gwzhenen coment or coment

yesterday, I vazher stoat-banat to maket-kazhing matematiken.

yesterday, I vazher stoat-banat ket to maket-kazhing matematiken.

yesterday, I wemse making matematiken.

yesterday, I wemse not making matematiken.

I ame making [o] I wemse making [o] I humse making [o] I fumse making

yu its making [o] yu wots making [o] yu hets making [o] yu futs making

he is making [o] he wos making [o] he hes making [o] he fus making

she is making [o] she wos making [o] she hes making [o] she fus making

wies somitch [o] wies foremitch [o] wies husemitch [o] wies fosemitch

yues sowitch [o] yues forewitch [o] yues husewitch [o] yues fosewitch

hies are making [o] hies werse making [o] hies hurse making [o] hies furse making

shies are making [o] shies werse making [o] shies hurse making [o] shies furse making

singletons

x = y <==> {...(n)...{x}...(n)...} = {...(n)...{y}...(n)...}

x = y <==> }...(-n)...}x{...(-n)...{ = }...(-n)...}y{...(-n)...{

x = y

{...(n)...{x}...(n)...} = {...(n)...{y}...(n)...}

}...(-n)...}{...(n)...{x}...(n)...}{...(-n)...{ = }...(-n)...}{...(n)...{y}...(n)...}{...(-n)...{

x = y

x = y

}...(-n)...}x{...(-n)...{ = }...(-n)...}y{...(-n)...{

{...(n)...{}...(-n)...}x{...(-n)...{}...(n)...} = {...(n)...{}...(-n)...}y{...(-n)...{}...(n)...}

x = y

quintica polinomi y serie exponencial

x^{5}+ax^{3}+(a^{2}/5)·x+c = 0

u^{5}+v^{5} = c

5uv( u^{3}+v^{3} ) = a·( u^{3}+v^{3} )

10·(uv)^{2}( u+v ) = (2a)·uv·(u+v)

a·uv(u+v) = (a^{2}/5)·(u+v)

x^{5}+5x^{3}+5x+c = 0

x^{5}+10x^{3}+20x+c = 0

f(x) = f(a)+c_{1}·(e^{x}+(-1)·e^{a})+c_{2}·(e^{x}+(-1)·e^{a})^{2}+...

... c_{n}·(e^{x}+(-1)·e^{a})^{n}+...

d_{x}[f(a)] = c_{1}·e^{a}

c_{1} = d_{x}[f(a)]·e^{(-a)}

d_{xx}^{2}[f(a)] = c_{1}·e^{a}+c_{2}e^{2a}

c_{2} = ( d_{xx}^{2}[f(a)]+(-1)·d_{x}[f(a)] )·e^{(-2)a} 

d_{xxx}^{3}[f(a)] = c_{1}e^{a}+c_{2}e^{2a}+c_{3}e^{3a}

c_{3} = ( d_{xxx}^{3}[f(a)]+(-1)·d_{xx}^{2}[f(a)] )·e^{(-3)a}

e^{x} = e^{a}+(e^{x}+(-1)·e^{a})

e^{(-x)} = ( 2+(-1)·e^{x} )+2·sum[ k = 2 --> oo ][ (-1)^{k}·(e^{x}+(-1))^{k} ]

cosh(x) = 1+sum[ k = 2 --> oo ][ (-1)^{k}·(e^{x}+(-1))^{k} ]

sinh(x) = ( e^{x}+(-1) )+(-1)·sum[ k = 2 --> oo ][ (-1)^{k}·(e^{x}+(-1))^{k} ]

espectroescopia tecnologia industrial

hf = a_{3}·(4/3)·pi·R^{3}+pi·RhP

hf = a_{3}·(4/3)·pi·(u+v)^{3}+pi·(u+v)hP

hf = a_{3}·(4/3)·pi·(u^{3}+3uv(u+v)+v^{3})+pi·(u+v)hP

hf = a_{3}·(4/3)·pi·(u^{3}+3uv(u+v)+v^{3})+pi·(u+v)hP

uv = ((hP)/a_{3})·(1/4)

(uv)^{3} = ((hP)/a_{3})^{3}·(1/64)

hf·u^{3} = a_{3}·(4/3)·pi·u^{6}+(1/3)·pi·(1/16)·( (hP)^{3}/(a_{3})^{2} )

u^{3} = ...

... ((1/2)·(1/(pi·a_{3}))·(3/4)·(hf+((hf)^{2}+(1/9)·pi^{2}·((hP)^{3}/a_{3}))^{(1/2)}))

v^{3} = ...

... ((1/2)·(1/(pi·a_{3}))·(3/4)·(hf+(-1)·((hf)^{2}+(1/9)·pi^{2}·(h^{3}/a_{3}))^{(1/2)}))

álgebra lineal

[Ab][ b != 0 ] ==>

( <a,b>,<b,c> )[o]( ( 1/det(A) )·( <c,(-b)>,<(-b),a> ) ) = ...

... ( <1,( ((-1)·ab·0)/det(A) )>,<( (bc·0)/det(A) ),1> )

( ( 1/det(A) )·( <c,(-b)>,<(-b),a> ) )[o]( <a,b>,<b,c> ) = ...

... ( <1,( (bc·0)/det(A) )>,<( ((-1)·ab·0)/det(A) ),1> )

( <a,0>,<0,c> )[o]( ( 1/det(A) )·( <c,0>,<0,a> ) ) = ...

... ( <1,( ((2a)·0)/det(A) )>,<( ((2c)·0)/det(A) ),1> )

( ( 1/det(A) )·( <c,0>,<0,a> ) )[o]( <a,0>,<0,c> ) = ...

... ( <1,( ((2c)·0)/det(A) )>,<( ((2a)·0)/det(A) ),1> )

( <x,b,b>,<b,y,b>,<b,b,z> )[o] ...

... ( ( 1/det(A) )·( <yz+(-1)·b^{2},b^{2}+(-1)·bz,b^{2}+(-1)·by> ) ) = ...

... ( <1,a·0,c·0> )

caos

Seguir voces de la mente <==> ...

... Seguir un Guardián de secretos de Slanesh.

Creyer que te ataca un hombre en la alma <==> ...

... No creyer que te ataca un Devorador de Almas de Khorne.

Apestar lo sexo <==> ...

... Follar con una Gran Inmundicia de Nurgle.

No creyer en esclavos infieles zombis <==> ...

... No creyer en un Señor de la Transformación de Zhentch.

precios recomendados

Precio recomendado:

1.25€

Bebida energética:

1.24+n = 2·(0.62)+(0.62) = 3·(0.62) = 1.86€

1.24+(n/2) = 2·(0.62)+(0.31) = 5·(0.31) = 1.55€

1.26+n = 3·(0.42)+(0.42) = 4·(0.42) = 1.68€

1.26+(n/3) = 3·(0.42)+(0.14) = 10·(0.14) = 1.40€

Precio recomendado:

1.10€

Café:

1.12+n = 2·(0.56)+(0.56) = 3·(0.56) = 1.68€

1.12+(n/2) = 2·(0.56)+(0.28) = 5·(0.28) = 1.40€

1.08+n = 3·(0.36)+(0.36) = 4·(0.36) = 1.44€

1.08+(n/3) = 3·(0.36)+(0.12) = 10·(0.12) = 1.20€

Precio recomendado:

0.55€

Refresco:

0.56+n = 2·(0.28)+(0.28) = 3·(0.28) = 0.84€

0.56+(n/2) = 2·(0.28)+(0.14) = 5·(0.14) = 0.70€

0.54+n = 3·(0.18)+(0.18) = 4·(0.18) = 0.72€

0.54+(n/3) = 3·(0.18)+(0.06) = 10·(0.06) = 0.60€

álgebra lineal

(f+g)(x) = f(x)+g(x)

(f·g)(x) = f(x)·g(x)

(s·f)(x) = s·f(x)

(f^{s})(x) = ( f(x) )^{s}

( s·(f+g) )(x) = s·( (f+g)(x) ) = s·( f(x)+g(x) ) = ...

... s·f(x)+s·g(x) = (s·f)(x)+(s·g)(x) = ( (s·f)+(s·g) )(x)

s·(f+g) = (s·f)+(s·g)

( (f·g)^{s} )(x) = ( (f·g)(x) )^{s} = ( f(x)·g(x) )^{s} = ...

... ( f(x) )^{s}·( g(x) )^{s} = f^{s}(x)·g^{s}(x) = ( f^{s}·g^{s} )(x)

(f·g)^{s} = f^{s}·g^{s}

simétrica de suma:

v(-x) = v(x)

anti-simétrica de suma:

u(-x) = (-1)·u(x)

simétrica de producto:

v(1/x) = v(x)

anti-simétrica de producto:

u(1/x) = (1/u(x))

[Eu(x)][Ev(x)][ u(x) anti-simétrica de suma & v(x) simétrica de suma & ...

... f(x) = (1/2)·( u(x)+v(x) ) ].

Demostración:

f(x) = (1/2)·( f(x)+f(x) ) = ...

... (1/2)·( f(x)+(-1)·f(-x)+f(-x)+f(x) ) = ...

... (1/2)·( u(x) = ( f(x)+(-1)·f(-x) )+v(x) = ( f(-x)+f(x) ) )

dim(f(x)) = (1/2)·( dim(u(x))+dim(v(x)) )

[Eu(x)][Ev(x)][ u(x) anti-simétrica de producto & v(x) simétrica de producto & ...

... f(x) = ( u(x)·v(x) )^{(1/2)} ].

Demostración:

f(x) = ( f(x)·f(x) )^{(1/2)} = ...

... ( ( f(x)/f(1/x) )·( f(1/x)·f(x) ) )^{(1/2)} = ...

... ( u(x) = ( f(x)/f(1/x) )+v(x) = ( f(1/x)·f(x) ) )^{(1/2)}

dim(f(x)) = ( dim(u(x))·dim(v(x)) )^{(1/2)}

s·<a_{ij}+b_{ij}> = s·( <a_{ij}>+<b_{ij}> ) = s·<a_{ij}>+s·<b_{ij}>

<a_{ij}·b_{ij}>^{s} = ( <a_{ij}>·<b_{ij}> )^{s} = <a_{ij}>^{s}·<b_{ij}>^{s}

simétrica:

v_{ji} = v_{ij}

anti-simétrica de suma:

u_{ji} = (-1)·u_{ij}

anti-simétrica de producto:

u_{ji} = (1/u_{ij})

[E<u_{ij}>][E<v_{ij}>][ <u_{ij}> anti-simétrica de suma & <v_{ij}> simétrica & ...

... <a_{ij}> = (1/2)·( <u_{ij}>+<v_{ij}> ) ].

Demostración:

<a_{ij}> = (1/2)·( <a_{ij}>+<a_{ij}> ) = ...

... (1/2)·( <a_{ij}>+(-1)·<a_{ji}>+<a_{ji}>+<a_{ij}> ) = ...

... (1/2)·( <( a_{ij}+(-1)·a_{ji} )>+<( a_{ji}+a_{ij} )> ) = ...

... (1/2)·( <u_{ij} = ( a_{ij}+(-1)·a_{ji} )>+<v_{ij} = ( a_{ji}+a_{ij} )> )

dim(a_{ij}) = (1/2)·( dim(u_{ij})+dim(v_{ij}) ) = (1/2)·( n^{2}+n^{2} ) = n^{2}

[E<u_{ij}>][E<v_{ij}>][ <u_{ij}> anti-simétrica de producto & <v_{ij}> simétrica & ...

... <a_{ij}> = ( <u_{ij}>·<v_{ij}> )^{(1/2)} ].

Demostración:

<a_{ij}> = ( <a_{ij}>·<a_{ij}> )^{(1/2)} = ...

... ( <a_{ij}>·<(1/a_{ji})>·<a_{ji}>·<a_{ij}> )^{(1/2)} = ...

... ( <( a_{ij}/a_{ji} )>·<( a_{ji}·a_{ij} )> )^{(1/2)} = ...

... ( <u_{ij} = ( a_{ij}/a_{ji} )>·<v_{ij} = ( a_{ji}·a_{ij} )> )^{(1/2)}

dim(a_{ij}) = ( dim(u_{ij})·dim(v_{ij}) )^{(1/2)} = ( n^{2}·n^{2} )^{(1/2)} = n^{2}

d_{x}[ ae^{2x}+be^{x} ] = 2ae^{2x}+be^{x}

( <2,0>,<0,1> )[o]<a,b> = <2a,b>

int[ ae^{2x}+be^{x} ] d[x] = (1/2)·ae^{2x}+(1/1)·be^{x}

( <(1/2),0>,<0,(1/1)> )[o]<a,b> = <(1/2)·a,(1/1)·b>

( <2,0>,<0,1> )[o]( <(1/2),0>,<0,(1/1)> ) = ( <1,(3/1)·0>,<(3/2)·0,1> )

( <(1/2),0>,<0,(1/1)> )[o]( <2,0>,<0,1> ) = ( <1,(3/2)·0>,<(3/1)·0,1> )

A[o]A^{[o](-1)} = [ a_{ii}=1 & a_{ij} = k_{ij}·0 ]

A^{[o](-1)}[o]A = [ a_{ii}=1 & a_{ji} = k_{ij}·0 ]

( <a,b>,<b,a> )[o]( ( 1/det(A) )·( <a,(-b)>,<(-b),a> ) ) = ...

... ( 1/det(A) )·( <a^{2}+(-1)·b^{2},(-1)·ab·0>,<ab·0,a^{2}+(-1)·b^{2}> )

( ( 1/det(A) )·( <a,(-b)>,<(-b),a> ) )[o]( <a,b>,<b,a> ) = ...

... ( 1/det(A) )·( <a^{2}+(-1)·b^{2},ab·0>,<(-1)·ab·0,a^{2}+(-1)·b^{2}> )

lagranians y ecuacions diferencials

(m/2)·d_{t}[x]^{2} = a_{3}·(4/3)·x^{3}+...

... (1/(2m))·( qgt )^{2}+(-1)·(a_{2}/2)·( e^{i·(a_{2}/m)^{(1/2)}·t} )^{2}

x(t) = [[(-2)]]( (-1)·(1/2)·( (2/m)·a_{3}·(4/3) )^{(1/2)}·t , ...

... ( ...

... (1/m^{2})·(qg)^{2}·(1/12)·t^{4}+...

... (1/4)·( e^{i·(a_{2}/m)^{(1/2)}·t} )^{2} ...

... )^{(-1)·(1/4)})

mecánica lineal:

energía:

mc·d_{t}[x(t)] = E_{1}(x)+...+E_{n}(x)

fuerza:

mc·d_{tt}^{2}[x(t)]·(1/d_{t}[x]) = d_{x}[ E_{1}(x)+...+E_{n}(x) ]

potencia:

mc·d_{tt}^{2}[x(t)] = d_{t}[ E_{1}(x)+...+E_{n}(x) ]

sin momento:

mc != mc·ln( d_{t}[x] )

mecánica clásica:

energía:

(m/2)·d_{t}[x(t)]^{2} = E_{1}(x)+...+E_{n}(x)

fuerza:

m·d_{tt}^{2}[x(t)] = d_{x}[ E_{1}(x)+...+E_{n}(x) ]

potencia:

m·d_{tt}^{2}[x(t)]·d_{t}[x(t)] = d_{t}[ E_{1}(x)+...+E_{n}(x) ]

momento:

m·d_{t}[x(t)] = int[ d_{x}[ E_{1}(x)+...+E_{n}(x) ] ] d[t]

mecánica enésima:

energía:

(1/n)·(m/c^{n+(-2)})·d_{t}[x(t)]^{n} = E_{1}(x)+...+E_{n}(x)

fuerza:

(m/c^{n+(-2)})·d_{t}[x(t)]^{n+(-2)}·d_{tt}^{2}[x(t)] = d_{x}[ E_{1}(x)+...+E_{n}(x) ]

potencia:

((mc)/c^{n+(-1)})·d_{t}[x(t)]^{n+(-1)}·d_{tt}^{2}[x(t)] = d_{x}[ E_{1}(x)+...+E_{n}(x) ]

momento:

n != 2 ==>

(m/c^{n+(-2)})·d_{t}[x(t)]^{n+(-1)} != (m/c^{n+(-2)})·(1/(n+(-1)))·d_{t}[x(t)]^{n+(-1)}

lagranians y ecuacions diferencials

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

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

( [[k]]( f(x),g(x) ) )^{n} = [[k·n]]( f(x),g(x) )

int[ [[k]]( f(x),g(x) ) ] d[x] = ...

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

(1/n)·(m/c^{n+(-2)})·d_{t}[x(t)]^{n} = (a_{k}/k)·x^{k}+E(t)

an+(-n) = ak  <==> a = ( n/(n+(-k)) ) 

x(t) = [[(n/(n+(-k)))]]( ( (n+(-k))/n )·( n·(c^{n+(-2)}/m)·(a_{k}/k) )^{(1/n)}·t , ...

... ( n·(c^{n+(-2)}/m)·int-...(n)...-int[ E(t) ] d[t]...(n)...d[t] )^{( (n+(-k))/n^{2} )} )

mecánica industrial:

oscilador harmónico elíptico en un campo constante:

mc·d_{t}[x(t)] = (-1)·(a_{2}/2)·x^{2}+(1/(2m))( qgt )^{2}

x(t) = [[(-1)]]( ( (1/(mc))·(a_{2}/2) )·t , ( (1/(mc))·(1/(6m))·(qg)^{2}·t^{3} )^{(-1)} )

oscilador harmónico hiperbólico en un campo constante:

mc·d_{t}[x(t)] = (a_{2}/2)·x^{2}+(1/(2m))( qgt )^{2}

x(t) = [[(-1)]]( ( (-1)·(1/(mc))·(a_{2}/2) )·t , ( (1/(mc))·(1/(6m))·(qg)^{2}·t^{3} )^{(-1)} )

d_{x}[ [[e]]( f(x),g(x) ) ]^{n} = ...

... ( [[e]]( f(x),g(x) )·d_{x}[f(x)] )^{n}+d_{x...x}^{n}[ ( e^{( g(x) ) } )^{n} ]

(1/n)·(m/c^{n+(-2)})·d_{t}[x(t)]^{n} = (a_{n}/n)·x^{n}+E(t)

x(t) = [[e]]( ( ( n·(c^{n+(-2)}/m)·(a_{n}/n) )^{(1/n)}·t , ...

... ln( ( n·(c^{n+(-2)}/m)·int-...(n)...-int[ E(t) ] d[t]...(n)...d[t] )^{(1/n)} ) )

mecánica clásica:

oscilador harmónico elíptico en un campo constante:

(m/2)·d_{t}[x(t)]^{2} = (-1)·(a_{2}/2)·x^{2}+(1/(2m))( qgt )^{2}

x(t) = [[e]]( ( (a_{2}/m) )^{(1/2)}·it , ln( ( (1/m)·(1/(12m))·(qg)^{2}·t^{4} )^{(1/2)} ) )

oscilador harmónico hiperbólico en un campo constante:

(m/2)·d_{t}[x(t)]^{2} = (a_{2}/2)·x^{2}+(1/(2m))( qgt )^{2}

x(t) = [[e]]( ( (a_{2}/m) )^{(1/2)}·t , ln( ( (1/m)·(1/(12m))·(qg)^{2}·t^{4} )^{(1/2)} ) )

teoría de cordes

h = (-1)·qg

(-1) [< u [< 1 & 1 [< v [< e

L(x,u,v) = qg·x(u,v)+h( (1/2)·u^{2}+ln(v) )

x(u,v) = ( (1/2)·u^{2}+ln(v) )

S_{uu} = int-int[ u^{2} ] d[u]d[u] = (1/12)·u^{4} = (1/12)·d_{u}[x]^{4}

S_{vv} = int-int[ (1/v^{2}) ] d[v]d[v] = ln(1/v) = ln( d_{v}[x] )

d_{x}[ H_{u}( d_{u}[x] ) ]^{(1/2)} = (1/12)·d_{u}[x]^{4} = (1/12)·u^{4}

H_{u}( d_{u}[x] ) = ( (1/12)·u^{4} )^{[o(x)o]2} = ...

... ( (1/60)·u^{5} )^{[o(u)o]2} [o(u)o] x = ...

... ( (1/1296)·u^{9} ) [o(u)o] x

H_{u}( d_{u}[x] ) = ( (1/1296)·d_{u}[x]^{9} ) [o(u)o] int[ d_{u}[x] ] d[u]

d_{x}[ H_{v}( d_{v}[x] ) ]^{(1/2)} = ln( d_{v}[x] ) = ln(1/v)

H_{v}( d_{v}[x] ) = ( ln(1/v) )^{[o(x)o]2} = ...

... ( ( ln(1/v) )^{2}·[er]_{k!:2}( ln(1/v) ) )^{[o(v)o]2} [o(v)o] x = ...

... ( (-1)·(1/3)·( ln(1/v) )^{3} [o(v)o] (1/2)·v^{2} ) [o(v)o] x

H_{v}( d_{v}[x] ) = ...

... ( (-1)·(1/3)·( ln( d_{v}[x] ) )^{3} [o(v)o] (1/2)·( 1/d_{v}[x] )^{2} ) [o(v)o] ...

.... int[ d_{v}[x] ] d[v]