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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 ...

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 ...

A statistical distribution for which the variables may take on a continuous range of values. Abramowitz and Stegun (1972, p. 930) give a table of the parameters of most ...