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A calibration form on a Riemannian manifold M is a differential p-form phi such that 1. phi is a closed form. 2. The comass of phi, sup_(v in ^ ^pTM, |v|=1)|phi(v)| (1) ...

The set of all sets is its own power set. Therefore, the cardinal number of the set of all sets must be bigger than itself.

For any sets A and B, their cardinal numbers satisfy |A|<=|B| iff there is a one-to-one function f from A into B (Rubin 1967, p. 266; Suppes 1972, pp. 94 and 116). It is easy ...

Let A and B be any sets, and let |X| be the cardinal number of a set X. Then cardinal exponentiation is defined by |A|^(|B|)=|set of all functions from B into A| (Ciesielski ...

Let g:R->R be a function and let h>0, and define the cardinal series of g with respect to the interval h as the formal series sum_(k=-infty)^inftyg(kh)sinc((x-kh)/h), where ...

According to Pólya, the Cartesian pattern is the resolution method for arithmetical or geometrical problems based on equations. The first step is to translate the question ...

A Cartesian tensor is a tensor in three-dimensional Euclidean space. Unlike general tensors, there is no distinction between covariant and contravariant indices for Cartesian ...

Let {a_n} be a series of positive terms with a_(n+1)<=a_n. Then sum_(n=1)^(infty)a_n converges iff sum_(k=0)^infty2^ka_(2^k) converges.

Cauchy conditions are initial conditions (time conditions) rather than boundary conditions (space conditions). An initial-value problem is often termed a Cauchy problem. ...

If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the ...