Search results
Results From The WOW.Com Content Network
Linkwitz–Riley filter is an example of practical implementation of partition of unity to separate input signal into two output signals containing only high- or low-frequency components. The Bernstein polynomials of a fixed degree m are a family of m +1 linearly independent single-variable polynomials that are a partition of unity for the unit ...
Generally, a partition is a division of a whole into non-overlapping parts. Among the kinds of partitions considered in mathematics are partition of a set or an ordered partition of a set, partition of a graph, partition of an integer, partition of an interval, partition of unity, partition of a matrix; see block matrix, and
Some authors treat a partition as a decreasing sequence of summands, rather than an expression with plus signs. For example, the partition 2 + 2 + 1 might instead be written as the tuple (2, 2, 1) or in the even more compact form (2 2, 1) where the superscript indicates the number of repetitions of a part.
If there is a remainder in solving a partition problem, the parts will end up with unequal sizes. For example, if 52 cards are dealt out to 5 players, then 3 of the players will receive 10 cards each, and 2 of the players will receive 11 cards each, since = +.
That is, one may partition the unit interval into the intervals [0, 1/2) and [1/2, 1]. Every real number x is either less than 1/2 or not; and likewise so is the fractional part of 2 n x . If the space X is compact and endowed with a topology, or is a metric space, then the topological entropy may also be defined.
As an example: the partition function for the isothermal-isobaric ensemble, the generalized Boltzmann distribution, divides up probabilities based on particle number, pressure, and temperature. The energy is replaced by the characteristic potential of that ensemble, the Gibbs Free Energy .
For example, the blood/gas partition coefficient of a general anesthetic measures how easily the anesthetic passes from gas to blood. [5] Partition coefficients can also be defined when one of the phases is solid, for instance, when one phase is a molten metal and the second is a solid metal, [6] or when both phases are solids. [7]
The partition topology provides an important example of the independence of various separation axioms. Unless P {\displaystyle P} is trivial, at least one set in P {\displaystyle P} contains more than one point, and the elements of this set are topologically indistinguishable : the topology does not separate points.