Unitary operatorIn functional analysis, a unitary operator is a surjective bounded operator on a Hilbert space that preserves the inner product. Unitary operators are usually taken as operating on a Hilbert space, but the same notion serves to define the concept of isomorphism between Hilbert spaces. A unitary element is a generalization of a unitary operator. In a unital algebra, an element U of the algebra is called a unitary element if UU = UU = I, where I is the identity element. Definition 1.
Spherical coordinate systemIn mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin; its polar angle measured from a fixed polar axis or zenith direction; and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the fixed axis, measured from another fixed reference direction on that plane.
Volume integralIn mathematics (particularly multivariable calculus), a volume integral (∫∫∫) refers to an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many applications, for example, to calculate flux densities, or to calculate mass from a corresponding density function.
G.992.1In telecommunications, ITU-T G.992.1 (better known as G.dmt) is an ITU standard for ADSL using discrete multitone modulation (DMT). G.dmt full-rate ADSL expands the usable bandwidth of existing copper telephone lines, delivering high-speed data communications at rates up to 8 Mbit/s downstream and 1.3 Mbit/s upstream. DMT allocates from 2 to 15 bits per channel (bin). As line conditions change, bit swapping allows the modem to swap bits around different channels, without retraining, as each channel becomes more or less capable.
