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[[Image:Icon_gpx.jpg|24px|link=]]Download the [[gpx file]] '''<wz tip="You may want to use right click on some browsers.">[[Media:AbedularCanencia-27Oct2013.gpx|for this track]]'''</wz>. | [[Image:Icon_gpx.jpg|24px|link=]]Download the [[gpx file]] '''<wz tip="You may want to use right click on some browsers.">[[Media:AbedularCanencia-27Oct2013.gpx|for this track]]'''</wz>. | ||
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+ | {{gpx|Media:AbedularCanencia-27Oct2013.gpx}} |
¿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.)
Blog:Sandbox File:laussy-jornada-divulgacion.ppt
$$ \newcommand{\Re}{\mathrm{Re}\,} \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)} $$
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>
http://www.youtube.com/watch?v=MZAKjKC7Gho http://www.youtube.com/watch?v=2_HXUhShhmY
# | Municipality | Autonomous community |
Pop. (2009) |
---|---|---|---|
1 | Madrid | ![]() |
3,255,944 |
2 | Barcelona | ![]() |
1,621,537 |
3 | Valencia | ![]() |
852,208 |
4 | Seville | ![]() |
703,206 |
5 | Zaragoza | ![]() |
674,317 |
6 | Málaga | ![]() |
568,305 |
7 | Murcia | ![]() |
436,870 |
8 | Palma | ![]() |
401,270 |
9 | Las Palmas | ![]() |
381,847 |
10 | Bilbao | ![]() |
354,860 |
11 | Alicante | ![]() |
334,757 |
12 | Córdoba | ![]() |
328,428 |
13 | Valladolid | ![]() |
317,864 |
14 | Vigo | ![]() |
297,332 |
15 | Gijón | ![]() |
277,554 |
16 | L'Hospitalet de Llobregat | ![]() |
257,038 |
17 | A Coruña | ![]() |
246,056 |
18 | Vitoria-Gasteiz | ![]() |
235,661 |
19 | Granada | ![]() |
234,325 |
20 | Elche | ![]() |
230,112 |
21 | Oviedo | ![]() |
224,005 |
22 | Santa Cruz de Tenerife | ![]() |
222,417 |
23 | Badalona | ![]() |
219,547 |
24 | Cartagena | ![]() |
211,996 |
25 | Terrassa | ![]() |
210,941 |
26 | Jerez de la Frontera | ![]() |
207,532 |
27 | Sabadell | ![]() |
206,493 |
28 | Móstoles | ![]() |
206,478 |
29 | Alcalá de Henares | ![]() |
204,574 |
30 | Pamplona | ![]() |
198,491 |
31 | Fuenlabrada | ![]() |
197,836 |
32 | Almería | ![]() |
188,810 |
33 | Leganés | ![]() |
186,066 |
34 | Donostia-San Sebastián | ![]() |
186,066 |
35 | Santander | ![]() |
182,700 |
36 | Castellón de la Plana | ![]() |
180,005 |
37 | Burgos | ![]() |
178,966 |
38 | Albacete | ![]() |
169,716 |
39 | Alcorcón | ![]() |
167,967 |
40 | Getafe | ![]() |
167,164 |
41 | Salamanca | ![]() |
155,619 |
42 | Logroño | ![]() |
152,107 |
43 | San Cristóbal de La Laguna | ![]() |
150,661 |
44 | Huelva | ![]() |
148,806 |
45 | Badajoz | ![]() |
148,334 |
46 | Tarragona | ![]() |
140,323 |
47 | Lleida | ![]() |
138.416 |
48 | Marbella | ![]() |
134,623 |
49 | León | ![]() |
134,305 |
50 | Cádiz | ![]() |
126,766 |
# | Municipality | Pop. (2009) |
---|---|---|
1 | Madrid ![]() |
3,255,944 |
2 | Barcelona ![]() |
1,621,537 |
3 | Valencia ![]() |
852,208 |
4 | Seville ![]() |
703,206 |
5 | Zaragoza ![]() |
674,317 |
6 | Málaga ![]() |
568,305 |
7 | Murcia ![]() |
436,870 |
8 | Palma ![]() |
401,270 |
9 | Las Palmas ![]() |
381,847 |
10 | Bilbao ![]() |
354,860 |
11 | Alicante ![]() |
334,757 |
12 | Córdoba ![]() |
328,428 |
13 | Valladolid ![]() |
317,864 |
14 | Vigo ![]() |
297,332 |
15 | Gijón ![]() |
277,554 |
16 | L'Hospitalet de Llobregat ![]() |
257,038 |
17 | A Coruña ![]() |
246,056 |
18 | Vitoria-Gasteiz ![]() |
235,661 |
19 | Granada ![]() |
234,325 |
20 | Elche ![]() |
230,112 |
21 | Oviedo ![]() |
224,005 |
22 | Santa Cruz de Tenerife ![]() |
222,417 |
23 | Badalona ![]() |
219,547 |
24 | Cartagena ![]() |
211,996 |
25 | Terrassa ![]() |
210,941 |
26 | Jerez de la Frontera ![]() |
207,532 |
27 | Sabadell ![]() |
206,493 |
28 | Móstoles ![]() |
206,478 |
29 | Alcalá de Henares ![]() |
204,574 |
30 | Pamplona ![]() |
198,491 |
31 | Fuenlabrada ![]() |
197,836 |
32 | Almería ![]() |
188,810 |
33 | Leganés ![]() |
186,066 |
34 | Donostia-San Sebastián ![]() |
186,066 |
35 | Santander ![]() |
182,700 |
36 | Castellón de la Plana ![]() |
180,005 |
37 | Burgos ![]() |
178,966 |
38 | Albacete ![]() |
169,716 |
39 | Alcorcón ![]() |
167,967 |
40 | Getafe ![]() |
167,164 |
41 | Salamanca ![]() |
155,619 |
42 | Logroño ![]() |
152,107 |
43 | San Cristóbal de La Laguna ![]() |
150,661 |
44 | Huelva ![]() |
148,806 |
45 | Badajoz ![]() |
148,334 |
46 | Tarragona ![]() |
140,323 |
47 | Lleida ![]() |
138,416 |
48 | Marbella ![]() |
134,623 |
49 | León ![]() |
134,305 |
50 | Cádiz ![]() |
126,766 |
File:AbedularCanencia-27Oct2013.gpx
File:AbedularCanencia-27Oct2013.gpx
Download the gpx file for this track.
Download the gpx file for this track.