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A ring homomorphism is a map f:R->S between two rings such that 1. Addition is preserved:f(r_1+r_2)=f(r_1)+f(r_2), 2. The zero element is mapped to zero: f(0_R)=0_S, and 3. ...

The negative derivative S(v)=-D_(v)N (1) of the unit normal N vector field of a surface is called the shape operator (or Weingarten map or second fundamental tensor). The ...

The set of "critical values" of a map u:R^n->R^n of map class C^1 has Lebesgue measure 0 in R^n.

An attracting set that has zero measure in the embedding phase space and has fractal dimension. Trajectories within a strange attractor appear to skip around randomly. A ...

The Bonne projection is a map projection that resembles the shape of a heart. Let phi_1 be the standard parallel, lambda_0 the central meridian, phi be the latitude, and ...

The Mercator projection is a map projection that was widely used for navigation since loxodromes are straight lines (although great circles are curved). The following ...

Let A_(k,i)(n) denote the number of partitions into n parts not congruent to 0, i, or -i (mod 2k+1). Let B_(k,i)(n) denote the number of partitions of n wherein 1. 1 appears ...

The study of map projections and the making of geographical maps.

If {f_n} is a sequence of nonnegative measurable functions, then intlim inf_(n->infty)f_ndmu<=lim inf_(n->infty)intf_ndmu. (1) An example of a sequence of functions for which ...

A binary operation f(x,y) is an operation that applies to two quantities or expressions x and y. A binary operation on a nonempty set A is a map f:A×A->A such that 1. f is ...