cordes

teletransportador de altura

de un piso:

EF

FG <==

de dos pisos:

EEF

0F0

FGG <==

de tres pisos:

EEEF

00F0

0F00

FGGG <==

E(u) = d_{u}[he^{iu}+he^{iv}]^{2} corriente interno

G(v) = d_{v}[he^{iu}+he^{iv}]^{2} corriente externo

kurd

I studish bin matematican in yur hawsan.

I nish studish bin matematican in yur hawsan.

I studish binted matematican in yur hawsan.

yu studish binted matematican in my hawsan.

yu wont to makish bin a cotish binted wizhish me?

I wont to makish bin a cotish binted wizhish yu.

I wont a cotish binted for to takish bin.

I nish wont a cotish binted for to takish bin.

contracte de depta

compres y després vens,

y recuperes els diners tenint benefici.

(-n)+n+m = m

te endeptes, menys de set anys, y després vens,

y pagues la depta tenint benefici.

n+(-n)+m = m

topología

A_{1} [<< ... [<< A_{n} <==> A_{1} [ || ] ... [ || ] A_{n} = A_{n}

x € A_{1} [ || ] ... [ || ] A_{n}

x € A_{n} [ || ] ... [ || ] A_{n}

x € A_{n}

x € A_{1} [ || ] ... [ || ] A_{n}

A_{1} [<< ... [<< A_{n} <==> A_{1} [ & ] ... [ & ] A_{n} = A_{1}

x € A_{1} [ & ] ... [ & ] A_{n}

x € A_{1}

x € A_{1} [ & ] ... [ & ] A_{n}

{a_{m},...,a_{i}}

}a_{m},...,a_{i}{

[ || ]-[ i = m --> n ][ {a_{m},..., a_{i}} ] = {a_{m},...,a_{n}}

[ & ]-[ i = m --> n ][ }a_{m},...,a_{i}{ ] = }a_{m},...,a_{n}{

x = a_{m} ==> ...(n+(-m))... ==> ( x = a_{m} || ... || x = a_{n}

x != a_{m} <== ...(n+(-m))... <== ( x != a_{m} & ... & x != a_{n}

{a_{i}}

}a_{i}{

[ || ]-[ i = m --> n ][ {a_{i}} ] = {a_{m},...,a_{n}}

[ & ]-[ i = m --> n ][ }a_{i}{ ] = }a_{m},...,a_{n}{

{a_{i},b_{i}}

}a_{i},b_{i}{

[ || ]-[ i = m --> n ][ {a_{i},b_{i}} ] = {a_{m},...,a_{n}} [ || ] {b_{m},...,b_{n}}

[ & ]-[ i = m --> n ][ }a_{i},b_{i}{ ] = }a_{m},...,a_{n}{ [ & ] }b_{m},...,b_{n}{

cuina

beicon fregit lila

ceba fregida groc

mungetes blanc

perfum de all blanc

2 destructors

sucre blanc

sal blanca

tomáquet fregit vermell

ceba fregida groc

butifarra fregida marró

macarrons blanc

2 destructors

1 constructor

gambes rosa

poma ocre

pastanaga taronja

enciam verd

mayonesa blanc

2 destructors

teoría de cordes imperial

f(u,v) = e^{iu}+e^{iv}

(1/2^{m})( S(u,v) )^{2m} = ...

... int-int[ e^{(1/m)·2iu}·e^{(1/m)·(iu+iv)}] d[u]d[u]+...

... int-int[ e^{(1/m)·2iv}·e^{(1/m)·(iv+iu)}] d[v]d[v] = ...

... int[ (1/(3i))·e^{3iu}e^{iv}] d[u]+...

... int[ (1/(3i))·e^{3iv}e^{iu}] d[v] = ...

... (1/m)·(1/(3i))·(1/(3i)^{m})·e^{m·3iu}e^{m·iv}+...

... (1/m)·(1/(3i))·(1/(3i)^{m})·e^{m·3iv}e^{m·iu}

serie

(1/pi)·int[ x^{2}·cos(kx) ] d[x] = ...

(1/pi)·(1/k)·int[ x^{2}·cos(kx)·k ] d[x] = ...

(1/pi)·(1/k)·( x^{2}sin(kx)+(-1)·int[ 2x·sin(kx) ] d[x] ) =

pi^{2} = (pi^{2}/3)+4·sum[ (1/k^{2}) ]

(1/pi)·int[ (-x)·sin(kx) ] d[x] = ...

(1/pi)·(1/k)·x·cos(kx)+(-1)·int[ cos(kx) ] d[x]

pi = (pi/2)+sum[ (1/k) ]

sum[ (1/k) ] = (1/2)·pi

0 < x < pi

(1/pi)·( int[ (-x)^{3}·sin(kx) ] d[x]+(-2)·(1/k^{2})·int[ (-x)·sin(kx) ] d[x] ) = ...

(1/k^{2})·int[ 3·(-x)^{2}·cos(kx)·k ] d[x] = ...

... (1/k^{2})·( 3·(-x)^{2}·(-1)·sin(kx)+(-1)·int[ 6x·sin(kx) ] d[x] )

pi^{3} = (pi^{3}/4)+(pi^{3}/2)+5·sum[ (1/k^{3}) ]

sum[ (1/k^{3}) ] = (pi^{3}/20)