¿Hey, whatcha doin on this page?
It's just where I put stuff that I'm experimenting on for possible f¯uture use.
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Fred has: 10 pineapples 5 kiwis
Script error
(that we use for Halloween specials)
Script error
$$ \begin{align*} \tag{1} a\ket{n}&=\sqrt{n}\ket{n-1}\,,&\bra{n}\,&a=\bra{n+1}\sqrt{n+1}\,,\\ \ud{a}\ket{n}&=\sqrt{n+1}\ket{n+1}\,,&\bra{n}\,&\ud{a}=\bra{n-1}\sqrt{n}\,, \end{align*} $$
$$ \begin{align*} \kern-1cm{(\mathrm{for}~i\le n+j)}\kern1cm a^i{\ud{a}}^j\ket{n}&={(n+j)!\over\sqrt{n!}\sqrt{(n+j-i)!}}\ket{n+j-i}\,,\\ \kern-1cm{(\mathrm{for}~i\le n)}\kern1cm a^{\dagger j}a^i\ket{n}&={\sqrt{n!}\sqrt{(n+j-i)!}\over(n-i)!}\ket{n+j-i}\,. \end{align*} $$
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
$$f(z) = \left( \prod_{j=1}^n \frac{z - z_j}{1 - \overline{z_j}z} \right) \left( \prod_{j=1}^m \frac{z - w_j}{1 - \overline{w_j}z} \right)^{-1} g(z)$$
$$ \newcommand{\Re}{\mathrm{Re}\,} \newcommand{\pFq}[5]{{}_{#1}\mathrm{F}_{#2} \left( \genfrac{}{}{0pt}{}{#3}{#4} \bigg| {#5} \right)} $$
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 |
This is a result, so we spare a minute to label the axes and make it a figure of its own, Fig. (1).
File:AbedularCanencia-27Oct2013.gpx
File:AbedularCanencia-27Oct2013.gpx
Download the gpx file for this track.
Download the gpx file for this track.
Download the gpx file for this track.
$$ax^2+bx+c$$
$$\color{red}{ax^2}+bx+c$$
\begin{array}{ l || r | r | r } % & All years\\ & (since 2003) & in 2015 \\ & Impact Factor & All years & in 2015 \\ \hline\hline Nature group~\footnote{Nature \textbf{457}:291 (2009); Nature Physics \textbf{6}:527 (2010); Nature Photonics \textbf{8}:550 (2014); Light: Science \& Applications \textbf{4}:e350 (2015); Nature Communication in press (2015).} & 12--40 & 5 & 2 \\ Phys.~Rev.~Lett.~\footnote{PRL in press (2015); PRL \textbf{115}:196402 (2015); PRL \textbf{114}:233601 (2015); PRL \textbf{113}:226401 (2014); PRL \textbf{112}:113602 (2014); PRL \textbf{109}:183601 (2012); PRL \textbf{105}:233601 (2010); PRL \textbf{104}:106402 (2010); PRL \textbf{103}:096404 (2009); PRL \textbf{101}:083601 (2008); PRL \textbf{93}:016402 (2004); PRL \textbf{91}:156403 (2003).} & 7.5 & 12 & 3 \\ New J. Phys.~\footnote{NJP in press (2015); NJP \textbf{17}:010201 (2015); NJP \textbf{15}:033036 (2013); NJP \textbf{13}:113014 (2011).} & 3.5 & 4 & 2 \\ Phys.~Rev.~A \& B~\footnote{PRA \textbf{91}:043807(2015); PRA \textbf{90}:052111(2014); PRB \textbf{90}:035413(2014); PRB \textbf{84}:195313(2011); PRB \textbf{84}:085320(2011); PRA \textbf{84}:043816(2011); PRB \textbf{81}:035302(2010); PRB \textbf{79}:235326(2009); PRB \textbf{79}:235325(2009); PRB \textbf{78}:085304(2008); PRB \textbf{76}:235317(2007); PRB \textbf{73}:115343(2006); PRB \textbf{73}:035315(2006); PRB \textbf{68}:085311(2003).} & 3 & 14 & 1 \\ Opt. Express, Physics Lett., Eur. Phys. Lett. \& similar & UNIQ3e2afc99dc60b181-MathJax-14-QINU & 13 & 0 \\ Lower Impact Factor journals & UNIQ3e2afc99dc60b181-MathJax-15-QINU & UNIQ3e2afc99dc60b181-MathJax-16-QINU & 0 \\ \hline Total && UNIQ3e2afc99dc60b181-MathJax-17-QINU & 8 \end{array}
This ...
Katia Lipovoï