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continuous symmetrization - translation to russian
MATHEMATICAL PRACTICE
Continuous model; Continuous Model; Continuous Modelling
continuous symmetrization
математика
непрерывная симметризация
continuous extension
![The graph of a [[cubic function]] has no jumps or holes. The function is continuous.](https://commons.wikimedia.org/wiki/Special:FilePath/Brent method example.svg?width=200 "The graph of a [[cubic function]] has no jumps or holes. The function is continuous.")
![section 2.1.3]]).](https://commons.wikimedia.org/wiki/Special:FilePath/Discontinuity of the sign function at 0.svg?width=200 "section 2.1.3]]).")
![Riemann sphere]] is often used as a model to study functions like the example.](https://commons.wikimedia.org/wiki/Special:FilePath/Function-1 x.svg?width=200 "Riemann sphere]] is often used as a model to study functions like the example.")
![The graph of a continuous [[rational function]]. The function is not defined for <math>x = -2.</math> The vertical and horizontal lines are [[asymptote]]s.](https://commons.wikimedia.org/wiki/Special:FilePath/Homografia.svg?width=200 "The graph of a continuous [[rational function]]. The function is not defined for <math>x = -2.</math> The vertical and horizontal lines are [[asymptote]]s.")
![oscillation]].](https://commons.wikimedia.org/wiki/Special:FilePath/Rapid Oscillation.svg?width=200 "oscillation]].")
.svg?width=200 "Point plot of Thomae's function on the interval (0,1). The topmost point in the middle shows f(1/2) = 1/2.")
FUNCTION SUCH THAT THE PREIMAGE OF AN OPEN SET IS OPEN
Continuity property; Continuous map; Continuous function (topology); Continuous (topology); Continuous mapping; Continuous functions; Continuous maps; Discontinuity set; Noncontinuous function; Discontinuous function; Continuity (topology); Continuous map (topology); Sequential continuity; Stepping Stone Theorem; Continuous binary relation; Continuous relation; Topological continuity; Right-continuous; Right continuous; Left continuous; Left-continuous; C^1; Continuous fctn; Cts fctn; E-d definition; Continuous variation; Continuity space; Continuous space; Real-valued continuous functions; Left-continuous function; Right-continuous function; Left- or right-continuous function; Continuity at a point; Continuous at a point; Continuous extension
математика
непрерывное расширение
discontinuous function
FUNCTION SUCH THAT THE PREIMAGE OF AN OPEN SET IS OPEN
Continuity property; Continuous map; Continuous function (topology); Continuous (topology); Continuous mapping; Continuous functions; Continuous maps; Discontinuity set; Noncontinuous function; Discontinuous function; Continuity (topology); Continuous map (topology); Sequential continuity; Stepping Stone Theorem; Continuous binary relation; Continuous relation; Topological continuity; Right-continuous; Right continuous; Left continuous; Left-continuous; C^1; Continuous fctn; Cts fctn; E-d definition; Continuous variation; Continuity space; Continuous space; Real-valued continuous functions; Left-continuous function; Right-continuous function; Left- or right-continuous function; Continuity at a point; Continuous at a point; Continuous extension
общая лексика
разрывная функция
математика
прерывная функция
Definition
continuous function
A function f : D -> E, where D and E are cpos, is continuous
if it is monotonic and
f (lub Z) = lub f z | z in Z
for all directed sets Z in D. In other words, the image of
the lub is the lub of any directed image.
All additive functions (functions which preserve all lubs)
are continuous. A continuous function has a {least fixed
point} if its domain has a least element, bottom (i.e. it
is a cpo or a "pointed cpo" depending on your definition of a
cpo). The least fixed point is
fix f = lub f^n bottom | n = 0..infinity
(1994-11-30)
Wikipedia
Continuous modelling
Continuous modelling is the mathematical practice of applying a model to continuous data (data which has a potentially infinite number, and divisibility, of attributes). They often use differential equations and are converse to discrete modelling.
Modelling is generally broken down into several steps:
- Making assumptions about the data: The modeller decides what is influencing the data and what can be safely ignored.
- Making equations to fit the assumptions.
- Solving the equations.
- Verifying the results: Various statistical tests are applied to the data and the model and compared.
- If the model passes the verification progress, putting it into practice.
- If the model fails the verification progress, altering it and subjecting it again to verification; if it persists in fitting the data more poorly than a competing model, it is abandoned.
