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A special ideal in a commutative ring R. The Jacobson radical is the intersection of the maximal ideals in R. It could be the zero ideal, as in the case of the integers.

Suppose that {f_n} is a sequence of measurable functions, that f_n->f pointwise almost everywhere as n->infty, and that |f_n|<=g for all n, where g is integrable. Then f is ...

For a group G, consider a subgroup H with elements h_i and an element x of G not in H, then xh_i for i=1, 2, ... constitute the left coset of the subgroup H with respect to x.

For a given function f(x) over a partition of a given interval, the lower sum is the sum of box areas m^*Deltax_k using the infimum m of the function f(x) in each subinterval ...

The result of a matrix multiplication.

A_m(lambda)=int_(-infty)^inftycos[1/2mphi(t)-lambdat]dt, (1) where the function phi(t)=4tan^(-1)(e^t)-pi (2) describes the motion along the pendulum separatrix. Chirikov ...

An octic curve is an algebraic curve of order eight. The pear curve is an example of an octic curve.

The symbol % used to indicate percent.

The symbol "+" which is used to denote a positive number or to indicate addition.

A polybe is a polyform formed from a polycubes by removing of half of each cube such that at least half of the original join between cubes is retained. The numbers of polybes ...