teoria de cordes

1 [o] (-1)

(m/n)·a_{n}·( x(u,v) )^{n} = h·( e^{u}+e^{(-v)} )

(m/n)·a_{n}·( x(u,v) )^{n} = h·( e^{(-u)}+e^{v} )

i [o] (-i)

(m/n)·a_{n}·( x(u,v) )^{n} = h·( e^{iu}+e^{(-i)v} )

(m/n)·a_{n}·( x(u,v) )^{n} = h·( e^{(-i)u}+e^{iv} )

k = e^{(1/4)·pi i} [o] j = e^{(-1)·(1/4)·pi·i}

(m/n)·a_{n}·( x(u,v) )^{n} = h·( e^{ku}+e^{jv} )

(m/n)·a_{n}·( x(u,v) )^{n} = h·( e^{ju}+e^{kv} )

(m/n)·a_{n}·( x(u,v) )^{n} = h·( e^{(-k)u}+e^{(-j)v} )

(m/n)·a_{n}·( x(u,v) )^{n} = h·( e^{(-j)u}+e^{(-k)v} )

(m/n)·a_{n}·( x(u,v) )^{n} = h·( (1/(n+1))·u^{n+1}+(-1)·(1/(n+1))·v^{n+1} )

(m/n)·a_{n}·( x(u,v) )^{n} = h·( (-1)·(1/(n+1))·u^{n+1}+(1/(n+1))·v^{n+1} )

H_{u}(u,v) = int[ x(u,v) ] d[u]

H_{v}(u,v) = int[ x(u,v) ] d[v]

d_{u}[ g(f(u,v)) ] = d_{f(u,v)}[ g(f(u,v)) ]·d_{u}[f(u,v)]

d_{v}[ g(f(u,v)) ] = d_{f(u,v)}[ g(f(u,v)) ]·d_{v}[f(u,v)]

H_{u}(u,v) = ( n/(1+n) )·( e^{u}+e^{(-v)} )^{(1/n)+1} ] [o(u)o] (-1)·e^{(-u)}

H_{v}(u,v) = ( n/(1+n) )·( e^{u}+e^{(-v)} )^{(1/n)+1} ] [o(v)o] (-1)·e^{v}

H_{u}(u,v) = ( n/(1+n) )·( e^{iu}+e^{(-i)v} )^{(1/n)+1} ] [o(u)o] e^{(-i)u}

H_{v}(u,v) = ( n/(1+n) )·( e^{iu}+e^{(-i)v} )^{(1/n)+1} ] [o(v)o] e^{iv}

H_{u}(u,v) = ( n/(1+n) )·( e^{ku}+e^{jv} )^{(1/n)+1} ] [o(u)o] i·e^{(-k)u}

H_{v}(u,v) = ( n/(1+n) )·( e^{ku}+e^{jv} )^{(1/n)+1} ] [o(v)o] (-i)·e^{(-j)v}

H_{u}(u,v) = ( n/(1+n) )·( e^{(-k)u}+e^{(-j)v} )^{(1/n)+1} ] [o(u)o] i·e^{ku}

H_{v}(u,v) = ( n/(1+n) )·( e^{(-k)u}+e^{(-j)v} )^{(1/n)+1} ] [o(v)o] (-i)·e^{jv}

H_{u}(u,v) = ...

... ( n/(1+n) )·( (1/(n+1))·u^{n+1}+(-1)·(1/(n+1))·v^{n+1} )^{(1/n)+1} ] [o(u)o] ...

... (1/((-n)+1))·u^{(-n)+1}

H_{v}(u,v) = ...

... ( n/(1+n) )·( (1/(n+1))·u^{n+1}+(-1)·(1/(n+1))·v^{n+1} )^{(1/n)+1} ] [o(v)o] ...

... (-1)·(1/((-n)+1))·v^{(-n)+1}

d_{x}[E_{u}(x,u)]^{(1/k)} = (1/2)·( S_{uu} )^{2}

d_{x}[E_{v}(x,v)]^{(1/k)} = (1/2)·( S_{vv} )^{2}

E_{u}(x,u) = ...

... (1/2)^{k}·u [o(u)o] ( (1/8)·e^{2u} )^{[o(u)o]2k} [o(u)o] x

E_{v}(x,v) = ...

... (1/2)^{k}·v [o(v)o] ( (-1)·(1/8)·e^{2(-v)} )^{[o(v)o]2k} [o(v)o] x

E_{u}(x,u) = ...

... (1/2)^{k}·u [o(u)o] ( (1/8i)·e^{2i·u} )^{[o(u)o]2k} [o(u)o] x

E_{v}(x,v) = ...

... (1/2)^{k}·v [o(v)o] ( (-1)·(1/8i)·e^{2(-i)·v} )^{[o(v)o]2k} [o(v)o] x

E_{u}(x,u) = ...

... (1/2)^{k}·u [o(u)o] ( (1/8k)·e^{2k·u} )^{[o(u)o]2k} [o(u)o] x

E_{v}(x,v) = ...

... (1/2)^{k}·v [o(v)o] ( (1/8j)·e^{2j·v} )^{[o(v)o]2k} [o(v)o] x

E_{u}(x,u) = ...

... (1/2)^{k}·u [o(u)o] ( (-1)·(1/8k)·e^{2(-k)·u} )^{[o(u)o]2k} [o(u)o] x

E_{v}(x,v) = ...

... (1/2)^{k}·v [o(v)o] ( (-1)·(1/8j)·e^{2(-j)·v} )^{[o(v)o]2k} [o(v)o] x

E_{u}(x,u) = ...

... (1/2)^{k}·u [o(u)o] ( ((2n)!/(2n+3)!)·u^{2n+3} )^{[o(u)o]2k} [o(u)o] x

E_{v}(x,v) = ...

... (1/2)^{k}·v [o(v)o] ( (-1)·((2n)!/(2n+3)!)·v^{2n+3} )^{[o(v)o]2k} [o(v)o] x

d_{x}[F_{u}(x,u)]^{(1/k)} = (1/2)·( S_{uu} )^{2}·x^{n}

d_{x}[F_{v}(x,v)]^{(1/k)} = (1/2)·( S_{vv} )^{2}·x^{n}

F_{u}(x,u) = ...

... (1/2)^{k}·u [o(u)o] ( int[ S_{uu} ] d[u] )^{[o(u)o]2k} [o(u)o] (1/(kn+1))·x^{kn+1}

F_{v}(x,v) = ...

... (1/2)^{k}·v [o(v)o] ( int[ S_{vv} ] d[v] )^{[o(v)o]2k} [o(v)o] (1/(kn+1))·x^{kn+1}