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...e a [[convex set]] that is given as an input to an optimization algorithm. Separation oracles are used as input to [[Ellipsoid method|ellipsoid methods]].<ref na ...nvex]] and [[Compact space|compact]] set in R^''n''. A '''strong separation oracle for ''K''''' is an oracle ([[black box]]) that, given a vector ''y'' ...

...leigh number, boundary layer formation, and the impact of varying Rayleigh numbers on the stability and transition of flow regimes. ==== 3.1 For Low Rayleigh Numbers (Ra < 10^3) ==== ...

...points has (''a,c'') and (''b,d'') as separating pairs. This '''point-pair separation''' is an invariant of projectivities of the line. The point-pair separation of points was written AC//BD by [[H. S. M. Coxeter]] in his textbook ''The ...

{{AFC comment|1=I've asked for comments on this draft at [[Talk:Flow separation]]. [[User:Curb Safe Charmer|Curb Safe Charmer]] ([[User talk:Curb Safe Char '''Boundary layer separation''' is a critical phenomenon in fluid dynamics that occurs when the flow of ...

...inary]] for ENS) and to each transition label a number <!-- or two natural numbers, to allow self-loops, as in Mukund --> <math>\tau(\ell)</math> such that co Mukund: event/state separation property, state separation property.<ref>{{Cite journal|last=Mukund|first=Madhavan|date=1992-12-01|tit ...

...ow the theorem relies on the [[axiom of pairing]] as well as an [[axiom of separation]], of which there are notable variations. A crucial role in the set theoret ...d simplicity, the section supposes a constructive set theory with ''full'' Separation, i.e. we allow for comprehension involving ''any'' proposition <math>P</mat ...

...}</ref><ref>{{cite book|last1=Svarovski|first1=Ladislav|title=Solid-Liquid Separation|date=31 October 2000|publisher=Elsevier |isbn=9780080541440|url=https://boo For example, the cubic mean of two numbers is: ...

...ond-order version of [[Zermelo set theory]] with a second-order version of separation, there exist models not isomorphic to any <math>V_\delta</math> for a limit ...

wherever ω is analytic (as can be seen by performing [[separation of variables]] and recovering the equation <math>\ln(\omega)+\omega = z</ma is a [[Eulerian number#Eulerian numbers of the second order|second-order Eulerian number]]. ...

...sult of this, the rule is optimally followed by atoms with medium [[atomic numbers]].<ref>E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra, Cambr ...2</math> and <math>J = 1</math> is <math>2 \beta</math> , twice as the separation between <math>J = 1</math> and <math>J = 0</math> is <math>\beta</math> ...

== Separation bounds == ...difference is at least 2^−''d'', it means that we can round all numbers to ''d'' bits of accuracy, and solve SRS in time polynomial in ''d''. ...

...alinski–Harabasz (CH) Index is defined as the ratio of the between-cluster separation (BCSS) to the within-cluster dispersion (WCSS), normalized by their number The numerator of the CH index is the between-cluster separation (BCSS) divided by its degrees of freedom. The number of degrees of freedom ...

|title=Random Numbers Fall Mainly in the Planes ...ence <math>u_1, u_2, \dots</math>. Let <math>1/\nu_t</math> be the maximal separation between covering parallel planes of the sequence <math>\{(u_{n+1:n+t}) \mid ...

...the [[clique number]] and the [[chromatic number]] of the graph. These two numbers are both [[NP-hard]] to compute. Tardos used her function to prove an exponential separation between the capabilities of monotone Boolean logic circuits and arbitrary c ...

...is high enough that the effects of gravitation and surface tension on the separation of the fluid from the nozzle are of secondary importance. This state is cha ...n actual applications, to assure a safe dispensing process, the real Weber-numbers chosen should be between 20 and 50. ...

...ed as comprising the elementary constituents. In the case of [[spin–charge separation]], for example, the electron can be viewed as a bound state of a '[[spinon] ....org/details/quantumunspeakab00bert/page/n404 389]–91}}</ref> Spin-charge separation into spinons and holons was detected in electrons in 1D SrCuO₂.< ...

where if in addition, {{mvar|Y}} is a vector space over the real numbers then we may add to this list: * {{annotated link|Hyperplane separation theorem}} ...

...aration may happen, while the retreating blade operates at much lower Mach numbers but the high values of AoA result in the stall (also see [[advancing blade ...omena have been identified to contribute to the delay in the onset of flow separation under unsteady condition:<ref name="Leishman2006">{{cite book |last1=Leishm ...

...g a variant of the [[ellipsoid method]]. This variant gets as input, a ''[[separation oracle]]'': a function that, given a vector '''y''' ≥ 0, returns one of the ...er <math>\mathbf{y}_t</math> of the current ellipsoid, and sends it to the separation oracle: ...

The decomposition of the <math>d^N</math>-dimensional tensor starts with the separation of the very left index, i.e., the first index <math>s_1</math>, which descr [[File:Left_mps_1.png|thumb|351x351px|The separation of physical degrees of freedom of the first site.]] ...