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The cylinder function is defined as C(x,y)={1 for sqrt(x^2+y^2)<=a; 0 for sqrt(x^2+y^2)>a. (1) The Bessel functions are sometimes also called cylinder functions. To find the ...

The normal to an ellipse at a point P intersects the ellipse at another point Q. The angle corresponding to Q can be found by solving the equation (P-Q)·(dP)/(dt)=0 (1) for ...

Let E be an elliptic curve defined over the field of rationals Q(sqrt(-d)) having equation y^2=x^3+ax+b with a and b integers. Let P be a point on E with integer coordinates ...

The sequence of numbers obtained by letting a_1=2, and defining a_n=lpf(1+product_(k=1)^(n-1)a_k) where lpf(n) is the least prime factor. The first few terms are 2, 3, 7, 43, ...

A graphoid consists of a set M of elements together with two collections C and D of nonempty subsets of M, called circuits and cocircuits respectively, such that 1. For any C ...

The group algebra K[G], where K is a field and G a group with the operation *, is the set of all linear combinations of finitely many elements of G with coefficients in K, ...

A presentation of a group is a description of a set I and a subset R of the free group F(I) generated by I, written <(x_i)_(i in I)|(r)_(r in R)>, where r=1 (the identity ...

A homogeneous space M is a space with a transitive group action by a Lie group. Because a transitive group action implies that there is only one group orbit, M is isomorphic ...

The notion of an inverse is used for many types of mathematical constructions. For example, if f:T->S is a function restricted to a domain S and range T in which it is ...

Let S be a mathematical statement, then the Iverson bracket is defined by [S]={0 if S is false; 1 if S is true, (1) and corresponds to the so-called characteristic function. ...