lagranià para-eléctric

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


d_{tt}[x(t)] = a^{(1/2)+(-1)(n/4)}·...
... ( a^{(-1)(1+(-n))/4)} )^{n/(1+(-n))}·a^{(-1)(1+(-n))/2)} = 1


( x(t) )^{n} = a^{(n/2)+(-1)(n^{2}/4)}·...
... ( a^{(-1)(1+(-n))(2+(-n))/4} )^{n/(1+(-n))} = 1


( x(t) ) = a^{(1/2)+(-1)(n/4)}·...
... ( a^{(-1)(1+(-n))/4} )^{(2+(-n))/(1+(-n))}·t^{(2+(-n))/(1+(-n))}


d_{tt}[x(t)] = a^{(1/4)+(-1)(n/4)}·...
... ( a^{(-1)(1+(-n))/4) )^{n/(1+(-n))}·a^{(-1)(1+(-n))/2)} = a^{(-1)(1/4)}


( x(t) )^{n} = a^{(n/4)+(-1)(n^{2}/4)}·...
... ( a^{(-1)(1+(-n))(2+(-n))/4} )^{n/(1+(-n))} = a^{(-1)(n/4)}


( x(t) ) = a^{(-1)(1/4)+(-1)(n/4)}·...
... ( a^{(-1)(1+(-n))/4} )^{(2+(-n))/(1+(-n))}·t^{(2+(-n))/(1+(-n))}


d_{tt}^{2}[x]= ( a^{(n+(-1))(1/4))}·x^{n}/t^{n} )
m·d_{tt}^{2}[x]= (k_{e}·pq)·x^{n}/(ct)^{n} )


a^{(n+(-1))(1/4))} = ( (k_{e}·pq)/(mc^{n}) )


a = ( (k_{e}·pq)/(mc^{n}) )^{( 1/(n+(-1))(1/4)) )}

ones para-electro-magnétiques y para-gravito-magnétiques

m·d_{tt}^{2}[x] = k·pq·( x^{n}/(ct)^{n} )+(-1)·kpq·( d_{t}[x]^{n}/c^{n} )
m·d_{tt}^{2}[x] = k·pq·( x^{n}/(ct)^{n} )+(-1)·kpq·( (d_{t}[x]^{n}·t^{n})/(ct)^{n} )


x(t) = vt


m·d_{tt}^{2}[x] = p·P[E]_{e}(x)+p·P[B]_{e}(x)


d_{tt}[ P[E]_{e}(x)+P[B]_{e}(x) ] = d_{xx}[ P[E]_{e}(x)+P[B]_{e}(x) ]·d_{t}[x]^{2}
d_{tt}[ P[E]_{e}(y)+P[B]_{e}(y) ] = d_{yy}[ P[E]_{e}(y)+P[B]_{e}(y) ]·d_{t}[y]^{2}
d_{tt}[ P[E]_{e}(z)+P[B]_{e}(z) ] = d_{zz}[ P[E]_{e}(z)+P[B]_{e}(z) ]·d_{t}[z]^{2}

para-magnetisme eléctric y para-magnetisme gravitatori

camp para-mangétic eléctric:
B_{e}(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) = ...
... (-1)·kq·< (d_{t}[x]·t)^{n}/(ct)^{n} , (d_{t}[y]·t)^{n}/(ct)^{n} , (d_{t}[z]·t)^{n}/(ct)^{n} >


flux[ B_{e}(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ] = ...
... (-1)·kq·(1/(ct)^{n})·A[n]-[ (x_{i})^{(-1)} ](d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t)·xyz


div[ B_{e}(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ] = ...
... (-1)·n·kq·( ...
... (1/(ct)^{n})·A[n+(-1)](d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) + ...
... (-1)(c/(ct)^{n+1}A[n]-[ d_{t}[x_{i}]^{(-1)} ](d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t)) ...
... )


camp para-mangétic gravitatori:
B_{g}(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) = ...
... kq·< (d_{t}[x]·t)^{n}/(ct)^{n} , (d_{t}[y]·t)^{n}/(ct)^{n} , (d_{t}[z]·t)^{n}/(ct)^{n} >


flux[ B_{g}(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ] = ...
... kq·(1/(ct)^{n})·A[n]-[ (x_{i})^{(-1)} ](d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t)·xyz


div[ B_{g}(d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ] = ...
... n·kq·( ...
... (1/(ct)^{n})·A[n+(-1)](d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) + ...
... (-1)(c/(ct)^{n+1}A[n]-[ d_{t}[x_{i}]^{(-1)} ](d_{t}[x]·t,d_{t}[y]·t,d_{t}[z]·t) ...
... )

potencial para-eléctric y para-gravitatori

potencial eléctric:
E_{e}(x,y,z) = kq·< x^{n}/(ct)^{n} , y^{n}/(ct)^{n} , z^{n}/(ct)^{n} >
V_{e}(x,y,z) = ( 1/(n+1) )·kq·(ct)·Q[n+1](x,y,z)
E_{e}(x,y,z) = grad[ V_{e}(x,y,z) ]


flux[ ∫ [ grad[ V_{e}(x,y,z) ] ]·< d[x],d[y],d[z]> ] = ( 1/(n+1) )·kq·Q[n](x,y,z)·xyz
div[ ∫ [ E_{e}(x,y,z) ]·< d[x],d[y],d[z]> ] = kq·Q[n](x,y,z)


potencial gravitatori:
E_{g}(x,y,z) = (-1)·kq·< x^{n}/(ct)^{n} , y^{n}/(ct)^{n} , z^{n}/(ct)^{n} >
V_{g}(x,y,z) = (-1)·( 1/(n+1) )·kq·(ct)·Q[n+1](x,y,z)
E_{g}(x,y,z) = grad[ V_{e}(x,y,z) ]


flux[ ∫ [ grad[ V_{g}(x,y,z) ] ]·< d[x],d[y],d[z]> ] = (-1)·( 1/(n+1) )·kq·Q[n](x,y,z)·xyz
div[ ∫ [ E_{g}(x,y,z) ]·< d[x],d[y],d[z]> ] = (-1)·kq·Q[n](x,y,z)


ecuacions de camp:
flux[ ∫ [ grad[ V_{e}(x,y,z) ] ]·< d[x],d[y],d[z]> ] = ∭ [ div[ ∫ [ E_{e}(x,y,z) ]·< d[x],d[y],d[z]> ] ] d[x]d[y]d[z]
flux[ ∫ [ grad[ V_{g}(x,y,z) ] ]·< d[x],d[y],d[z]> ] = ∭ [ div[ ∫ [ E_{g}(x,y,z) ]·< d[x],d[y],d[z]> ] ] d[x]d[y]d[z]

camps para-eléctrics y para-gravitatoris

camp eléctric:
E_{e}(x,y,z) = kq·< x^{n}/(ct)^{n} , y^{n}/(ct)^{n} , z^{n}/(ct)^{n} >


flux[ E_{e}(x,y,z) ] = kq·(1/(ct)^{n})·Q[n]-[ (x_{i})^{-1} ](x,y,z)·xyz
div[ E_{e}(x,y,z) ] = n·kq·( (1/(ct)^{n})·Q[n+(-1)](x,y,z) +...
... (-1)(c/(ct)^{n+1})·Q[n]-[ d_{t}[x_{i}]^{(-1)} ](x,y,z)) )


camp gravitatori:
E_{g}(x,y,z) = (-1)·kq·< x^{n}/(ct)^{n} , y^{n}/(ct)^{n} , z^{n}/(ct)^{n} >


flux[ E_{g}(x,y,z) ] = (-1)·kq·(1/(ct))·Q[n]-[ (x_{i})^{-1} ](x,y,z)·xyz
div[ E_{g}(x,y,z) ] = (-1)·n·kq·( (1/(ct)^{n})·Q[n+(-1)](x,y,z) + ...
... (-1)(c/(ct)^{n+1})·Q[n]-[ d_{t}[x_{i}]^{(-1)} ](x,y,z)) )


ecuacions de camp:
flux[ E_{e}(x,y,z) ] = ∭ [ div[ E_{e}(x,y,z) ] ] d[x]d[y]d[z]
flux[ E_{g}(x,y,z) ] = ∭ [ div[ E_{g}(x,y,z) ] ] d[x]d[y]d[z]


ecuacions de camp del temps:
d_{t}[ div[ E_{e}(x,y,z) ] ] = Lap[ E_{e}(x,y,z) ] [o] (d_{t}[x]+d_{t}[y]+d_{t}[z])
d_{t}[ div[ E_{g}(x,y,z) ] ] = Lap[ E_{g}(x,y,z) ] [o] (d_{t}[x]+d_{t}[y]+d_{t}[z])

ecuacions diferencials: binomi

d_{t}[x]^{n}+d_{t}[y]^{n} = (x+y)^{2}


x = ( ( 2^{(1/n)}·(n+(-2))/n )·t )^{( n/(n+(-2)) )}
y = ( ( 2^{(1/n)}·(n+(-2))/n )·t )^{( n/(n+(-2)) )}


d_{t}[x]^{n}+d_{t}[y]^{n} = (x+y)^{3}


x = ( ( 2^{(2/n)}·(n+(-3))/n )·t )^{( n/(n+(-3)) )}
y = ( ( 2^{(2/n)}·(n+(-3))/n )·t )^{( n/(n+(-3)) )}


d_{t}[x]^{n}+d_{t}[y]^{n} = (x+y)^{m}


x = ( ( 2^{((m+(-1))/n)}·(n+(-m))/n )·t )^{( n/(n+(-m)) )}
y = ( ( 2^{((m+(-1))/n)}·(n+(-m))/n )·t )^{( n/(n+(-m)) )}


d_{t}[x]^{n}+d_{t}[y]^{n} = (x+y)^{(1/m)}


x = ( ( 2^{((1/m)+(-1))}·(n+(-1)(1/m))/n )·t )^{( n/(n+(-1)(1/m)) )}
y = ( ( 2^{((1/m)+(-1))}·(n+(-1)(1/m))/n )·t )^{( n/(n+(-1)(1/m)) )}

pitagoras

1+1+1=3
3·(1+1+1)=9
9·(1+1+1)=27
27·(1+1+1)=81


3^{(n+(-1))}( x^{n}+y^{n}+z^{n} ) = R^{n}


2+2+2=6
3·(4+4+4)=36
9·(8+8+8)=216


(1/2)+(1/2)+(1/2)=(3/2)
3·((1/4)+(1/4)+(1/4))=(9/4)
9·((1/8)+(1/8)+(1/8))=(27/8)