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Gauss stated the reciprocity theorem for the case n=4 x^4=q (mod p) (1) can be solved using the Gaussian integers as ...

Any bounded planar region with positive area >A placed in any position of the unit square lattice can be translated so that the number of lattice points inside the region ...

A Borel set is an element of a Borel sigma-algebra. Roughly speaking, Borel sets are the sets that can be constructed from open or closed sets by repeatedly taking countable ...

A Banach space X has the approximation property (AP) if, for every epsilon>0 and each compact subset K of X, there is a finite rank operator T in X such that for each x in K, ...

Tracing through the connections of a branchial graph gives rise to the notion of a kind of space in which states on different branches of history are laid out. In particular, ...

The least number of unknotted arcs lying above the plane in any projection. The knot 05-002 has bridge number 2. Such knots are called 2-bridge knots. There is a one-to-one ...

A Tschirnhausen transformation can be used to take a general quintic equation to the form x^5-x-a=0, where a may be complex.

Brown numbers are pairs (m,n) of integers satisfying the condition of Brocard's problem, i.e., such that n!+1=m^2 where n! is the factorial and m^2 is a square number. Only ...

The Bump-Ng theorem (and also the title of the paper in which it was proved) states that the zeros of the Mellin transform of Hermite functions have real part equal to 1/2.

Gives a matrix representation b_i of a braid group in terms of (n-1)×(n-1) matrices. A -t always appears in the (i,i) position. b_1 = [-t 0 0 ... 0; -1 1 0 ... 0; 0 0 1 ... ...