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In the theory of transfinite ordinal numbers, 1. Every well ordered set has a unique ordinal number, 2. Every segment of ordinals (i.e., any set of ordinals arranged in ...

A function with k continuous derivatives is called a C^k function. In order to specify a C^k function on a domain X, the notation C^k(X) is used. The most common C^k space is ...

The problem of finding the number of different ways in which a product of n different ordered factors can be calculated by pairs (i.e., the number of binary bracketings of n ...

An axiomatic system is said to be categorical if there is only one essentially distinct representation for it. In particular, the names and types of objects within the system ...

For every p, the kernel of partial_p:C_p->C_(p-1) is called the group of cycles, Z_p={c in C_p:partial(c)=0}. (1) The letter Z is short for the German word for cycle, ...

A chamfered icosahedron, also called a tritruncated rhombic triacontahedron, is a polyhedron obtained by chamfering a regular icosahedron. The illustration above shows ...

A Gaussian quadrature-like formula over the interval [-1,1] which has weighting function W(x)=x. The general formula is int_(-1)^1xf(x)dx=sum_(i=1)^nw_i[f(x_i)-f(-x_i)]. n ...

Let r and s be positive integers which are relatively prime and let a and b be any two integers. Then there is an integer N such that N=a (mod r) (1) and N=b (mod s). (2) ...

A general class of means introduced by Italian mathematician Oscar Chisini (pronounced keeseenee) in 1929. Given a function of n variables f(x_1,...,x_n), the Chisini mean of ...

A cipher is an algorithm that converts data (plaintext) to an obfuscated form that is not directly readable. Ciphers are usually used with the intention of hiding the ...