Search results
Results From The WOW.Com Content Network
in a removable discontinuity, the distance that the value of the function is off by is the oscillation; in a jump discontinuity, the size of the jump is the oscillation (assuming that the value at the point lies between these limits of the two sides); in an essential discontinuity, oscillation measures the failure of a limit to exist.
The concept of continuity for functions between metric spaces can be strengthened in various ways by limiting the way depends on and c in the definition above. Intuitively, a function f as above is uniformly continuous if the δ {\displaystyle \delta } does not depend on the point c .
In statistics, econometrics, political science, epidemiology, and related disciplines, a regression discontinuity design (RDD) is a quasi-experimental pretest–posttest design that aims to determine the causal effects of interventions by assigning a cutoff or threshold above or below which an intervention is assigned.
Let be a real-valued monotone function defined on an interval. Then the set of discontinuities of the first kind is at most countable.. One can prove [5] [3] that all points of discontinuity of a monotone real-valued function defined on an interval are jump discontinuities and hence, by our definition, of the first kind.
In magnetohydrodynamics (MHD), shocks and discontinuities are transition layers where properties of a plasma change from one equilibrium state to another. The relation between the plasma properties on both sides of a shock or a discontinuity can be obtained from the conservative form of the MHD equations, assuming conservation of mass, momentum, energy and of .
See the proofs for continuity and discontinuity above for the construction of appropriate neighbourhoods, where has maxima. f {\displaystyle f} is Riemann integrable on any interval and the integral evaluates to 0 {\displaystyle 0} over any set.
In particular, the many definitions of continuity employ the concept of limit: roughly, a function is continuous if all of its limits agree with the values of the function. The concept of limit also appears in the definition of the derivative : in the calculus of one variable, this is the limiting value of the slope of secant lines to the graph ...
Continuity (fiction), consistency of plot elements, such as characterization, location, and costuming, within a work of fiction (this is a mass noun) Continuity (setting) , one of several similar but distinct fictional universes in a broad franchise of related works (this is a count noun)