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Let L be a language of the first-order logic. Assume that the language L has the following sets of nonlogical symbols: 1. C is the set of constant symbols of L. (These are ...

The universal product code (UPC) is a 12-digit number and associated machine-readable bar code used to identify products being purchased in grocery stores. UPCs encode an ...

Let L be a language of first-order predicate logic, let I be an indexing set, and for each i in I, let A_i be a structure of the language L. Let u be an ultrafilter in the ...

The identity element of an additive monoid or group or of any other algebraic structure (e.g., ring, module, abstract vector space, algebra) equipped with an addition. It is ...

The bivariate normal distribution is the statistical distribution with probability density function P(x_1,x_2)=1/(2pisigma_1sigma_2sqrt(1-rho^2))exp[-z/(2(1-rho^2))], (1) ...

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

A Boolean algebra is a mathematical structure that is similar to a Boolean ring, but that is defined using the meet and join operators instead of the usual addition and ...

There are two definitions of the Carmichael function. One is the reduced totient function (also called the least universal exponent function), defined as the smallest integer ...

A prime number p is called circular if it remains prime after any cyclic permutation of its digits. An example in base-10 is 1,193 because 1,931, 9,311, and 3,119 are all ...

While many computations admit shortcuts that allow them to be performed more rapidly, others cannot be sped up. Computations that cannot be sped up by means of any shortcut ...