivial normal subgroups: A_4 and ...

Socrates is reported to have stated: "One thing I know is that I know nothing."

Let P(1/x) be a linear functional acting according to the formula <P(1/x),phi> = Pint(phi(x))/xdx (1) = ...

The geometry of the Lie group R semidirect product with R^2, where R acts on R^2 by (t,(x,y))->(e^tx,e^(-t)y).

A surface harmonic of degree l which is premultiplied by a factor r^l. Confusingly, solid harmonics are also known as "spherical harmonics" (Whittaker and Watson 1990, p. ...

An odd composite number N is called a Somer-Lucas d-pseudoprime (with d>=1) if there exists a nondegenerate Lucas sequence U(P,Q) with U_0=0, U_1=1, D=P^2-4Q, such that ...

There are (at least) two equations known as Sommerfeld's formula. The first is J_nu(z)=1/(2pi)int_(-eta+iinfty)^(2pi-eta+iinfty)e^(izcost)e^(inu(t-pi/2))dt, where J_nu(z) is ...

where R[mu+nu-lambda+1]>0, R[lambda]>-1, 0<a<b, J_nu(x) is a Bessel function of the first kind, Gamma(x) is the gamma function, and _2F_1(a,b;c;x) is a hypergeometric ...

A local source is a node of a directed graph with no entering edges (Borowski and Borwein 1991, p. 401; left figure), and a global source (often simply called a source) is a ...

A 3-multiperfect number P_3. Six sous-doubles are known (120, 672, 523776, 459818240, 1476304896, and 51001180160; OEIS A005820), and these are believed to comprise all ...