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...3}{4}a^2 \cot \frac{\pi}{23} = 23r^2 \tan \frac{\pi}{23} \simeq 41.8344\,a^2,</math> where <math>a</math> is side length and <math>r</math> is the inrad ...nconstructible <math>n</math>-gons}}</ref> on account of the [[23 (number)|number 23]] being neither a [[Fermat prime|Fermat]] nor [[Pierpont prime#Polygon c ...

P = \frac{1}{2}\rho\pi R^2 v^3 C_p(\lambda) P = \frac{1}{2\lambda^3}\rho\pi R^5 \omega^3 C_p(\lambda) ...

...plane]] and three-dimensional space to spaces with any finite or infinite number of [[dimension]]s. A Hilbert space is a [[vector space]] equipped with an [ ...kes two vectors {{math|'''x'''}} and {{math|'''y'''}}, and produces a real number {{math|'''x''' ⋅ '''y'''}}. If {{math|'''x'''}} and {{math|'''y'''}} are re ...

..., and the corresponding silhouette coefficient is often used to select the number of clusters. The work on cluster analysis led to a book titled Finding Grou ...ional Data | journal = Technometrics | date = 2021 | volume = 63 | issue = 2 | pages = 184–198 | issn = 0040-1706 | eissn = 1537-2723 | doi = 10.1080/00 ...

...|language=en}}</ref> The law provides a mathematical model to predict the number of cycles to failure ('''N''') based on the applied stress amplitude <math> ...</ref> a graphical representation of stress amplitude ('''S''') versus the number of cycles to failure ('''N'''). By plotting these curves for different mate ...

In [[number theory]], an '''average order of an arithmetic function''' is some simpler * An average order of {{math|''d''(''n'')}}, the [[Divisor function|number of divisors]] of {{math|''n''}}, is {{math|log ''n''}}; ...

...[Shilov system]], [[sigma bond metathesis]], [[oxidative addition]], and 1,2 addition reactions. ...The process is simplified down into three main steps: (1) C-H activation, (2) a redox reaction to form an octahedral intermediate, followed by (3) the f ...

...=Sahimi|first2=M.|date=2003-07-13|publisher=CRC Press|isbn=978-0-203-22153-2|language=en}}</ref> Flory'''–'''Stockmayer theory is a special case of [[ra ...the probability of chain termination is independent of chain length, and (2) multifunctional co-monomers react randomly with growing polymer chains.<re ...

...tra kind of "potential switching" Metropolis trial move (taken every fixed number of steps), such that the single sampling from the "mixed" ensemble suffices ...is modified, and the sampling should devote equal times (rather than equal number of time steps) to the two ensembles. ...

...ications]]|volume=73|issue=3|pages=241–266|doi=10.1016/S0166-8641(96)00075-2|arxiv=math/9509211|s2cid=14946860}}</ref> proved that Hurewicz's conjecture ...f sets of reals|journal=[[Topology and Its Applications]]|volume=116|issue=2|pages=243–253|doi=10.1016/S0166-8641(00)00079-1|arxiv=math/0001051|s2cid=14 ...

...ora crassa | journal = Fungal Genetics and Biology | volume = 30 | issue = 2 | pages = 147–53 | date = July 2000 | pmid = 11017770 | doi = 10.1006/fgbi. ...

...ng is referred to as [[Chargaff's rules|Chargaff's rule]] or ''parity rule 2''.<ref name="refname2"/> Three years later, Watson and Crick used this fac ...rate is presumably equal. This phenomenon is referred to as ''parity rule 2''. Hence, the second parity rule only exists when there is no mutation or s ...

...<ref>[http://www.mcs.anl.gov/research/projects/mpi/mpi-standard/mpi-report-2.0/node144.htm Intercommunicator Collective Operations]. The Message Passing ...of message size), the communication cost per word <math>\beta</math>, the number of processing units <math>p</math> and the input size per node <math>n</mat ...

...The American Journal of Human Genetics |language=English |volume=78 |issue=2 |pages=350–356 |doi=10.1086/500054 |issn=1537-6605 |pmc=1380242 |pmid=16400 ...ayesian]] approach (the latter being appropriate when dealing with a large number of [[candidate gene]]s). ...

...ower with [[rational number|rational]], [[real number|real]] and [[complex number]]s. ::<math>F_{n} = F_{n-1}\!\left(2^{1/2^n}\right), \quad \text{for}\ n \geq 1</math> ...

...solvent molecules. At a potential difference of, for example, {{mvar|U}} = 2&nbsp;V and a molecular thickness of {{mvar|d}} = 0.4&nbsp;nm, the electric :<math>E = \frac{U}{d} = \frac{2\ \text{V}}{0.4\ \text{nm}} = 5000\ \text{kV/mm}</math> ...

...th>X</math>, and all <math>r_1, r_2, \ldots</math> are non-negative [[real number]]s that sum to <math>1</math> (that is, such that <math>\sum_{i=1}^{\infty} ...oceedings of the American Mathematical Society|language=en|volume=43|issue=2|pages=439–442|doi=10.1090/S0002-9939-1974-0334132-8|issn=0002-9939|doi-acce ...

...Weyl |first = H. |journal = Zeitschrift für Physik |volume = 46 |issue = 1–2 |pages = 1–46 |s2cid = 121036548}}</ref> and [[Eugene Wigner]].<ref name="W ...rst1 = G. S.|last2 = Wolf|first2 = E.|journal = Physical Review D|volume = 2|issue = 10|pages = 2161–2186}}</ref><ref>{{cite journal |doi=10.1103/PhysRe ...

{{DISPLAYTITLE:2_&thinsp;22 honeycomb}} !bgcolor=#e7dcc3 colspan=2|'''2₂₂''' honeycomb ...

...year=1979|title=On properties of a well-known graph or what is your Ramsey number? Topics in graph theory.|journal=Annals of the New York Academy of Sciences ...ue=2 | pages=173–186 }}</ref><ref>Casper Goffman. ''And what is your Erdos number?'', [[American Mathematical Monthly]], vol. 76 (1979), p. 791</ref> where t ...