Lipschitz continuity (2100 bytes)
5: ...pschitz continuous''' (or is said to satisfy a '''Lipschitz condition''') if there exists a constant
13: ...for the [[Germany|German]] mathematician [[Rudolf Lipschitz]].
15: Every Lipschitz continuous map is [[uniformly continuous]], and h...
17: Lipschitz continuous maps with Lipschitz constant ''K'' = 1 are called '''[[short map]]s''...
20: Lipschitz continuity is an important condition in the existence and un...

Rudolf Lipschitz (833 bytes)
1: '''Rudolph Otto Sigismund Lipschitz''' ([[May 14]], [[1832]] - [[October 7]], [[1903]...
3: Lipschitz gave his name to the [[Lipschitz continuity]] condition; in fact he worked in a broad range o...
7: ...Mathematicians/Lipschitz.html Biography of Rudolf Lipschitz]
9: [[Category:1832 births|Lipschitz, Rudolf]]
10: [[Category:1903 deaths|Lipschitz, Rudolf]]

Continuity (7268 bytes)
1: ''For the use of the word'' continuity ''in [[mathematics]], see [[continuous function]]...
3: ...e forms of [[media]], such as [[comic books]], '''continuity''' has also come to mean a set of contiguous even...
5: ...olely to pay attention to and attempt to maintain continuity across the chaotic and typically non-linear produ...
7: ==Continuity errors==
8: ...a shooting schedule. There are two main types of continuity errors.

Continuity (topology) (3981 bytes)
2: ...this definition only "uses" open sets, this makes continuity of a function a '''topological property''', depen...
4: == Formulations of Continuity ==
6: Several equivalent formulations of continuity can be made, and each is useful in different situ...
11: <center>[[image:continuity_topology.png|Continuity of a function at a point]]</center>

Modulus of continuity (2823 bytes)
1: ...re subsumed by the explicit use of the modulus of continuity.
7: ...ositive number. We define the '''local modulus of continuity''' at the point ''t'' by
11: ...ity''' (sometimes called the '''global modulus of continuity''') is defined by
17: Intuitively, the smaller the modulus of continuity the smoother the function is.
21: ... connection between smoothness and the modulus of continuity is not obvious. For example, for <math>f=\sin(x^2...

Reboot (continuity) (4752 bytes)
1: ...ries [[fiction]], means to discard all previous [[continuity]] in the series and start anew. Effectively, all...
3: ... owner of the creation declares that the rebooted continuity is now the official version.
5: ... applied to [[comic book]]s, where the prevailing continuity can be very important to the progress of future i...
10: ...es. One of the goals of the event was to make DC continuity less complicated and more modern, and this invovl...
12: ...their careers without any mention of the previous continuity (except for tacit allusions).

Continuity equation (2483 bytes)
5: In [[electromagnetic theory]], the '''continuity equation''' is derived from two of [[Maxwell's eq...
24: which is the continuity equation.
27: ...nge of charge density is negative. Therefore the continuity equation amounts to a conservation of charge.
31: In [[fluid dynamics]], a '''continuity equation''' is an equation
40: ... the conservation of probability also yields a '''continuity equation''', mark P(x,t) as [[probability density...

Continuity of government (496 bytes)
1: '''Continuity of government''' (COG) is the principle of establ...
7: * [[Continuity of Operations Plan]] (US)

Continuity correction (1264 bytes)
9: ...his addition of 1/2 to (lower-case) ''x'' is a '''continuity correction'''.
11: A continuity correction can also be applied when other discret...

Scott continuity (655 bytes)
13: ...ed suprema. This is in fact equivalent to being [[continuity (topology)|continuous]] with respect to the [[Sco...

Semi-continuity (3791 bytes)
1: ...n (mathematics)|function]]s that is weaker than [[continuity]]. A real-valued function ''f'' is '''upper semi-...

Continuity test (172 bytes)
1: In [[electronics]], a '''continuity test''' refers to checking an [[electric circuit]...

Uniform continuity (2627 bytes)
1: ...effect small changes in the output ''f''(''x'') ("continuity"), and furthermore the ''size'' of the changes in...
12: Every [[Lipschitz continuous]] map between two metric spaces is uni...
18: ...ural and general setting for the study of uniform continuity are the [[uniform space|uniform spaces]].
25: [[de:Lipschitz-Stetigkeit]]
26: [[es:Lipschitz continua]]

Absolute continuity (2002 bytes)
3: ==Absolute continuity of real functions==
13: ...ction|continuous]]. Every [[Lipschitz continuity| Lipschitz-continuous]] [[function (mathematics)|function]] ...
17: ==Absolute continuity of measures==
25: ...bsolute continuity of real functions and absolute continuity of measures==

Continuity property (4632 bytes)
1: In [[mathematics]], the '''continuity property''' may be presented as follows.
51: ...dict the continuity of f, using the definition of continuity for the real line.
130: This is more than enough to disprove continuity, that is show that there exists an x_0 such that ...

Illusory continuity of tones (1118 bytes)
1: ...dth="250"><tr><td align="center">[[Image:Illusory_Continuity_of_Tones.png]]</td></tr><tr><td><small><i>An asce...
3: ...the amplitude of the tone in the region of the discontinuity not decrease or increase too abruptly.
5: [[Media:Illusory continuity of tones.ogg|Listen to a demonstration]]
8: ...mo/illusions.html A demonstration of the illusory continuity of tones (and others)] at the [[Kyushu Institute ...

Continuity of Operations Plan (7722 bytes)
1: ...e had '''Continuity of Operations Plans''' (or '''Continuity of Government''') plans. During the [[Cold War]],...
3: ...y theories]] on the supposed "true agenda" of the Continuity of Operations program. Much of the government's ...
14: ...ated. Now, the bunkers are used for more mundane continuity-of-operations purposes, and the government worker...
16: ...e W. Bush|George W. Bush Administration]] put the Continuity of Operations plan into effect for the first time...
24: ...aredness Circular 65]], "Federal Executive Branch Continuity of Operations (COOP)", July 26, 1999

Paleolithic Continuity Theory (1190 bytes)
1: The '''Paleolithic Continuity Theory''' (PCT) suggests that the [[Indo-European...
3: ... archaeological data indicating European cultural continuity.
18: ...ttp://www.rastko.org.yu/filologija/alinei/malinei-continuity.html PCT outline]

Uniform absolute continuity (752 bytes)
16: * [[Absolute continuity]]

Business continuity planning (12738 bytes)
1: [[Image:BCPLifecycle.gif|thumb|Business continuity planning life cycle]]
2: ...e 'worst case scenario' [[paradigm]] for business continuity planning.
34: ...al outcome from any potential threat. A business continuity plan may also document additional impact scenario...
63: ...hieve organizational acceptance that the business continuity solution satisfies the organization's recovery re...
103: * "A Guide to Business Continuity Planning" by James C. Barnes

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