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= NavBox = | = NavBox = | ||
− | {{ | + | <googlemap lat="32.546813" lon="11.953125" type="terrain" zoom="2" controls="small" width="730" height="400"> |
− | + | (F) 16.846091,-99.915515, La Quebrada, {{thisday|17|March|2005}}. | |
− | + | (F) 16.856761,-99.867810, [[Acapulco]], {{thisday|16|March|2005}}. | |
− | + | 40.031002, 15.675370, [[Maratea]], {{thisday|16|September|2005}} (F) on {{thisday|16|September|2009}}. | |
− | + | 51.504639,-0.171509, Hyde park, {{thisday|5|November|2005}}. | |
− | }} | + | 51.503475,-0.119663, Eye of London, {{thisday|3|November|2005}}. |
+ | 51.515356,-0.173908, Cardiff hotel, {{thisday|2|November|2005}}. | ||
+ | 48.858235,2.294569, Tour Eiffel, {{thisday|30|December|2005}}. | ||
+ | 40.638484,-4.049767, Collado Villalba, {{thisday|19|February|2006}}. | ||
+ | 40.415408,-3.707155, Plaza Mayor, February 2006. | ||
+ | 39.4739,-0.375728, Valencia, {{thisday|15|March|2006}}. | ||
+ | 45.527860,3.339433, [[Usson]], {{thisday|7|April|2006}}, last on {{thisday|23|April|2011}}. | ||
+ | 45.621629,3.205498, Montpeyroux, {{thisday|14|April|2006}}. | ||
+ | 45.517621,3.437181, Pierre du Moine Blanc, {{thisday|18|April|2006}}. | ||
+ | 40.414004,-3.681951, Parque del Retiro, {{thisday|27|April|2006}}. | ||
+ | 40.947857,-4.117859, Segovia, {{thisday|30|April|2006}}; (E) on {{thisday|9|September|2009}}. | ||
+ | 40.418084,-3.714258, Palacio Real, {{thisday|3|May|2006}}. | ||
+ | 40.641771,-4.155211, Valle de los Caídos, {{thisday|8|July|2006}}. | ||
+ | 40.589118,-4.147448, El Escorial, {{thisday|8|July|2006}}. | ||
+ | 48.208547,16.373010, Vienna, {{thisday|23|July|2006}}. | ||
+ | 48.055350,16.130969, Heiligenkreuz Abbey, {{thisday|27|July|2006}}. | ||
+ | 48.04534,16.096109, Mayerling, {{thisday|27|July|2006}}. | ||
+ | 48.842444,2.321878, Tour Montparnasse, {{thisday|2|August|2006}}. | ||
+ | 48.881082,2.383109, les Buttes Chaumont, {{thisday|2|August|2006}}. | ||
+ | 48.861816,2.398036, Père Lachaise, {{thisday|2|August|2006}}. | ||
+ | 48.886218,2.343130, Sacré Cœur, {{thisday|2|August|2006}}. | ||
+ | 45.047265,3.885179, Puy-en-Velay, [[August (2006)]]. | ||
+ | 44.853547,0.483402, Bergerac, {{thisday|18|August|2006}}. | ||
+ | 43.708769,-1.052911, Dax, {{thisday|19|August|2006}}. | ||
+ | 43.776447,-1.418469, Vieux Bouceau, {{thisday|19|August|2006}}. | ||
+ | 43.653637,-0.684931, Saint-Cricq-Chalosse, {{thisday|20|August|2006}}. | ||
+ | 44.830789,-0.572673, Bordeaux, {{thisday|21|August|2006}}. | ||
+ | 45.321166,3.696032, La Chaise-Dieu, {{thisday|27|August|2006}}. | ||
+ | 51.894643,-0.418401, [[Luton]]'s Wardown Park Museum, {{thisday|1|October|2006}}. | ||
+ | (F) 48.857039, 2.362410, Hotel Carnavalet, {{thisday|20|October|2006}}. | ||
+ | 51.525972,-0.124799, [[London]], {{thisday|4|November|2006}}. | ||
+ | 50.920355,-1.293576, Botleigh Grange Hotel, {{thisday|5|November|2006}}. | ||
+ | 53.380466,-1.470289, [[Sheffield]], {{thisday|7|November|2006}}. | ||
+ | 41.414044,2.152387, Parque Güell, {{thisday|17|November|2006}}. | ||
+ | 45.587339,3.128500, Champeix, November 2006. | ||
+ | </googlemap> | ||
=== week-end paris === | === week-end paris === |
¿Hey, whatcha doin on this page?
It's just where I put stuff that I'm experimenting on for possible f¯uture use.
Contents |
$$ \begin{align*} \tag{1} a\ket{n}&=\sqrt{n}\ket{n-1}\,,&\bra{n}\,&a=\bra{n+1}\sqrt{n+1}\,,\\ \ud{a}\ket{n}&=\sqrt{n+1}\ket{n+1}\,,&\bra{n}\,&\ud{a}=\bra{n-1}\sqrt{n}\,, \end{align*} $$
$$ \begin{align*} \kern-1cm{(\mathrm{for}~i\le n+j)}\kern1cm a^i{\ud{a}}^j\ket{n}&={(n+j)!\over\sqrt{n!}\sqrt{(n+j-i)!}}\ket{n+j-i}\,,\\ \kern-1cm{(\mathrm{for}~i\le n)}\kern1cm a^{\dagger j}a^i\ket{n}&={\sqrt{n!}\sqrt{(n+j-i)!}\over(n-i)!}\ket{n+j-i}\,. \end{align*} $$
arial font algerian font bookman font braggadocio font courier font desdemona font garamond font modern font symbol font (These are pretty silly.) wingdings font (As are these.)
$$ \newcommand{\Re}{\mathrm{Re}\,} \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)} $$
We consider, for various values of $s$, the $n$-dimensional integral \begin{align} \tag{2} W_n (s) &:= \int_{[0, 1]^n} \left| \sum_{k = 1}^n \mathrm{e}^{2 \pi \mathrm{i} \, x_k} \right|^s \mathrm{d}\boldsymbol{x} \end{align} % which occurs in the theory of uniform random walk integrals in the plane, where at each step a unit-step is taken in a random direction. As such, the integral (2) expresses the $s$-th moment of the distance to the origin after $n$ steps.
By experimentation and some sketchy arguments we quickly conjectured and strongly believed that, for $k$ a nonnegative integer \begin{align} \tag{3} W_3(k) &= \Re \, \pFq32{\frac12, -\frac k2, -\frac k2}{1, 1}{4}. \end{align} Appropriately defined, (3) also holds for negative odd integers. The reason for (3) was long a mystery, but it will be explained at the end of the paper.
\[ \begin{aligned} \label{def:1} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned} \]
\begin{aligned} \tag{4} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}
<google1 style="2"></google1>
Do you know this formula of mine <m>\frac{2\pi^2}{q}\int_0^\infty f(r)J_1(qr)rdr</m>?
21, May (2010) 17, August (2010)
<plot> set pm3d at s solid set palette rgb -6,-15,-7 unset colorbox set ticslevel 0 unset ztics unset surface set samples 70 set isosamples 70,70 complex(x,y)=x*{1,0}+y*{0,1} mandel(x,y,z,n) = (abs(z)>2.0 || n>=1000)? log(n): mandel(x,y,z*z+complex(x,y),n+1) a=-0.38 b=-0.612 set multiplot set origin 0,0 set size 0.55,0.77 splot [-0.5:0.5][-0.5:0.5] mandel(a,b,complex(x,y),0) set origin 0.35,-0.15 set size 0.7,0.96 set view 0,0,,, splot [-0.5:0.5][-0.5:0.5] mandel(a,b,complex(x,y),0) </plot>
<music>
\relative c' { e16-.->a(b gis)a-.->c(d b)c-.->e(f dis)e-.->a(b a) gis(b e)e,(gis b)b,(e gis)gis,(b e)e,(gis? b e) }
</music>
<music> \new Pianostaff << \new Staff { \time 2/2 \clef violin \key cis \minor \relative c \context Staff << \new Voice { \voiceOne
r4 cis8 dis e4 fis gis8 fis gis a gis fis e gis fis e fis gis fis e dis fis e dis e fis e d cis e d cis d e d cis b d cis b cis d cis b a cis b a b cis b a gis b a2 r cis2.
} \new Voice { \voiceTwo
e,8 gis a b cis dis bis cis dis4 r r2 r1 r1 r4 fis, b b b a8 gis a2 gis1~ gis8 gis fis eis fis2 gis2.
} \new Voice { \voiceThree \stemDown
s1 s s s s2. fis4 eis2 fis
} >> } \new Staff { \clef bass \time 2/2 \key cis \minor \relative c' \context Staff << \new Voice { \voiceOne
s1 r4 gis cis cis cis bis8 ais bis2 cis1 b2. s4 s1 b2 cis~ cis~ cis8 cis b a gis2.
} \new Voice { \voiceTwo
\stemUp cis,1 bis2 e dis1 \stemDown cis4 e a a a gis8 fis gis2~ \stemUp gis fis gis1 a2 fis~ fis8 fis e dis e4
} \new Voice { \voiceThree
\stemDown cis4 b a2 gis4 r4 g2\rest e1\rest e1\rest e1\rest r4 cis' fis fis fis eis8 dis eis2 fis r r
} >> } >> </music>
<googlemap lat="32.546813" lon="11.953125" type="terrain" zoom="2" controls="small" width="730" height="400"> (F) 16.846091,-99.915515, La Quebrada, 17 March (2005). (F) 16.856761,-99.867810, Acapulco, 16 March (2005). 40.031002, 15.675370, Maratea, 16 September (2005) (F) on 16 September (2009). 51.504639,-0.171509, Hyde park, 5 November (2005). 51.503475,-0.119663, Eye of London, 3 November (2005). 51.515356,-0.173908, Cardiff hotel, 2 November (2005). 48.858235,2.294569, Tour Eiffel, 30 December (2005). 40.638484,-4.049767, Collado Villalba, 19 February (2006). 40.415408,-3.707155, Plaza Mayor, February 2006. 39.4739,-0.375728, Valencia, 15 March (2006). 45.527860,3.339433, Usson, 7 April (2006), last on 23 April (2011). 45.621629,3.205498, Montpeyroux, 14 April (2006). 45.517621,3.437181, Pierre du Moine Blanc, 18 April (2006). 40.414004,-3.681951, Parque del Retiro, 27 April (2006). 40.947857,-4.117859, Segovia, 30 April (2006); (E) on 9 September (2009). 40.418084,-3.714258, Palacio Real, 3 May (2006). 40.641771,-4.155211, Valle de los Caídos, 8 July (2006). 40.589118,-4.147448, El Escorial, 8 July (2006). 48.208547,16.373010, Vienna, 23 July (2006). 48.055350,16.130969, Heiligenkreuz Abbey, 27 July (2006). 48.04534,16.096109, Mayerling, 27 July (2006). 48.842444,2.321878, Tour Montparnasse, 2 August (2006). 48.881082,2.383109, les Buttes Chaumont, 2 August (2006). 48.861816,2.398036, Père Lachaise, 2 August (2006). 48.886218,2.343130, Sacré Cœur, 2 August (2006). 45.047265,3.885179, Puy-en-Velay, August (2006). 44.853547,0.483402, Bergerac, 18 August (2006). 43.708769,-1.052911, Dax, 19 August (2006). 43.776447,-1.418469, Vieux Bouceau, 19 August (2006). 43.653637,-0.684931, Saint-Cricq-Chalosse, 20 August (2006). 44.830789,-0.572673, Bordeaux, 21 August (2006). 45.321166,3.696032, La Chaise-Dieu, 27 August (2006). 51.894643,-0.418401, Luton's Wardown Park Museum, 1 October (2006). (F) 48.857039, 2.362410, Hotel Carnavalet, 20 October (2006). 51.525972,-0.124799, London, 4 November (2006). 50.920355,-1.293576, Botleigh Grange Hotel, 5 November (2006). 53.380466,-1.470289, Sheffield, 7 November (2006). 41.414044,2.152387, Parque Güell, 17 November (2006). 45.587339,3.128500, Champeix, November 2006. </googlemap>
Days | Pet (salida-llegada ida) (salida-llegada vuelta) |
Beb (salida-llegada ida) (salida-llegada vuelta) |
Prices | Total (€) |
---|---|---|---|---|
15-18 | 20:30-22:30 10:15-12:20 |
06:35-08:10 21:30-23:00 |
103+109 | 212 |
15-18 | 20:30-22:30 10:15-12:20 |
12:55-14:35 10:25-11:55 |
103+136 | 239 |
15-18 | 18:30-20:35 10:00-12:10 |
12:55-14:35 10:25-11:55 |
126+136 | 262 |
22-25 | 7:05-9:10 12:30-14:35 |
06:35-08:10 21:30-23:00 |
113+109 | 222 |
22-25 | 7:05-9:10 12:30-14:35 |
10:35-12:15 16:05-17:35 |
113+136 | 249 |