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A complex translation is a map of the form z|->z+a, where a is a fixed complex number, which corresponds to translation (shifting) of points the complex plane by the complex ...

The rank of a graph G is defined as r(G)=n-c, where n is the number of vertices on G and c is the number of connected components (Biggs 1993, p. 25).

As shown by Schur (1916), the Schur number S(n) satisfies S(n)<=R(n)-2 for n=1, 2, ..., where R(n) is a Ramsey number.

For a subgroup H of a group G, the index of H, denoted (G:H), is the cardinal number of the set of left cosets of H in G (which is equal to the cardinal number of the set of ...

An element of an extension field of a field F which is not algebraic over F. A transcendental number is a complex number which is transcendental over the field Q of rational ...

The real part R[z] of a complex number z=x+iy is the real number not multiplying i, so R[x+iy]=x. In terms of z itself, R[z]=1/2(z+z^_), where z^_ is the complex conjugate of ...

Let S(x) denote the number of positive integers not exceeding x which can be expressed as a sum of two squares (i.e., those n<=x such that the sum of squares function ...

The common logarithm is the logarithm to base 10. The notation logx is used by physicists, engineers, and calculator keypads to denote the common logarithm. However, ...

A flexagon made by folding a strip into adjacent equilateral triangles. The number of states possible in a hexaflexagon is the Catalan number C_5=42.

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges ...