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An elderly Tibetan woman holding a prayer wheel demonstrates the continuity theory. Despite their age, older adults generally maintain the same traditions and beliefs. The continuity theory of normal aging states that older adults will usually maintain the same activities, behaviors, relationships as they did in their earlier years of life. [1]
A stronger form of continuity is uniform continuity. In order theory, especially in domain theory, a related concept of continuity is Scott continuity. As an example, the function H(t) denoting the height of a growing flower at time t would be considered continuous.
In an everyday example, there is a continuity equation for the number of people alive; it has a "source term" to account for people being born, and a "sink term" to account for people dying. Any continuity equation can be expressed in an "integral form" (in terms of a flux integral ), which applies to any finite region, or in a "differential ...
Continuity editing, a form of film editing that combines closely related shots into a sequence highlighting plot points or consistencies Continuity (fiction) , consistency of plot elements, such as characterization, location, and costuming, within a work of fiction (this is a mass noun)
In the theory of differential equations, Lipschitz continuity is the central condition of the Picard–Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial value problem. A special type of Lipschitz continuity, called contraction, is used in the Banach fixed-point theorem. [2]
In calculus and real analysis, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity. The notion of absolute continuity allows one to obtain generalizations of the relationship between the two central operations of calculus — differentiation and integration .
Continuous function; Absolutely continuous function; Absolute continuity of a measure with respect to another measure; Continuous probability distribution: Sometimes this term is used to mean a probability distribution whose cumulative distribution function (c.d.f.) is (simply) continuous.
For example, with density nonuniform in space but constant in time, the continuity equation to be added to the above set would correspond to: = So the case of constant and uniform density is the only one not requiring the continuity equation as additional equation regardless of the presence or absence of the incompressible constraint.