* A. R. Rajwade, ''Squares'', London Mathematical Society Lecture Note Series '''171''' Cambridge University Press (1993) {{ISBN|0-521-42668-5}} {
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Note that the geometry of special relativity theory (cf. [[Space-time|Space-time
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Note that a lower bound for the first eigenvalue, without any curvature assumpti
...</td></tr><tr><td valign="top">[a2]</td> <td valign="top"> P. Buser, "A note on the isoperimetric constant" ''Ann. Sci. Ecole Norm. Sup.'' , '''15'''
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<TR><TD valign="top">[a1]</TD> <TD valign="top"> E. Barbier, "Note sur le problème de l'ainguille et le jeu du joint couvert" ''J. Math. Pur
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Note that this norm differs from the [[operator norm]] of $A$ (for instance beca
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...liations on surfaces) are equivalent (cf. also [[Lamination|Lamination]]). Note also that the construction shows that the (weighted) train track is in a se
...nd laminations in higher-dimensional manifolds (see [[#References|[a2]]]). Note that a notion close to the notion of train track is already contained in [[
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* A. R. Rajwade, ''Squares'', London Mathematical Society Lecture Note Series '''171''' Cambridge University Press (1993) {{ISBN|0-521-42668-5}} {
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...<TD valign="top">[a4]</TD> <TD valign="top"> E.A. Michael, "Yet another note on paracompact spaces" ''Proc. Amer. Math. Soc.'' , '''10''' (1959) pp.
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Note that $A_5$ is the non-Abelian simple group of smallest possible order.
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...to algebraic geometry and topology'', London Mathematical Society Lecture Note Series '''217''' Cambridge University Press (1995) {{ISBN|0-521-46755-1}} {
* A. R. Rajwade, ''Squares'', London Mathematical Society Lecture Note Series '''171''' Cambridge University Press (1993) {{ISBN|0-521-42668-5}} {
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Note that the best coordinates are neither the normal nor the harmonic ones, but
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...properties. This Ray resolvent is associated to a semi-group $(\hat P_t)$ (note that $\hat P_0$ need not be the identity: existence of branching points), q
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.... H. Greaves, G. Harman, M. N. Huxley; London Mathematical Society Lecture Note Series '''237''', Cambridge University Press (1997) {{ISBN|0-521-58957-6}}
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...</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> R.R. Hall, "A note on Farey series" ''J. London Math. Soc.'' , '''2''' (1970) pp. 139–148
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...On graphs with least eigenvalue $−2$'' London Mathematical Society Lecture Note Series '''314''' Cambridge University Press(2004) {{ISBN|0-521-83663-8}} {{
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...ce $ X $ onto a topological space $ B $ (i.e., a [[Fibration|fibration]]). Note that $ X $, $ B $ and $ \pi $ are also called the '''total space''', the ''
...f(b) \stackrel{\text{df}}{=} (\pi \circ F)[{\pi^{\leftarrow}}[\{ b \}]] $. Note that $ F $ is a [[Covering|covering]] of $ f $ and that $ \pi_{1} \circ F =
5 KB (754 words) - 01:34, 10 December 2016
...en formal system is decidable, then such a system is said to be complete. (Note that it is impossible to require that all, and not just the closed, formula
2 KB (251 words) - 22:25, 26 July 2012
* A. R. Rajwade, ''Squares'', London Mathematical Society Lecture Note Series '''171''' Cambridge University Press (1993) {{ISBN|0-521-42668-5}} {
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...$(A_1\mathbin{\&}\dotsb\mathbin{\&}A_n)\supseteq(B_1\lor\dotsb\lor B_m)$ (note that an empty conjunction denotes truth, and an empty disjunction denotes f
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...f an already defined population of objects under study. It is essential to note that the condition which defines the species is to be understood in the int
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This result had been conjectured by M.A. Lavrent'ev in 1938. Note that the exponential function shows that there is no such result for $n=2$.
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* Neumann, B.H. ''A note on algebraically closed groups'' ''J. Lond. Math. Soc.'' '''27''' (1952) 24
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...1]</TD> <TD valign="top"> B. Jessen, J. Marcinkiewicz, A. Zygmund, "Note on the differentiability of multiple integrals" ''Fund. Math.'' , '''25'''
2 KB (271 words) - 14:20, 14 February 2020
...oof of the expression for $S_n$ see, e.g., [[#References|[a1]]], Thm. 422. Note that the series $\sum 1/p$ extended over all prime numbers $p$ diverges als
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Note that the same point in the boundary of $ D $
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Note that, when $B (t)$ is constant, \eqref{e:conclusion2} coincides with \eqref
|valign="top"|{{Ref|Gr}}|| T. H. Gronwall, "Note on the derivatives with respect to a parameter of the solutions of a system
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..., then the series converges if $\alpha> 1$ and diverges if $\alpha\leq 1$. Note that for \eqref{e:Gauss} to be valid it is necessary (but not sufficient) t
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Note that a Lebesgue point is, therefore, a point where $f$ is [[Approximate con
2 KB (254 words) - 12:03, 14 December 2012
...M. Cohn, ''Skew Field Constructions'', London Mathematical Society lecture note series '''27''', Cambridge University Press (1977) {{ISBN|0-521-21497-1}}
2 KB (267 words) - 17:01, 23 November 2023
...l); in $P_1 * P_2$, then all such pairs have $p_1 \prec p_2$ (series). We note that $+$ is commutative but $*$ is not.
2 KB (254 words) - 18:50, 14 November 2023
...is, by definition, the set of morphisms in $\mathfrak{K}$ from $X$ to $T$. Note that any two final objects of a category are (canonically) isomorphic, and
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===Historical note===
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...TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top"> N. Jacobson, "A note on automorphisms and derivations of Lie algebras" ''Proc. Amer. Math. Soc.
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...TD></TR><TR><TD valign="top">[a8]</TD> <TD valign="top"> I. Stavrov, "A note on generalized Osserman manifolds" ''Preprint'' (1998)</TD></TR></table>
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Note that it is then an eigen value of the integral operator defined by $ K( x
2 KB (306 words) - 08:05, 6 June 2020
Note that for $ W $
2 KB (304 words) - 15:36, 11 February 2022
<TR><TD valign="top">[a2]</TD> <TD valign="top"> Z. Jelonek, "A note about the extension of polynomial embeddings" ''Bull. Polon. Acad. Sci. Ma
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.../TR><TR><TD valign="top">[a5]</TD> <TD valign="top"> J.O. Hennefeld, "A note on the Arens products" ''Pacific J. Math.'' , '''26''' (1968) pp. 115–
<TR><TD valign="top">[a9]</TD> <TD valign="top"> Á. Rodriguez-Palacios, "A note on Arens regularity" ''Quart. J. Math. Oxford Ser. (2)'' , '''38''' : 149
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Cf. also [[Differential invariant|Differential invariant]]. Note however that for differential invariants not only tensor bundles but also (
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...4)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> S. Okubo, "Note on unitary symmetry in strong interactions" ''Progress Theor. Phys.'' , ''
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<TR><TD valign="top">[a2]</TD> <TD valign="top"> H.J.J. te Riele, "A Note on the Catalan–Dickson Conjecture" , ''Mathematics of Computation'' '''27
2 KB (331 words) - 14:02, 12 November 2023
...amental group|fundamental group]] $\pi_1 (\Omega)$ of $\Omega$ is trivial. Note that the connectedness assumptions guarantees that, if $\gamma$ can be defo
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...ussian for $d \geq 3$ and non-Gaussian for $d = 2$ ([[#References|[a7]]]). Note that for $d \geq 2$ the Wiener sausage is a sparse object: since the Browni
to leading order. Note that, apparently, a large deviation below the scale of the mean "squeezes
9 KB (1,317 words) - 16:09, 11 February 2024
<TR><TD valign="top">[3]</TD> <TD valign="top"> L. Gårding, "Note on continuous representations of Lie groups" ''Proc. Nat. Acad. Sci. USA''
3 KB (401 words) - 18:39, 17 October 2016
...e analogy with the classical definition of probability is evident. One may note that in the [[Bertrand paradox|Bertrand paradox]], which is connected with
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...<TD valign="top">[a1]</TD> <TD valign="top"> E.M. Alfsen, P. Holm, "A note on compact representations and almost periodicity in topological groups" '
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is well defined. Note that the real part of $ T $
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<TR><TD valign="top">[a2]</TD> <TD valign="top"> R.D. Carmichael, "Note on a new number theory function" ''Bull. Amer. Math. Soc.'' , '''16''' (1
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<TR><TD valign="top">[a1]</TD> <TD valign="top"> J. Leech, "Note on sphere packings" ''Canad. J. Math.'' , '''19''' (1967) pp. 251–267<
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...n coverings (cf. [[Nerve of a family of sets|Nerve of a family of sets]]). Note that a geometric complex is also a cellular complex (cf. [[Cell complex|Cel
3 KB (419 words) - 17:16, 7 February 2011
Note that if $\varepsilon = - 1$ and $K ( a , b ) \equiv 0$ (identically), then
Note that a "triple system" in the sense discussed above is totally different
8 KB (1,154 words) - 19:44, 27 February 2021
* {{Ref|a1}} E. Catalan, "Note sur une équation aux différences finies" ''J. Math. Pures Appl.'' , '''3
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Note that this definition, which is commonly used now (see [[#References|[a1]]],
3 KB (411 words) - 08:09, 6 June 2020
...nts of this relation process these words to yield the same result. One may note that if some binary relation is decidable (cf. [[Decidable set|Decidable se
3 KB (392 words) - 17:21, 7 February 2011
Note that, as an obvious corollary, if the interval $I$ has length larger than $
2 KB (342 words) - 12:49, 6 October 2012
...rsal algebra, and by the set of all closed subsets in a topological space (note that while the meet of a family of closed sets is their set-theoretic inter
3 KB (459 words) - 12:03, 23 November 2023
* A. R. Rajwade, ''Squares'', London Mathematical Society Lecture Note Series '''171''' Cambridge University Press (1993) {{ISBN|0-521-42668-5}}{{
3 KB (439 words) - 16:55, 25 November 2023
...psilon(m) = 1$ for all $m$ and its inverse $\mu$, the [[Möbius function]]. Note that $\phi = \mu * N_1$, where $N_1(n) = n$ for all $n$, and that $\tau = \
3 KB (419 words) - 20:15, 19 November 2017
...d></tr><tr><td valign="top">[12]</td> <td valign="top"> B. Kamiński, "A note on $K$-systems" ''Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys.'' ,
7 KB (1,037 words) - 16:58, 1 July 2020
...End}(P,{+})$ be the ring of endomorphisms of the additive group of $P$ and note that $\text{End}(P,{+})$ is a left [[module]] over $P$. There is a one-to-o
3 KB (470 words) - 19:10, 9 November 2016
<TR><TD valign="top">[5]</TD> <TD valign="top"> Y. Nakai, "Note on the intersection of an algebraic variety with the generic hyperplane" ''
3 KB (451 words) - 11:57, 23 April 2017
...quivalent (over $\Sigma ^ { * }$) if they have exactly the same solutions. Note that only systems of equations without constants are considered here. Howev
...]] and rings of integer $( 2 \times 2 )$-matrices in [[#References|[a5]]]. Note that in the latter proof an algebraic structure with two operations, namely
7 KB (1,052 words) - 16:57, 1 July 2020
from physics rather than economics or sociology", as Fortet puts it in his note
interesting. Let us note particularly his work on the
11 KB (1,766 words) - 18:41, 6 March 2024
...[a3]</TD> <TD valign="top"> S. Grandlund, P. Lindqvist, O. Martio, "Note on the PWB-method in the non-linear case" ''Pacific J. Math.'' , '''125'''
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Note that a triple system in this sense is completely different from, e.g., the
3 KB (525 words) - 10:13, 30 April 2018
...</TD></TR><TR><TD valign="top">[a5]</TD> <TD valign="top"> M. Mazur, "A note on the growth of Davenport's constant" ''Manuscr. Math.'' , '''74''' (199
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...with weights $w _ { 1 } = ( 1 + c ) / 2$ and $w _ { 2 } = ( 1 - c ) / 2$. Note that if the weights are given by $w _ { 1 } = ( 1 + \operatorname { sign }
...reversing the order of differencing in the predictor and corrector steps. Note that the MacCormack scheme (a11) is not written in conservative form (a2).
16 KB (2,341 words) - 19:00, 26 March 2023
...gy principal series instead of non-degenerate continuous principal series.
Note that <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.
8 KB (1,022 words) - 17:01, 7 February 2011
...<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
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...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
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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 $\mathcal{C}$.
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...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
...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>
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<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
It is important to note that the $\Gamma^k_{ij}$ are not the components of a tensor field. In fact
3 KB (550 words) - 10:36, 23 May 2017
Note that as the Poisson density is given by $f(y_i|x_i)=\frac{1}{y_i!}\exp[y_il
$\mbox{var}[Y_{it}]=\sigma_{itt}.$ Note that both $\mu_{it}$ and $\sigma_{itt}$ are functions of $\beta.$ But, when
15 KB (2,382 words) - 10:19, 10 March 2024
...u_n = a \right\}$ and $\left\{0 \le n \le 2^{k+1} - 1 : u_n = b \right\}$. Note that this partition is conjectured to be the unique partition of the set $\
[[unavoidable pattern]]s in strings. Note that such combinatorial properties were used to solve various algebraic pro
10 KB (1,633 words) - 08:05, 26 November 2023
...product of the fibres $\a^{-1}(c)\subseteq A$ and $\b^{-1}(c)\subseteq B$. Note also that (binary) products (cf.
3 KB (575 words) - 10:30, 23 November 2013
<TR><TD valign="top">[a1]</TD> <TD valign="top"> K.A.H. Gravett, "Note on a result of Krull" ''Proc. Cambridge Philos. Soc.'' , '''52''' (1956) pp
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* ''In case you encounter any problems with the new software just drop a note on the [[Talk:Main_Page | discussion page]] of this page.''
4 KB (605 words) - 06:08, 22 May 2020
<tr><td valign="top">[a1]</td> <td valign="top"> F. Beukers, "A note on the irrationality of $\zeta ( 3 )$" ''Bull. London Math. Soc.'' , '''11
3 KB (525 words) - 20:51, 23 January 2024
Note that each point is incident with 2 lines, each line is incident with 2 poin
4 KB (592 words) - 17:43, 16 March 2023
...TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top"> A.B. Cruse, "A note on one-factors in certain regular multigraphs" ''Discrete Math.'' , '''18'
4 KB (619 words) - 09:30, 19 January 2021
Note that in some of the literature dealing with webs, nets and pencils in the s
(Note that a square matrix $ P ( \lambda ) $
20 KB (3,056 words) - 08:25, 6 June 2020
...pposed to the $n$ Gershgorin discs in (a2). But it is equally important to note that the eigenvalue inclusions of (a2) and (a5) use the exact same data fro
10 KB (1,639 words) - 07:05, 15 February 2024
'''Note:''' if you decided not to use the folder ''Documents/EOM_Scripts'', you ne
'''Note:''' the It's All Text add-on saves temporary files in <nowiki>Library/Appli
10 KB (1,689 words) - 13:29, 13 November 2014
...td></tr><tr><td valign="top">[a6]</td> <td valign="top"> P. Traczyk, "A note on rotant links" ''J. Knot Th. Ramifications'' , '''8''' : 3 (1999) pp.
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