miércoles, 3 de mayo de 2023

física y topología y teoría-de-cuerdas

Ley:

d_{tt}^{2}[x] = (1/m)·F(t)

d_{t}[x] = (1/m)·int[ F(t) ]d[t]

x(t) = (1/m)·int-int[ F(t) ]d[t]d[t]

Deducción:

m·d_{tt}^{2}[x] = F(t)

d_{t}[x] = int[ d_{tt}^{2}[x] ]d[t] = int[ (1/m)·F(t) ]d[t] = (1/m)·int[ F(t) ]d[t]

x(t) = int[ d_{t}[x] ]d[t] = int[ (1/m)·int[ F(t) ]d[t] ]d[t] = (1/m)·int-int[ F(t) ]d[t]d[t]


Fumretzen-ten-dut-zû-tek més-nek tabaki-koak que ayere-dut.

Fumretzen-ten-dut-zû-tek ménus-nek tabaki-koak que ayere-dut.


Abans-nek dels déxum sisotzok,

no fumretzen-ten-dut-zava-tek

Després-nek dels déxum sisotzok,

fumretzen-ten-dut-zava-tek


Fumu-puesh mésh tabacu que ayere-dush

Fumu-puesh menush tabacu que ayere-dush


Abansh he-puesh compratu-dush,

un pernatúne-y de puerku.

Desprésh he-puesh compratu-dush,

un pernatúne-y de senglare-dush


Fumû més tabac que ahir

Fumû menys tabac que ahir


Constructor:

més [o] més-nek [o] mésh [o] méh

Destructor:

menys [o] ménus-nek [o] menush [o] menuh


Mi familia me está haciendo seguidores no siguiendo-me,

y no amar al próximo como a si mismo,

no vos quejéis si el mundo prójimo se cree que soy Jesucristo,

porque lo hacéis vosotros con vuestro rezo.

Se lo cree mucho el mundo que soy el mesías,

porque no es ninguien profeta en su tierra.


Teorema: [ fracción continua ]

2n = < 0,0,2n >

2n+1 = < 1,0,2n >


Clásico:

oveja [o] ovella

oreja [o] orella


ojo [o] ull

piojo [o] piull


Blindaje [o] Blindatjje

Rodaje [o] Rodatjje

Lenguaje [o] Llenguatjje

Hormaje [o] Formatjje [ Queso ]


Definición: [ de topología ]

[AD_{k}][ D_{k} € E ==> ( [ || ]-[k = 1]-[n][ D_{k} ] € E & [&]-[k = 1]-[n][ D_{k} ] € E ) ]

[A¬D_{k}][ ¬D_{k} € E ==> ( [&]-[k = 1]-[n][ ¬D_{k} ] € E & [ || ]-[k = 1]-[n][ ¬D_{k} ] € E ) ]

Definición: [ de morfismo-topológico ]

f( [ || ]-[k = 1]-[n][ D_{k} ] ) = [ || ]-[k = 1]-[n][ f(D_{k}) ]

f( [&]-[k = 1]-[n][ D_{k} ] ) = [&]-[k = 1]-[n][ f(D_{k}) ]

Teorema:

Sea ( E = { 0,D_{1},...(n)...,D_{n},A } & B = [ || ]-[k = 1]-[n][ D_{k} ] & B [<< A ) ==>

Si f(x) es un morfismo-topológico ==> ...

... f( interior[E] ) [ || ] f( exterior[E] ) = f(A).

Si f(x) es un morfismo-topológico ==> ...

... f( interior[E] ) [&] f( exterior[E] ) = f(0).

Demostración:

f( interior[E] ) = [ || ]-[k = 1]-[n][ f(D_{k}) ] = f( [ || ]-[k = 1]-[n][ D_{k} ] ) = f(B)

f( exterior[E] ) = [&]-[k = 1]-[n][ f(A [ \ ] D_{k}) ] = f( A [ \ ] [ || ]-[k = 1]-[n][ D_{k} ] ) = f(A [ \ ] B)

Base topológica:

B = [ || ]-[k = 1]-[n][ D_{k} ]

A [ \ ] B = [&]-[k = 1]-[n][ (A [ \ ] D_{k}) ]

C = [&]-[k = 1]-[n][ D_{k} ]

A [ \ ] C = [ || ]-[k = 1]-[n][ (A [ \ ] D_{k}) ]

Teorema:

Sea E = { 0,{x},{z,y},{x,y},{z},{x,y,z} }

Si f(x) es un morfismo-topológico ==> ...

... f( interior[E] ) [ || ] f( exterior[E] ) = f({x,y,z}).

Si f(x) es un morfismo-topológico ==> ...

... f( interior[E] ) [&] f( exterior[E] ) = f(0).

Demostración:

f( interior[E] ) = f({x}) [ || ] f({x,y}) = f({x,y})

f( exterior[E] ) = f({z,y}) [&] f({z}) = f({z})

Base topológica:

{x,y} = {x} [ || ] {x,y}

{z} = {z,y} [&] {z}

{x} = {x} [&] {x,y}

{y,z} = {z} [ || ] {z,y}

Teorema:

Sea E = { 0,[(-n),n]_{R},( ((-a),(-n))_{R} [ || ] (n,a)_{R} ),((-a),a)_{R} } & n < a

Si f(x) es un morfismo-topológico ==> ...

... f( interior[E] ) [ || ] f( exterior[E] ) = f(((-a),a)_{R}).

Si f(x) es un morfismo-topológico ==> ...

... f( interior[E] ) [&] f( exterior[E] ) = f(0).

Demostración:

( (-a) < x < (-n) < n < a || (-a) < (-n) [< x [< n < a || (-a) < (-n) < n < x < a ) ==> (-a) < x < a

( ( x < (-n) || n < x ) & (-n) [< x [< n ) ==> ( ¬( (-n) [< n ) & (-n) [< n )

[ (MP) [Ez][ x [< z & z [< y ] <==> x [< y ]

Base topológica:

[(-n),n]_{R} = [ || ]-[k = 1]-[n][ [(-k),k]_{R} ]

((-a),(-n))_{R} [ || ] (n,a)_{R} = [&]-[k = 1]-[n][ ((-a),(-k))_{R} [ || ] (k,a)_{R} ]

[(-1),1]_{R} = [&]-[k = 1]-[n][ [(-k),k]_{R} ]

((-a),(-1))_{R} [ || ] (1,a)_{R} = [ || ]-[k = 1]-[n][ ((-a),(-k))_{R} [ || ] (k,a)_{R} ]

Teorema:

Sea E = { 0,n,m,n+m }

Si f(x) es un morfismo-topológico ==> ...

... max{ f( interior[E] ),f( exterior[E] ) } = f(n+m).

Si f(x) es un morfismo-topológico ==> ...

... min{ f( interior[E] ),f( exterior[E] ) } = f(0).

Demostración:

f( interior[E] ) = max{ f(n),f(n+m) } = f(n+m)

f( exterior[E] ) = min{ f(m),f(0) } = f(0)

Base topológica:

n+m = max{ n,n+m }

0 = min{ m,0 }

n = min{ n,n+m }

m = max{ m,0 }

Teorema:

Sea E = { 0,(1/n),( 1+(-1)·(1/n) ),1 }

Si f(x) es un morfismo-topológico ==> ...

... max{ f( interior[E] ),f( exterior[E] ) } = f(1).

Si f(x) es un morfismo-topológico ==> ...

... min{ f( interior[E] ),f( exterior[E] ) } = f(0).

Demostración:

f( interior[E] ) = max{ f(1/n),f(1) } = f(1)

f( exterior[E] ) = min{ f(1+(-1)·(1/n)),f(0) } = f(0)

Base topológica:

1 = max{ (1/n),1 }

0 = min{ ( 1+(-1)·(1/n) ),0 }

(1/n) = min{ (1/n),1 }

( 1+(-1)·(1/n) ) = max{ ( 1+(-1)·(1/n) ),0 }


Compactificación de Alexandroff de los enteros:

Base topológica:

2p+1 = max{1,2p+1}

0 = min{0,2p}

1 = min{1,2p+1}

2p = max{0,2p}

[r]_{2m} = { p : [Ek][ p = (2m)·k+r ] } ==> ...

... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] = Z

[r]_{2m+1} = { p : [Ek][ p = (2m+1)·k+r ] } ==> ...

... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] [ || ] D_{r = 2m} = Z

Compactificación de Alexandroff de los polinomios:

2p+1 = max{1,2p+1}

0 = min{0,2p}

1 = min{1,2p+1}

2p = max{0,2p}

[r(x)]_{2m} = ...

... { P(x) : [Ek(x)][ P(x) = m(x)·k(x)+r(x) & grado(m(x)) = (2m) & grado(r(x)) = r ] } ==> ...

... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] = Z[x]

[r(x)]_{2m+1} = ...

... { P(x) : [Ek(x)][ P(x) = m(x)·k(x)+r(x) & grado(m(x)) = (2m+1) & grado(r(x)) = r ] } ==> ...

... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] [ || ] D_{r = 2m} = Z[x]

Compactificación de Alexandroff de los racionales:

Base topológica:

2p+1 = max{1,2p+1}

0 = min{0,2p}

1 = min{1,2p+1}

2p = max{0,2p}

[r]_{2m} = { (p/q) : [Ek][ (p/q) = (2m)·(k/q)+(r/q) ] } ==> ...

... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] = Q

[r]_{2m+1} = { (p/q) : [Ek][ (p/q) = (2m+1)·(k/q)+(r/q) ] } ==> ...

... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] [ || ] D_{r = 2m} = Q

Compactificación de Alexandroff de las fracciones polinómicas:

2p+1 = max{1,2p+1}

0 = min{0,2p}

1 = min{1,2p+1}

2p = max{0,2p}

[r(x)]_{2m} = ...

... { ( P(x)/Q(x) ) : [Ek(x)][ ( P(x)/Q(x) ) = m(x)·( k(x)/Q(x) )+( r(x)/Q(x) ) & ...

... grado(m(x)) = (2m) & grado(r(x)) = r ] } ==> ...

... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] = Q[x]

[r(x)]_{2m+1} = ...

... { ( P(x)/Q(x) ) : [Ek(x)][ ( P(x)/Q(x) ) = m(x)·( k(x)/Q(x) )+( r(x)/Q(x) ) & ...

... grado(m(x)) = (2m+1) & grado(r(x)) = r ] } ==> ...

... [ || ]-[r = 0]-[2m+(-1)][ D_{r = 2p} [ || ] D_{r = 2p+1} ] [ || ] D_{r = 2m} = Q[x]


Compactificación de Garriga-Alexandroff de los enteros:

Base topológica:

4p+3 = max{4p+1,4p+3}

4p = min{4p,4p+2}

4p+1 = min{4p+1,4p+3}

4p+2 = max{4p,4p+2}

[r]_{4m} = { p : [Ek][ p = (4m)·k+r ] } ==> ...

... [ || ]-[r = 0]-[4m+(-1)][ D_{r = 4p} [ || ] D_{r = 4p+2} [ || ] D_{r = 4p+1} [ || ] D_{r = 4p+3} ] = Q

[r]_{4m+1} = { p : [Ek][ p = (4m+1)·k+r ] } ==> ...

... [ || ]-[r = 0]-[4m+(-1)][ D_{r = 4p} [ || ] D_{r = 4p+2} [ || ] D_{r = 4p+1} [ || ] D_{r = 4p+3} ] ...

... [ || ] D_{4m} = Q

[r]_{4m+2} = { p : [Ek][ p = (4m+2)·k+r ] } ==> ...

... [ || ]-[r = 0]-[4m+(-1)][ D_{r = 4p} [ || ] D_{r = 4p+2} [ || ] D_{r = 4p+1} [ || ] D_{r = 4p+3} ] ...

... [ || ] D_{4m} [ || ] D_{4m+1} = Q

[r]_{4m+3} = { p : [Ek][ p = (4m+3)·k+r ] } ==> ...

... [ || ]-[r = 0]-[4m+(-1)][ D_{r = 4p} [ || ] D_{r = 4p+2} [ || ] D_{r = 4p+1} [ || ] D_{r = 4p+3} ] ...

... [ || ] D_{4m} [ || ] D_{4m+1} [ || ] D_{4m+2} = Q


Definición:[ de morfismo-topológico compacto ]

[EA][EB][ A = (a,b)_{R} & B = (¬b,¬a)_{R} & A [ || ] B = rec(f) ]

Teorema:

Si f(n) = n ==> f(n) es un morfismo-topológico compacto.

Demostración:

f(max{a_{1},...,a_{n}}) = max{a_{1},...,a_{n}} = max{f(a_{1}),...,f(a_{n})}

f(min{a_{1},...,a_{n}}) = min{a_{1},...,a_{n}} = min{f(a_{1}),...,f(a_{n})}

Base topológica:

0 = min{0,n}

n+1 = max{1,n+1}

1 = min{1,n+1}

n = max{0,n}

(0,n]_{R} [ || ] [1,n+1)_{R} [<< (0,oo)_{R}

Teorema:

Si f(n) = (1/n) ==> f(n) es un morfismo-topológico dual compacto.

Demostración:

f(max{a_{1},...,a_{n}}) = ( 1/max{a_{1},...,a_{n}} ) = min{(1/a_{1}),...,(1/a_{n})} =...

... min{f(a_{1}),...,f(a_{n})}

f(min{a_{1},...,a_{n}}) = ( 1/min{a_{1},...,a_{n}} ) = max{(1/a_{1}),...,(1/a_{n})} =...

... max{f(a_{1}),...,f(a_{n})}

Base topológica:

0 = min{0,( 1+(-1)·(1/n) )}

1 = max{1,(1/n)}

(1/n) = min{1,(1/n)}

( 1+(-1)·(1/n) ) = max{0,( 1+(-1)·(1/n) )}

[0,( 1+(-1)·(1/n) ]_{R} [ || ] [(1/n),1]_{R} [<< [0,1]_{R}

Teorema:

Si f(n) = n+p ==> f(n) es un morfismo-topológico compacto.

Demostración:

f(max{a_{1},...,a_{n}}) = max{a_{1},...,a_{n}}+p = max{a_{1}+p,...,a_{n}+p} = ...

... max{f(a_{1}),...,f(a_{n})}

f(min{a_{1},...,a_{n}}) = min{a_{1},...,a_{n}}+p = min{a_{1}+p,...,a_{n}+p} = ...

... min{f(a_{1}),...,f(a_{n})}

Base topológica:

p = min{p,n+p}

(n+p)+1 = max{p+1,(n+p)+1}

p+1 = min{p+1,(n+p)+1}

n+p = max{p,n+p}

(p,n+p]_{R} [ || ] [p+1,(n+p)+1)_{R} [<< (p,oo)_{R}

Teorema:

Si f(n) = (1/n)+p ==> f(n) es un morfismo-topológico dual no compacto.

Demostración:

f(max{a_{1},...,a_{n}}) = ( 1/max{a_{1},...,a_{n}} )+p = min{(1/a_{1}),...,(1/a_{n})}+p = ...

 min{(1/a_{1})+p,...,(1/a_{n})+p )} = min{f(a_{1}),...,f(a_{n})}

f(min{a_{1},...,a_{n}}) = ( 1/min{a_{1},...,a_{n}} )+p = max{(1/a_{1}),...,(1/a_{n})}+p = ...

 max{(1/a_{1})+p,...,(1/a_{n})+p} = max{f(a_{1}),...,f(a_{n})

rec(f) = [p,p+1]_{R} & [En][ n = 1 & rec(f) = [p,(-p)]_{R} [ || ] [p+1,p+1]_{R} ]


Teorema:

No es ninguien profeta en su tierra, siendo un Peráclito

porque quizás lo hacen Peráclito,

saltando-se algún mandamiento como el ama al próximo como a ti mismo.

Demostración:

Es alguien profeta en su tierra, no siendo un Peráclito

aunque lo hacen Peráclito,

saltando-se algún mandamiento como el ama al próximo como a ti mismo.


Ley:

Si t = d·( ( 1/(d_{t}[x]+v) )+( 1/(d_{t}[x]+(-v)) ) ) ==>

d_{t}[x] = (1/t)·( d+( d^{2}+(tv)^{2} )^{(1/2)} )

x(t) = ln(t) [o(t)o] ( dt+( (1/3)·( d^{2}+(tv)^{2} )^{(3/2)} [o(t)o] (1/v)^{2}·ln(t) ) )

d_{tt}^{2}[x] = (-1)·(1/t)^{2}·( d+( d^{2}+(tv)^{2} )^{(1/2)} )+v^{2}·( d^{2}+(tv)^{2} )^{(-1)·(1/2)}


Ley:

F(u,x) = a·mc^{2}·S(u)·(ax)^{n}

F(v,x) = a·mc^{2}·S(v)·(ax)^{n}

E(u,x) = mc^{2}·int[S(u)]d[u] [o(u)o] ( 1/(n+1) )·(ax)^{n+1}

E(v,x) = mc^{2}·int[S(v)]d[v] [o(v)o] ( 1/(n+1) )·(ax)^{n+1}

Ley:

F(u,x) = mc^{2}·S(u)·(1/x)

F(v,x) = mc^{2}·S(v)·(1/x)

E(u,x) = mc^{2}·int[S(u)]d[u] [o(u)o] ln(x)

E(v,x) = mc^{2}·int[S(v)]d[v] [o(v)o] ln(x)

Ley: [ de cuerda hetero-tópica de métrica básica ]

Si ( S(u) = (1/4)·e^{2it·u} & S(v) = (1/4)·e^{2it·v} ) ==>

E(u,x) = mc^{2}·(1/8)·(1/(it))·e^{2it·u} [o(u)o] ( 1/(n+1) )·(ax)^{n+1}

E(v,x) = mc^{2}·(1/8)·(1/(it))·e^{2it·v} [o(v)o] ( 1/(n+1) )·(ax)^{n+1}

Ley: [ de cuerda elíptica de métrica básica ]

Si ( S(u) = (1/2)·( (n+1)/(2n+1) )·(tu)^{2n+2} & S(v) = (1/2)·( (n+1)/(2n+1) )·(tu)^{2n+2} ) ==>

E(u,x) = mc^{2}·(1/2)·( (n+1)/(4n^{2}+8n+3) )·(1/t)·(tu)^{2n+3} [o(u)o] ( 1/(n+1) )·(ax)^{n+1}

E(v,x) = mc^{2}·(1/2)·( (n+1)/(4n^{2}+8n+3) )·(1/t)·(tv)^{2n+3} [o(v)o] ( 1/(n+1) )·(ax)^{n+1}


Definición:

( f(ax) )^{n}+1 = ( f(ax) )^{[n]}

Teorema:

( f(ax) )^{n}+( f(ax) )^{m} = ( f(ax) )^{m}·( ( f(ax) )^{n+(-m)}+1 ) = ...

... ( f(ax) )^{m}·( f(ax) )^{[n+(-m)]} = ( f(ax) )^{m+[n+(-m)]}

Ley:

Si d_{t}[x] = v·( (ax)^{n}+1 ) ==>

x(t) = (1/a)·( ( (-1)·[n]+1 )·avt )^{( 1/( (-1)·[n]+1 ) )}

d_{t}[x] = v·( ( (-1)·[n]+1 )·avt )^{( [n]/( (-1)·[n]+1 ) )}

d_{tt}^{2}[x] = av^{2}·[n]·( ( (-1)·[n]+1 )·avt )^{( ( 2·[n]+(-1) )/( (-1)·[n]+1 ) )}

Ley:

Si d_{t}[x] = v·( (ax)^{n}+(ax)^{m} ) ==>

x(t) = (1/a)·( ( (-1)·(m+[n+(-m)])+1 )·avt )^{( 1/( (-1)·(m+[n+(-m)])+1 ) )}

d_{t}[x] = v·( ( (-1)·(m+[n+(-m)])+1 )·avt )^{( (m+[n+(-m)])/( (-1)·(m+[n+(-m)])+1 ) )}

d_{tt}^{2}[x] = av^{2}·(m+[n+(-m)])·...

... ( ( (-1)·(m+[n+(-m)])+1 )·avt )^{( ( 2·(m+[n+(-m)])+(-1) )/( (-1)·(m+[n+(-m)])+1 ) )}

Ley:

Si d_{t}[x] = v·( e^{nax}+1 ) ==>

x(t) = (1/a)·(1/[n])·(-1)·ln( (-1)·[n]·avt )

d_{t}[x] = (1/a)·(1/[n])·(-1)·(1/t)

d_{tt}^{2}[x] = (1/a)·(1/[n])·(1/t)^{2}

Ley:

Si d_{t}[x] = v·( e^{nax}+e^{max} ) ==>

x(t) = (1/a)·( 1/(m+[n+(-m)]) )·(-1)·ln( (-1)·(m+[n+(-m)])·avt )

d_{t}[x] = (1/a)·( 1/(m+[n+(-m)]) )·(-1)·(1/t)

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


Ley: [ del abrazo al cojín ]

z(x) = < 1,1,x,(1/x) > es un placer

z(x) = < 1,1,(-x),(-1)·(1/x) > es un placer

(1/x) = brazo derecho adalto y brazo izquierdo abajo.

(-1)·(1/x) = brazo derecho abajo y brazo izquierdo adalto.


Ley: [ de sexo de chocho ]

z(x) = < (1/n),2e^{ix},2e^{(-1)·ix},n·(1/4) > es un placer

Con más de n = 4,

de polla = 0111-111111,

de chocho 111-1110111-111

ya no hay placer en ser el símbolo > 1 

Ley: [ de sexo de culo ]

z(x) = < (-n),2e^{ix},2e^{(-1)·ix},n+(-4)·cos(x) > es un dolor

Con más de n = 4,

5 violaciones,

ya no hay dolor en ser el símbolo > 0 

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