Note that if $n=m$ the formula reduces to
4 KB (606 words) - 16:10, 23 November 2012
...the Python [https://mwclient.readthedocs.io/en/latest/ mwclient] library. Note that this library is used by me for the [[User:Maximilian_Janisch/latexlist
5 KB (682 words) - 20:39, 23 March 2023
...pivotal role in the ordinary triangle inequality, by a triangle function. Note that for a function $ d $
...ant probabilistic pseudo-metric space is a transformation generated space. Note that $ F _ {pq } = F _ {f ( p ) f ( q ) } $,
12 KB (1,757 words) - 08:07, 6 June 2020
Note that it is the upper semi-circle and can also be given by (the upper part o
6 KB (792 words) - 10:59, 29 May 2020
...} }= \{ ( u _ { \lambda } ) _ { \lambda \in \Lambda }$ ; confidence 0.956 NOTE: it looks like \} is missing
...images/b/b130/b130070/b1300707.png ; $|m | = | n | = 1$ ; confidence 0.956 NOTE: a | at the beginning is probably missing
43 KB (5,120 words) - 18:59, 18 May 2020
...obtained by solving a non-linear equation. All other problems are linear. (Note: the theory may also be built around $ R _ {l} $,
4 KB (657 words) - 22:13, 5 June 2020
...This was already stated in the seminal work of I.M. Gel'fand around 1940. Note that there is a deep related question. Let $A$ be a [[Fréchet algebra|Fré
...s. Indeed, it is known just which Banach algebras arise in this situation. Note that the proof of this theorem requires the assumption of the [[Continuum h
11 KB (1,760 words) - 16:56, 1 July 2020
...a rational number but is an integer when $F$ is a Frobenius endomorphism. Note that more generally we say a finite group is a ''finite group of Lie type''
...e a semidirect product decomposition $\mbf{P} = \mbf{U} \rtimes \mbf{L}$, (note in particular we have $\mbf{L}$ is contained in the [[Normalizer of a subse
48 KB (8,458 words) - 18:22, 13 August 2023
...aluate, as it depends on three arguments: $\alpha$, $\beta$ and $\theta$. (Note that $\theta$ is not restricted to be a Euclidean parameter; it can also be
...fficiency of $T$ with respect to $V$, with notation $e ^ { s } ( T , V )$. Note that
15 KB (2,246 words) - 16:10, 11 February 2024
when $\theta$ varies in $\Theta ( \mu )$. Note that $\mu ^ { \prime } \in \mathcal{M} ( E )$ is such that the two sets $F
...replaced by $\bar{X} _ { n } = 1 / n ( X _ { 1 } + \ldots + X _ { n } )$. Note that since $M _ { F }$ is an open set, and from the strong [[Law of large n
10 KB (1,596 words) - 15:30, 1 July 2020
...space-times (cf. [[Penrose cosmic censorship|Penrose cosmic censorship]]). Note that in the physics literature there are various conflicting definitions of
4 KB (606 words) - 19:47, 24 November 2023
...></tr><tr><td valign="top">[a8]</td> <td valign="top"> R. Fleissner, "A note on Baire 1 Darboux functions" ''Real Anal. Exch.'' , '''3''' (1977-78) {
11 KB (1,541 words) - 16:46, 1 July 2020
Note that every completely-continuous mapping (or [[Compact mapping|compact mapp
4 KB (600 words) - 00:06, 15 February 2024
...| \Sigma | ^ { n / 2 } | \Psi | ^ { p / 2 } } \times$ ; confidence 0.913 NOTE: it looks like something is missing at the end
...; $[ x , y ] = ( G x , y ) , \quad x , y \in \cal K ),$ ; confidence 0.906 NOTE: why is there a parentesis closed that was never opened?
45 KB (5,453 words) - 18:03, 19 May 2020
...imply $x \ast z \in I$. It is known that always $(x \ast z) \ast z \in I$. Note that in a positive implicative BCK-algebra, every ideal is implicative. Imp
5 KB (892 words) - 02:43, 15 February 2024
Note that the adjoint of the X-ray transform can be traced back to the Buffon ne
4 KB (682 words) - 06:33, 10 May 2022
...istic and applies only in the case where $X$ is smooth. It is important to note that this is the only known method in mathematics to prove the existence of
...ram $X \rightarrow Y \leftarrow X ^ { + }$ is called a flip (or log flip). Note that $- ( K _ { X } + B )$ is $\phi$-ample.
11 KB (1,780 words) - 14:48, 3 February 2024
.../td></tr><tr><td valign="top">[a2]</td> <td valign="top"> K. Borsuk, "A note on the theory of shape of compacta" ''Fund. Math.'' , '''67''' (1970) pp
4 KB (699 words) - 15:31, 1 July 2020
Meyer's note
particular, we note his "Essai sur une exposition nouvelle de
11 KB (1,779 words) - 16:32, 4 March 2024
Note that $ L _ {0} $)
5 KB (757 words) - 22:15, 5 June 2020