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The z-score associated with the ith observation of a random variable x is given by z_i=(x_i-x^_)/sigma, where x^_ is the mean and sigma the standard deviation of all ...

The Abel-Plana formula gives an expression for the difference between a discrete sum and the corresponding integral. The formula can be derived from the argument principle ...

Informally, the term asymptotic means approaching a value or curve arbitrarily closely (i.e., as some sort of limit is taken). A line or curve A that is asymptotic to given ...

An automorphism is an isomorphism of a system of objects onto itself. The term derives from the Greek prefix alphaupsilontauomicron (auto) "self" and ...

In 1850, Bravais demonstrated that crystals were comprised of 14 different types of unit cells: simple cubic, body-centered cubic, face-centered cubic; simple tetragonal, ...

A CW-complex is a homotopy-theoretic generalization of the notion of a simplicial complex. A CW-complex is any space X which can be built by starting off with a discrete ...

A Cartesian product of any finite or infinite set I of copies of Z_2, equipped with the product topology derived from the discrete topology of Z_2. It is denoted Z_2^I. The ...

The partial differential equation u_t+u_(xxxxx)+30uu_(xxx)+30u_xu_(xx)+180u^2u_x=0.

Let P be a finite partially ordered set. A chain in P is a set of pairwise comparable elements (i.e., a totally ordered subset). The partial order length of P is the maximum ...

Given a factor a of a number n=ab, the cofactor of a is b=n/a. A different type of cofactor, sometimes called a cofactor matrix, is a signed version of a minor M_(ij) defined ...