∫ [0 --> 1]-[f(x)] d[x]=( f(1/n)+...(n)...+f(n/n) )·m(n)
∫ [0 --> a]-[f(x)] d[x]=( f(a·(1/n))+...(n)...+f(a·(n/n)) )·( a·m(n) )
∫ [a --> b]-[f(x)] d[x]= ∫ [0 --> b]-[f(x)] d[x]+(-1)·∫ [0 --> a]-[f(x)] d[x]
∫ [0 --> 1]-[1] d[x]=( 1+...(n)...+1 )·(1/n)
∫ [0 --> 1]-[x] d[x]=( (1/n)+...(n)...+(n/n) )·(1/(n+1))
∫ [0 --> 1]-[x^{2}] d[x]=( (1/n)^{2}+...(n)...+(n/n)^{2} )·( 2n/((n+1)(2n+1)) )
∫ [0 --> 1]-[x^{3}] d[x]=( (1/n)^{3}+...(n)...+(n/n)^{3} )·( n/((n+1)(n+1)) )
∫ [0 --> 1]-[x^{4}] d[x]=( (1/n)^{4}+...(n)...+(n/n)^{4} )·( 2n·3n^{2}/((n+1)(2n+1)(3n^{2}+3n+(-1))) )
∫ [0 --> 1]-[x^{5}] d[x]=( (1/n)^{5}+...(n)...+(n/n)^{5} )·( n·2n^{2}/((n+1)(n+1)(2n^{2}+2n+(-1))) )
∫ [0 --> 1]-[e^{x}] d[x]=( e^{(0/n)}+e^{(1/n)}+...(n)...+e^{( (n+(-1))/n )} )·( e^{(1/n)}+(-1) )
jueves, 26 de septiembre de 2019
martes, 24 de septiembre de 2019
mecanisme de gauge: SU(3) cromodinámica de quarks
g_{x}(t) = e^{(x+(-y))·i·t}·f_{x}(t)
g_{y}(t) = e^{(y+(-z))·i·t}·f_{y}(t)
g_{z}(t) = e^{(z+(-x))·i·t}·f_{z}(t)
g_{x}(t)·g_{y}(t)·g_{z}(t) = f_{x}(t)·f_{y}(t)·f_{z}(t)
d_{t}[g_{x}(t)]·d_{t}[g_{y}(t)]·d_{t}[g_{z}(t)] = ...
... d_{t}[f_{x}(t)]·d_{t}[f_{y}(t)]·d_{t}[f_{z}(t)]+...
... (x+(-y))(y+(-z))(z+(-x))·(-i)·f_{x}(t)·f_{y}(t)·f_{z}(t) = 0
d_{t}[g_{x}(t)]·d_{t}[g_{y}(t)]·d_{t}[g_{z}(t)] = 0
g_{x}(t)·g_{y}(t)·g_{z}(t) = x·( y^{2}+(-1)·z^{2} )+y·( z^{2}+(-1)·x^{2} )+z·( x^{2}+(-1)·y^{2} )
f_{x}(t)·f_{y}(t)·f_{z}(t) = x·( y^{2}+(-1)·z^{2} )+y·( z^{2}+(-1)·x^{2} )+z·( x^{2}+(-1)·y^{2} )
f_{x}(t) = (1+x+(-y))·e^{(x+(-y))·(-i)·t}
f_{y}(t) = (1+y+(-z))·e^{(y+(-z))·(-i)·t}
f_{z}(t) = (1+z+(-x))·e^{(z+(-x))·(-i)·t}
x^{2}+y^{2}+z^{2} = 1
unificació:
( cos( Z·(1+(-1)q^{2}) )sin( qW ) )^{2}+( sin( Z·(1+(-1)q^{2}) )sin( qW ) )^{2}+( cos( qW ) )^{2} = 1
( cos( Z·(1+(-1)q^{2}) )cos( qW ) )^{2}+( sin( Z·(1+(-1)q^{2}) )cos( qW ) )^{2}+( sin( qW ) )^{2} = 1
g_{y}(t) = e^{(y+(-z))·i·t}·f_{y}(t)
g_{z}(t) = e^{(z+(-x))·i·t}·f_{z}(t)
g_{x}(t)·g_{y}(t)·g_{z}(t) = f_{x}(t)·f_{y}(t)·f_{z}(t)
d_{t}[g_{x}(t)]·d_{t}[g_{y}(t)]·d_{t}[g_{z}(t)] = ...
... d_{t}[f_{x}(t)]·d_{t}[f_{y}(t)]·d_{t}[f_{z}(t)]+...
... (x+(-y))(y+(-z))(z+(-x))·(-i)·f_{x}(t)·f_{y}(t)·f_{z}(t) = 0
d_{t}[g_{x}(t)]·d_{t}[g_{y}(t)]·d_{t}[g_{z}(t)] = 0
g_{x}(t)·g_{y}(t)·g_{z}(t) = x·( y^{2}+(-1)·z^{2} )+y·( z^{2}+(-1)·x^{2} )+z·( x^{2}+(-1)·y^{2} )
f_{x}(t)·f_{y}(t)·f_{z}(t) = x·( y^{2}+(-1)·z^{2} )+y·( z^{2}+(-1)·x^{2} )+z·( x^{2}+(-1)·y^{2} )
f_{x}(t) = (1+x+(-y))·e^{(x+(-y))·(-i)·t}
f_{y}(t) = (1+y+(-z))·e^{(y+(-z))·(-i)·t}
f_{z}(t) = (1+z+(-x))·e^{(z+(-x))·(-i)·t}
x^{2}+y^{2}+z^{2} = 1
unificació:
( cos( Z·(1+(-1)q^{2}) )sin( qW ) )^{2}+( sin( Z·(1+(-1)q^{2}) )sin( qW ) )^{2}+( cos( qW ) )^{2} = 1
( cos( Z·(1+(-1)q^{2}) )cos( qW ) )^{2}+( sin( Z·(1+(-1)q^{2}) )cos( qW ) )^{2}+( sin( qW ) )^{2} = 1
mecanisme electrodébil
F(t) = e^{( qW+Z·(1+(-1)q^{2}) )·i·t}·f(t)
G(t) = e^{(-1)·( qW+Z·(1+(-1)q^{2}) )·i·t}·g(t)
F(t)·G(t) = f(t)·g(t)
d_{t}[F(t)]·d_{t}[G(t)] = d_{t}[f(t)]·d_{t}[g(t)]+( qW+Z·(1+(-1)q^{2}) )^{2}·f(t)·g(t) = 0
f(t) = e^{( qW+Z·(1+(-1)q^{2}) )·t}
g(t) = e^{(-1)·( qW+Z·(1+(-1)q^{2}) )·t}
mecanisme de gauge
f(x) = e^{qi}·P(x)
g(x) = e^{(-1)qi}·Q(x)
f(x)g(x) = P(x)Q(x)
qi·( e^{qi}·P(x)·e^{(-1)qi}·d_{x}[Q(x)] + (-1)e^{qi}·d_{x}[P(x)]·e^{(-1)qi}·Q(x) ) = 0
P(x)·d_{x}[Q(x)] + (-1)d_{x}[P(x)]·Q(x) = 0
d_{x}[f(x)]d_{x}[g(x)] = d_{x}[P(x)]d_{x}[Q(x)]+q^{2}P(x)Q(x)
d_{x}[f(x)]d_{x}[g(x)]+f(x)g(x) = d_{x}[P(x)]d_{x}[Q(x)]+(1+q^{2})P(x)Q(x)= 0
P(x) = e^{(1+q^{2})^{(1/2)}ix}
Q(x) = e^{(1+q^{2})^{(1/2)}ix}
d_{x}[f(x)]d_{x}[g(x)]+f(x)g(x) = d_{x}[P(x)]d_{x}[Q(x)]+(1+q^{2})P(x)Q(x) = (-1)qi
P(x) = cos( (1+q^{2})^{(1/2)}ix )
Q(x) = sin( (1+q^{2})^{(1/2)}ix )
P(x) = cos( (-1)(1+q^{2})^{(1/2)}ix )
Q(x) = sin( (-1)(1+q^{2})^{(1/2)}ix )
d_{x}[f(x)]d_{x}[g(x)]+f(x)g(x) = d_{x}[P(x)]d_{x}[Q(x)]+(1+q^{2})P(x)Q(x) = qi
P(x) = cosh( (1+q^{2})^{(1/2)}ix )
Q(x) = sinh( (1+q^{2})^{(1/2)}ix )
P(x) = cosh( (-1)(1+q^{2})^{(1/2)}ix )
Q(x) = sinh( (-1)(1+q^{2})^{(1/2)}ix )
g(x) = e^{(-1)qi}·Q(x)
f(x)g(x) = P(x)Q(x)
qi·( e^{qi}·P(x)·e^{(-1)qi}·d_{x}[Q(x)] + (-1)e^{qi}·d_{x}[P(x)]·e^{(-1)qi}·Q(x) ) = 0
P(x)·d_{x}[Q(x)] + (-1)d_{x}[P(x)]·Q(x) = 0
d_{x}[f(x)]d_{x}[g(x)] = d_{x}[P(x)]d_{x}[Q(x)]+q^{2}P(x)Q(x)
d_{x}[f(x)]d_{x}[g(x)]+f(x)g(x) = d_{x}[P(x)]d_{x}[Q(x)]+(1+q^{2})P(x)Q(x)= 0
P(x) = e^{(1+q^{2})^{(1/2)}ix}
Q(x) = e^{(1+q^{2})^{(1/2)}ix}
d_{x}[f(x)]d_{x}[g(x)]+f(x)g(x) = d_{x}[P(x)]d_{x}[Q(x)]+(1+q^{2})P(x)Q(x) = (-1)qi
P(x) = cos( (1+q^{2})^{(1/2)}ix )
Q(x) = sin( (1+q^{2})^{(1/2)}ix )
P(x) = cos( (-1)(1+q^{2})^{(1/2)}ix )
Q(x) = sin( (-1)(1+q^{2})^{(1/2)}ix )
d_{x}[f(x)]d_{x}[g(x)]+f(x)g(x) = d_{x}[P(x)]d_{x}[Q(x)]+(1+q^{2})P(x)Q(x) = qi
P(x) = cosh( (1+q^{2})^{(1/2)}ix )
Q(x) = sinh( (1+q^{2})^{(1/2)}ix )
P(x) = cosh( (-1)(1+q^{2})^{(1/2)}ix )
Q(x) = sinh( (-1)(1+q^{2})^{(1/2)}ix )
lunes, 23 de septiembre de 2019
lógica dual
frase:
quizás p(x) y entonces también q(x)
¬p(x) or ( p(x) ==> q(x) )
frase negada:
p(x) pero no q(x)
p(x) & ( p(x) & ¬q(x) )
frase:
quizás no p(x) y entonces tampoco q(x)
p(x) or ( ¬p(x) ==> ¬q(x) )
frase negada:
no p(x) pero q(x)
¬p(x) & ( ¬p(x) & q(x) )
frase:
quizás p(x) y entonces no q(x)
¬p(x) or ( p(x) ==> ¬q(x) )
frase negada:
p(x) pero también q(x)
p(x) & ( p(x) & q(x) )
frase:
quizás no p(x) y entonces q(x)
p(x) or ( ¬p(x) ==> q(x) )
frase negada:
no p(x) pero tampoco q(x)
¬p(x) & ( ¬p(x) & ¬q(x) )
lógica dual
frase:
p(x) y entonces también q(x)
p(x) & ( p(x) ==> q(x) )
frase negada:
quizás p(x) pero q(x)
¬p(x) or ( p(x) & ¬q(x) )
frase:
no p(x) y entonces tampoco q(x)
¬p(x) & ( ¬p(x) ==> ¬q(x) )
frase negada:
quizás no p(x) pero q(x)
p(x) or ( ¬p(x) & q(x) )
frase:
p(x) y entonces no q(x)
p(x) & ( p(x) ==> ¬q(x) )
frase negada:
quizás p(x) pero también q(x)
¬p(x) or ( p(x) & q(x) )
frase:
no p(x) y entonces q(x)
¬p(x) & ( ¬p(x) ==> q(x) )
frase negada:
quizás p(x) pero tampoco q(x)
p(x) or ( ¬p(x) & ¬q(x) )
p(x) y entonces también q(x)
p(x) & ( p(x) ==> q(x) )
frase negada:
quizás p(x) pero q(x)
¬p(x) or ( p(x) & ¬q(x) )
frase:
no p(x) y entonces tampoco q(x)
¬p(x) & ( ¬p(x) ==> ¬q(x) )
frase negada:
quizás no p(x) pero q(x)
p(x) or ( ¬p(x) & q(x) )
frase:
p(x) y entonces no q(x)
p(x) & ( p(x) ==> ¬q(x) )
frase negada:
quizás p(x) pero también q(x)
¬p(x) or ( p(x) & q(x) )
frase:
no p(x) y entonces q(x)
¬p(x) & ( ¬p(x) ==> q(x) )
frase negada:
quizás p(x) pero tampoco q(x)
p(x) or ( ¬p(x) & ¬q(x) )
sábado, 21 de septiembre de 2019
teoria de cordes accions polinomiques
acció tri-romboide
rombo-rombo-rombo
E(u,v)E(u,v)E(u,v)G(u,v)+G(u,v)F(u,v)F(u,v)E(u,v)+E(u,v)G(u,v)G(u,v)G(u,v)
F(u,v)F(u,v)F(u,v)E(u,v)+E(u,v)G(u,v)G(u,v)F(u,v)+F(u,v)E(u,v)E(u,v)E(u,v)
G(u,v)G(u,v)G(u,v)F(u,v)+F(u,v)E(u,v)E(u,v)G(u,v)+G(u,v)F(u,v)F(u,v)F(u,v)
acció penta-pentagono
pentagon-pentagon=pentàgon=pentagon-pentagon
E(u,v)E(u,v)E(u,v)E(u,v)G(u,v)+G(u,v)G(u,v)G(u,v)E(u,v)E(u,v)+E(u,v)E(u,v)F(u,v)G(u,v)G(u,v)+
G(u,v)G(u,v)E(u,v)E(u,v)E(u,v)+E(u,v)G(u,v)G(u,v)G(u,v)G(u,v)
F(u,v)F(u,v)F(u,v)F(u,v)E(u,v)+E(u,v)E(u,v)E(u,v)F(u,v)F(u,v)+F(u,v)F(u,v)G(u,v)E(u,v)E(u,v)+
E(u,v)E(u,v)F(u,v)F(u,v)F(u,v)+F(u,v)E(u,v)E(u,v)E(u,v)E(u,v)
G(u,v)G(u,v)G(u,v)G(u,v)F(u,v)+F(u,v)F(u,v)F(u,v)G(u,v)G(u,v)+G(u,v)G(u,v)E(u,v)F(u,v)F(u,v)+
F(u,v)F(u,v)G(u,v)G(u,v)G(u,v)+G(u,v)F(u,v)F(u,v)F(u,v)F(u,v)
rombo-rombo-rombo
E(u,v)E(u,v)E(u,v)G(u,v)+G(u,v)F(u,v)F(u,v)E(u,v)+E(u,v)G(u,v)G(u,v)G(u,v)
F(u,v)F(u,v)F(u,v)E(u,v)+E(u,v)G(u,v)G(u,v)F(u,v)+F(u,v)E(u,v)E(u,v)E(u,v)
G(u,v)G(u,v)G(u,v)F(u,v)+F(u,v)E(u,v)E(u,v)G(u,v)+G(u,v)F(u,v)F(u,v)F(u,v)
acció penta-pentagono
pentagon-pentagon=pentàgon=pentagon-pentagon
E(u,v)E(u,v)E(u,v)E(u,v)G(u,v)+G(u,v)G(u,v)G(u,v)E(u,v)E(u,v)+E(u,v)E(u,v)F(u,v)G(u,v)G(u,v)+
G(u,v)G(u,v)E(u,v)E(u,v)E(u,v)+E(u,v)G(u,v)G(u,v)G(u,v)G(u,v)
F(u,v)F(u,v)F(u,v)F(u,v)E(u,v)+E(u,v)E(u,v)E(u,v)F(u,v)F(u,v)+F(u,v)F(u,v)G(u,v)E(u,v)E(u,v)+
E(u,v)E(u,v)F(u,v)F(u,v)F(u,v)+F(u,v)E(u,v)E(u,v)E(u,v)E(u,v)
G(u,v)G(u,v)G(u,v)G(u,v)F(u,v)+F(u,v)F(u,v)F(u,v)G(u,v)G(u,v)+G(u,v)G(u,v)E(u,v)F(u,v)F(u,v)+
F(u,v)F(u,v)G(u,v)G(u,v)G(u,v)+G(u,v)F(u,v)F(u,v)F(u,v)F(u,v)
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