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...tps://encyclopediaofmath.org/wiki/Approximate_continuity|title=Approximate continuity|website=Encyclopedia of Mathematics|access-date=January 7, 2025}}</ref> Thi ...er |first=H. |title=Geometric measure theory |publisher=[[Springer Science+Business Media|Springer-Verlag]] |series=Die Grundlehren der mathematischen Wissensc ...

to be [[Semi-continuity#Lower_semicontinuity|lower semi-continuous]] in the [[weak topology]], for |publisher=Springer Science+Business Media, LLC ...

...ast=Levin |first=Vladimir |date=1 March 1999 |publisher=[[Springer Science+Business Media]] |location=Germany |pages=7–32 |language=en |doi=10.1023/A:100875302 ...ues. Then if <math>f</math> is cyclically monotone, there exists an [[semi-continuity|upper semicontinuous]] convex function <math>F:U\to \mathbb{R}</math> such ...

The '''maximum theorem''' provides conditions for the [[continuous function|continuity]] of an [[Optimization (mathematics)|optimized]] function and the set of it ...Analysis| volume = 1: Theory| year = 1997| publisher = Springer-Science + Business Media, B. V| pages = 84}} They consider the case that <math>\Theta</math> a ...

A function is [[Semi-continuity|upper semicontinuous]] if and only if its hypograph is [[Closed set|closed] ...le.com/books?id=4hIq6ExH7NoC&pg=PA8|year=2007|publisher=Springer Science & Business Media|isbn=978-3-540-32696-0|pages=8–9|edition=3rd}}</ref> ...

...ne |author-link=Saunders Mac Lane |year=1969 |publisher=[[Springer Science+Business Media|Springer, Berlin, Heidelberg]] |pages=192–200 |chapter=One universe a ...ne |author-link=Saunders Mac Lane |year=1998 |publisher=[[Springer Science+Business Media|Springer, New York, NY]] |isbn=978-0-387-90036-0 |ref=ML1998}} ...

...| author2 = J. E. Marsden | edition = 3rd | publisher = [[Springer Science+Business Media|Springer-Verlag]] | year = 1993 | isbn = 0-387-97918-2}}</ref> ...at <math>\nabla\cdot \mathbf{u}^{n+1} = 0</math>, which is the divergence (continuity) condition, thereby deriving the following Poisson equation for <math>\,p^{ ...

...delays, particularly with the most popular toys. So, the entrepreneur or business manager will buy speculatively. Another example is a [[furniture]] store. ...ncreased variables and complexity, and thus decreased flexibility, for the business enterprise. ...

...metric | journal=Inventiones Mathematicae | publisher=Springer Science and Business Media LLC | volume=219 | issue=1 | date=19 July 2019 | issn=0020-9910 | doi ...t | title=Liouville quantum gravity and the Brownian map II: Geodesics and continuity of the embedding | journal=The Annals of Probability | publisher=Institute ...

...ath> is the [[relative entropy]] of ''Q'' [[Absolutely continuous#Absolute continuity of measures|<<]] ''P''.<ref name="FS10">{{Cite encyclopedia|last1=Follmer|f {{Portal bar|Business|Mathematics|Money|Science|Technology}} ...

...in Action: Continuous and Lipschitz Optimization, 1996 Springer Science & Business Media'', page 57.</ref><ref group=note>The theorem, as set out and shown fo The definition of <math> E</math>, the continuity of <math> X(t)</math> and the hypothesis <math> z < X_a = X(a)</math> imply ...

...dinate of ''f''(''x'') is nonzero; say, ''i'' = 0 for simplicity. Then, by continuity, there is an open affine neighborhood ''U'' of ''x'' such that for all ''x'' in ''U'' and by continuity for all ''x'' in ''X'' as long as the ''f''_''i'''s do not vanish ...

CZM maintains continuity conditions mathematically; despite physical separation. It eliminates singu ...dbook of experimental solid mechanics|date=2008|publisher=Springer Science+Business Media|others=Sharpe, William N.|isbn=978-0-387-30877-7|location=Boston, MA| ...

...example, in the fourteenth century the notions of ''[[Continuous function|continuity]]'' of functions and ''[[motion]]'' were studied by the [[Oxford Calculator ...and the "Taylor" rule for series expansions| publisher=[[Springer Science+Business Media|Springer-Verlag]]|year=1993|journal=[[Archive for History of Exact Sc ...

...Physics A: Materials Science & Processing | publisher=Springer Science and Business Media LLC | volume=63 | issue=2 | year=1996 | issn=0947-8396 | doi=10.1007/ ...rnal of Advanced Manufacturing Technology | publisher=Springer Science and Business Media LLC | volume=18 | issue=5 | date=2001-09-01 | issn=0268-3768 | doi=10 ...

...imilarity methods for differential equations (Vol. 13). Springer Science & Business Media.</ref><ref>Barenblatt, G. I., Barenblatt, G. I., & Isaakovich, B. G. The continuity and energy equation reduce to ...

...ounted Wearable Computer Displays |website=www.sbir.gov |publisher=[[Small Business Innovation Research]], [[United States Government]] |location=U.S. }}</ref> ...pupil positions.<ref name=":0" /> In case of device malfunction or loss in continuity due to the user blinking their eyes, the device switches back to the acquis ...

...], [[continuous function|continuity]] and [[derivative]]s.{{efn|Limits and continuity can be defined in [[general topology]] without reference to real numbers, b ...r2-link = Ubiratan D'Ambrosio |year = 2000 |publisher = [[Springer Science+Business Media|Springer]] |isbn = 978-1-4020-0260-1 }}.</ref> ...

...e's radius. Since flow is leakless, the total flow rate into a junction [[Continuity equation|must]] be the total flow rate out:<math display="block">\sum_{\tex ...=Leaf vein structure might help improve battery life |work=[[International Business Times]] |agency=[[Yahoo! News]] |url=https://uk.news.yahoo.com/leaf-vein-st ...

...in Ancient Civilizations'' ([[Berlin]]/[[Heidelberg]]: [[Springer Science+Business Media|Springer Verlag]], 1983), [https://books.google.com/books?id=-pTzCAAA ...t deal with all the cases.<ref>{{Cite book| publisher = Springer Science & Business Media| isbn = 978-3-642-51599-6| last = Waerden| first = Bartel L. van der| ...