mecànica cuàntica

( h^{2}/(2ml) )·d_{x}[f(x)] = ( E_{n}+q·A(x) )·f(x)

f(x) = sum[ (1/k!)·( ( (2ml)/h^{2} )·x [o(x)o] ( E_{n}·x+q·int[ A(x) ] d[x] ) [o(x)o] x )^{k} ]

( h^{2}/(2m) )·d_{xx}^{2}[f(x)] = ( E_{n}+q·A(x) )·f(x)

f(x) = ...

... sum[ (1/k!)·( ( (2m)/h^{2} )^{(1/3)}·x [o(x)o] ( E_{n}+q·A(x) )^{[o(x)o](1/3)} [o(x)o] x )^{k} ]

d_{x}[ ( f(x) [o(x)o] g(x) )^{k} ] = ...

... ( f(x) [o(x)o] g(x) )^{k} [o(x)o] ( f(x) [o(x)o] g(x) )^{[o(x)o]2}

d_{x}[ ( f(x) [o(x)o] g(x) )^{k} ] = ...

... k·( f(x) [o(x)o] g(x) )^{k+(-1)}·( d_{x}[f(x)]·d_{x}[g(x)] )

demostració per isomorfisme de grups.

f( d_{x}[f(x)]·d_{x}[g(x)] ) = int[ d_{x}[f(x)]·d_{x}[g(x)] ] d[ f(x) [o(x)o] g(x) ]

f( k·( f(x) [o(x)o] g(x) )^{k+(-1)} ) = ( f(x) [o(x)o] g(x) )^{k}

desigualtats

ln(n!) [< 1+...+n

n+1 [< n+n = 2n [< e^{n+1}

ln(n+1) [< n+1

n [< 1+...+n

1 [< n [< n+1

n [< e^{1}+...+e^{n}

1 [< e [< e^{n+1}

1+...+(1/n) [< n

( 1/(n+1) ) [< (1/n) [< 1

tecnología industrial: obra y construcción

paleta triangular y cemento

PV = px·(1/2)·ab

paleta rectangular y yeso

PV = px·ab

molde de pilar y hormigón

PV = p·(2x+2y)·ab

pilares de hierro y hormigón

PV = qg·u_{i}

mallado de hierro y hormigón

PV = qg·u_{i}^{j}

música

[12+01][12+01][12+01][12+02][12+01][12+02][12+01][12+02]

[12+01][12+01][12+01][12+02][12+01][12+02][00+08][...] = 3·5·13·k

[12+07][12+07][12+07][12+08][12+07][12+08][12+07][12+08]

[12+07][12+07][12+07][12+08][12+07][12+08][12+02][...] = 3·5·19·k

contra

[00+05] ==> [12+05]+(-1)·[12+01]+(-1)·01 = 03

[00+05] ==> [12+05]+(-1)·[12+02]+(-1)·01 = 02

[00+05] ==> [00+08]+(-1)·[00+05]+(-1)·01 = 02

[00+06] ==> [12+06]+(-1)·[12+01]+(-1)·01 = 04

[00+06] ==> [12+06]+(-1)·[12+02]+(-1)·01 = 03

[00+06] ==> [00+08]+(-1)·[00+06]+(-1)·01 = 01

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)