...<TR><TD valign="top">[2]</TD> <TD valign="top"> D. Gale, O. Gross, "A note on polynomial and separable games" ''Pacific J. Math.'' , '''8''' : 4 (1
3 KB (435 words) - 17:32, 5 June 2020
...linear, then $x=\mathsf{E}(X|Y=y)=\mu_x+\rho(\sigma_x/\sigma_y)(y-\mu_y)$. Note that the product of the two slopes is $\rho^2$.
4 KB (683 words) - 07:24, 24 March 2023
...complicated. For an elegant and concise proof see 2.10.43 of {{Cite|Fe}}. Note that a Lipschitz extension with a non-optimal constant can be easily achiev
2 KB (382 words) - 23:44, 27 June 2014
...countable collection $\{E_i\}$ of ''disjoint'' elements of $\mathcal{S}$. Note that, since we assume $\mu (\emptyset) = 0$, a measure is always finitely a
3 KB (459 words) - 14:45, 19 September 2012
...ub-formulas. Consider, for instance, a formula $P$ with probability $0.5$. Note that its negation, $\neg P$, will also have probability $0.5$. Now one woul
3 KB (515 words) - 13:25, 18 July 2014
Note that the random effects in \ref{lin mix eff model 1} implicitly imply
$\Sigma_i V_i^{-1}$ and $I_{n_i} - \Sigma_i V_i^{-1}$, respectively. Note that
7 KB (1,124 words) - 11:03, 4 April 2016
...fect if $\sigma ( n ) = 2 n$ (cf. also [[Perfect number|Perfect number]]). Note that some authors call a number $n$ abundant if $\sigma ( n ) \geq 2 n$. Cl
...d></tr><tr><td valign="top">[a20]</td> <td valign="top"> H.N. Shapiro, "Note on a theorem of Dickson" ''Bull. Amer. Math. Soc.'' , '''55''' (1949) pp
15 KB (2,194 words) - 05:54, 15 February 2024
...point in each direction at least $| D ( C ) |$ times. It is interesting to note that this is true even for differentiable locally one-to-one curves which a
3 KB (505 words) - 16:52, 1 July 2020
...usual "tensor products" give monoidal categories — whence the notation. Note that one cannot identify all isomorphic objects in $\mathcal{C}$.
4 KB (612 words) - 14:59, 6 April 2023
...relations between them, complex functioning, hierarchy of structure, etc. Note that the terms complex system and "large (scale) system" are not synonymo
4 KB (532 words) - 17:22, 7 February 2011
...that $\mathbf{x} ^ { 0 }$ is kept constant in the differentiation of $f$. Note that, like $f$, $D f / D t$ is a function of $\mathbf{x} ^ { 0 }$ and $t$ b
...(a10) serves as a formula for the material derivative in the spatial form. Note that the first term on the right-hand side of this formula, namely $\partia
12 KB (1,877 words) - 17:01, 1 July 2020
...</td></tr><tr><td valign="top">[a11]</td> <td valign="top"> R. Rado, "A note on Bernoullian numbers" ''J. London Math. Soc.'' , '''9''' (1934) pp. 88
8 KB (1,206 words) - 16:55, 1 July 2020
Note that the $ \gamma _ {jk } ^ {i} $
by the [[Euler theorem|Euler theorem]] on homogeneous functions. Note that $ G ^ {i} $,
10 KB (1,411 words) - 10:58, 29 May 2020
::: Yes, I see, you are right. I just did not note the turn from positive to signed; sorry. --[[User:Boris Tsirelson|Boris Tsi
3 KB (479 words) - 06:09, 22 July 2012
...of $\phi$ and $\operatorname{conv} ( E )$ is the convex hull of a set $E$. Note that (a1) is a combination of an improvement of a Hartman–Wintner theorem
Note that this theorem is equivalent to the Helson–Szegö theorem on weighted
14 KB (2,017 words) - 06:44, 15 February 2024
Note that if $G$ is an $M$-group and if $q$ is a unit of $B ( G )$, then conjuga
...} \neq 0$. Of course, $\sigma$ is $X$-outer when $\Phi _ { \sigma } = 0$. Note that, in the case of semi-prime rings, $\operatorname{Inn} ( R )$ need not
9 KB (1,402 words) - 13:37, 25 November 2023
...a8]</TD> <TD valign="top"> E.M. Wright, "Burnside's lemma: a historical note" ''J. Combin. Th. B'' , '''30''' (1981) pp. 89–90</TD></TR>
3 KB (516 words) - 22:29, 1 December 2014
<TR><TD valign="top">[2]</TD> <TD valign="top"> G.H. Hardy, "Note on Ramanujan's trigonometrical function $c_q(n)$ and certain series of arit
3 KB (502 words) - 14:27, 17 March 2023
Note that this kind of triple system is completely different from the combinator
3 KB (559 words) - 16:43, 15 March 2023
In his 1849 note, Listing showed that the figure-eight knot, Fig.a1b, and its mirror image a
3 KB (496 words) - 07:37, 18 March 2023