Mecànica Cuàntica y Mecanisme de Gauge y Relativitat

Hamiltonià de Heisenberg-Srôdinguer:

Lley:

ihc·d_{r}[f(r)] = E(r)·P[ (-oo) [< r [< oo ]·f(r)

f(r) = e^{( 1/(ih) )·int[ (1/c)·E(r)·P[ (-oo) [< r [< oo ] ]d[r]}

Lagranià de Heisenberg-Srôdinguer:

Lley:

(-1)·( h^{2}/m )·d_{r}[f(r)]^{2} = E(r)·P[ (-oo) [< r [< oo ]·( f(r) )^{2}

f(r) = e^{( 1/(ih) )·int[ ( m·E(r)·P[ (-oo) [< r [< oo ] )^{(1/2)} ]d[r]}

Lleys de Heisenberg-Srôdinguer-Newton:

Lley:

ihc·d_{r}[f(r)] = pqg·r·(1/pi)·( 1/(1+(ar)^{2}) )·f(r)

f(r) = e^{( 1/(ih) )·(1/c)·(1/a)·(1/pi)·( ...

... ( ( pq·(g/a)·(1/2)·(ar)^{2} ) [o(ar)o] arc-tan(ar) ) ...

... )

Lley:

(-1)·( h^{2}/m )·d_{r}[f(r)]^{2} = pqg·r·(1/pi)·( 1/(1+(ar)^{2}) )·( f(x) )^{2}

f(r) = e^{( 1/(ih) )·(1/a)·(1/pi)·( ...

... ( m·( pq·(g/a)·(1/2)·(ar)^{2} ) [o(ar)o] arc-tan(ar) )^{[o(ar)o](1/2)}} ...

... )

Lleys de Heisenberg-Srôdinguer-Newton-Parabólic:

Lley:

ihc·d_{r}[f(r)] = ( (-1)·pqg·r+E )·(1/pi)·( 1/(1+(ar)^{2}) )·f(x)

f(x,y) = e^{( 1/(ih) )·(1/c)·(1/a)·(1/pi)·( ...

... ( (-1)·pq·(g/a)·(1/2)·(ar)^{2}+E·ar ) [o(ar)o] arc-tan(ar) ...

... )

Lley:

(-1)·( h^{2}/m )·d_{r}[f(r)]^{2} = ( (-1)·pqg·r+E )·(1/pi)·( 1/(1+(ar)^{2}) )·( f(x) )^{2}

f(r) = e^{( 1/(ih) )·(1/a)·(1/pi)·( ...

... ( m·( (-1)·pq·(g/a)·(1/2)·(ar)^{2}+E·ar ) [o(ar)o] arc-tan(ar) )^{[o(ar)o](1/2)}} ...

... )

Mecanisme de Heisenberg-Higgs:

Lley:

(ih)^{n}·d_{x}[f_{1}(x)]·...(n)...·d_{x}[f_{n}(x)] = ...

... ( p(1) )·...(n)...( p(n) )·f_{1}(x)·...(n)...f_{n}(x)

f_{k}(x) = e^{( 1/(ih) )·int[ p(k) ]d[x]}

Mecanisme de Srôdinguer-Higgs:

Lley:

( (ih)/c )^{n}·d_{t}[f_{1}(t)]·...(n)...·d_{t}[f_{n}(t)] = ...

... ( p(1) )·...(n)...( p(n) )·f_{1}(t)·...(n)...f_{n}(t)

f_{k}(t) = e^{( 1/(ih) )·int[ c·p(k) ]d[t]}

Invariant Gauge de Heisenberg-Higgs:

Lley:

Si ( A_{1}(x) = f_{1}(x)·B_{1}(x) & ...(n)... & A_{n}(x) = f_{n}(x)·B_{n}(x) ) ==> ...

... A_{1}(x)·...(n)...·A_{n}(x) = B_{1}(x)·...(n)...·B_{n}(x)

Invariant Gauge de Srôdinguer-Higgs:

Lley:

Si ( A_{1}(t) = f_{1}(t)·B_{1}(t) & ...(n)... & A_{n}(t) = f_{n}(t)·B_{n}(t) ) ==> ...

... A_{1}(t)·...(n)...·A_{n}(t) = B_{1}(t)·...(n)...·B_{n}(t)

Teoría electro-débil:

SU(2):

3 Neutrins:

Lley:

(-1)·h^{2}·d_{x}[f(x)]·d_{x}[g(x)] = p(f)·p(g)·f(x)·g(x)

p(f)·p(g) = (a+(-b))·(b+(-a))·( mc·x )^{2}

f(x) = e^{( 1/(ih) )·mc·(1/2)·x^{2}·(a+(-b))}

g(x) = e^{( 1/(ih) )·mc·(1/2)·x^{2}·(b+(-a))}

Bosó nuclear de Wienenberg:

Lley:

(-1)·(h/c)^{2}·d_{t}[f(t)]·d_{t}[g(t)] = p(f)·p(g)·f(t)·g(t)

p(f)·p(g) = (u+(-v))·(v+(-u))·( mc·t )^{2}

f(t) = e^{( 1/(ih) )·mc^{2}·(1/2)·t^{2}·(u+(-v))}

g(t) = e^{( 1/(ih) )·mc^{2}·(1/2)·t^{2}·(v+(-u))}

U(2,1):

3 Leptons:

Lley:

(-1)·h^{2}·d_{x}[f(x)]·d_{x}[g(x)] = p(f)·p(g)·f(x)·g(x)

p(f)·p(g) = (-1)·( mc·ax )^{2}

f(x) = e^{( 1/(ih) )·mc·(1/2)·x^{2}·a}

g(x) = e^{(-1)·( 1/(ih) )·mc·(1/2)·x^{2}·a}

Bosó eléctric de Glashow:

Lley:

(-1)·(h/c)^{2}·d_{t}[f(t)]·d_{t}[g(t)] = p(f)·p(g)·f(t)·g(t)

p(f)·p(g) = (-1)·( mc·ut )^{2}

f(t) = e^{( 1/(ih) )·mc^{2}·(1/2)·t^{2}·u}

g(t) = e^{(-1)·( 1/(ih) )·mc^{2}·(1/2)·t^{2}·u}

Teoría gravito-electro-forta:

SU(3):

9 Quarks:

Lley:

(-i)·h^{3}·d_{x}[f(x)]·d_{x}[g(x)]·d_{x}[h(x)] = p(f)·p(g)·p(h)·f(x)·g(x)·h(x)

p(f)·p(g)·p(h) = (a+(-b))·(b+(-d))·(d+(-a))·( mc·x )^{3}

f(x) = e^{( 1/(ih) )·mc·(1/2)·x^{2}·(a+(-b))}

g(x) = e^{( 1/(ih) )·mc·(1/2)·x^{2}·(b+(-d))}

h(x) = e^{( 1/(ih) )·mc·(1/2)·x^{2}·(d+(-a))}

Lley:

(-i)·(h/c)^{3}·d_{t}[f(t)]·d_{t}[g(t)]·d_{t}[h(t)] = p(f)·p(g)·p(h)·f(t)·g(t)·h(t)

p(f)·p(g)·p(h) = (u+(-v))·(v+(-w))·(w+(-u))·( mc·t )^{3}

f(t) = e^{( 1/(ih) )·mc^{2}·(1/2)·t^{2}·(u+(-v))}

g(t) = e^{( 1/(ih) )·mc^{2}·(1/2)·t^{2}·(v+(-w))}

h(t) = e^{( 1/(ih) )·mc^{2}·(1/2)·t^{2}·(w+(-u))}

Lley:

(-i)·h^{3}·d_{x}[f(x)]·d_{x}[g(x)]·d_{x}[h(x)] = p(f)·p(g)·p(h)·f(x)·g(x)·h(x)

p(f)·p(g)·p(h) = (-1)·(a+(-b))·(b+(-d))·(d+(-a))·( mc·x )^{3}

f(x) = e^{(-1)·( 1/(ih) )·mc·(1/2)·x^{2}·(a+(-b))}

g(x) = e^{(-1)·( 1/(ih) )·mc·(1/2)·x^{2}·(b+(-d))}

h(x) = e^{(-1)·( 1/(ih) )·mc·(1/2)·x^{2}·(d+(-a))}

Lley:

(-i)·(h/c)^{3}·d_{t}[f(t)]·d_{t}[g(t)]·d_{t}[h(t)] = p(f)·p(g)·p(h)·f(t)·g(t)·h(t)

p(f)·p(g)·p(h) = (-1)·(u+(-v))·(v+(-w))·(w+(-u))·( mc·t )^{3}

f(t) = e^{(-1)·( 1/(ih) )·mc^{2}·(1/2)·t^{2}·(u+(-v))}

g(t) = e^{(-1)·( 1/(ih) )·mc^{2}·(1/2)·t^{2}·(v+(-w))}

h(t) = e^{(-1)·( 1/(ih) )·mc^{2}·(1/2)·t^{2}·(w+(-u))}

U(3,2):

9 Hexatrons:

Lley:

(-i)·h^{3}·d_{x}[f(x)]·d_{x}[g(x)]·d_{x}[h(x)] = p(f)·p(g)·p(h)·f(x)·g(x)·h(x)

p(f)·p(g)·p(h) = (a+b)·ab·( mc·x )^{3}

f(x) = e^{(-1)·( 1/(ih) )·mc·(1/2)·x^{2}·a}

g(x) = e^{( 1/(ih) )·mc·(1/2)·x^{2}·(a+b)}

h(x) = e^{(-1)·( 1/(ih) )·mc·(1/2)·x^{2}·b}

Lley:

(-i)·(h/c)^{3}·d_{t}[f(t)]·d_{t}[g(t)]·d_{t}[h(t)] = p(f)·p(g)·p(h)·f(t)·g(t)·h(t)

p(f)·p(g)·p(h) = (u+v)·uv·( mc·t )^{3}

f(t) = e^{(-1)·( 1/(ih) )·mc^{2}·(1/2)·t^{2}·u}

g(t) = e^{( 1/(ih) )·mc^{2}·(1/2)·t^{2}·(u+v)}

h(t) = e^{(-1)·( 1/(ih) )·mc^{2}·(1/2)·t^{2}·v}

Lley:

(-i)·h^{3}·d_{x}[f(x)]·d_{x}[g(x)]·d_{x}[h(x)] = p(f)·p(g)·p(h)·f(x)·g(x)·h(x)

p(f)·p(g)·p(h) = (-1)·(a+b)·ab·( mc·x )^{3}

f(x) = e^{( 1/(ih) )·mc·(1/2)·x^{2}·a}

g(x) = e^{(-1)·( 1/(ih) )·mc·(1/2)·x^{2}·(a+b)}

h(x) = e^{( 1/(ih) )·mc·(1/2)·x^{2}·b}

Lley:

(-i)·(h/c)^{3}·d_{t}[f(t)]·d_{t}[g(t)]·d_{t}[h(t)] = p(f)·p(g)·p(h)·f(t)·g(t)·h(t)

p(f)·p(g)·p(h) = (-1)·(u+v)·uv·( mc·t )^{3}

f(t) = e^{( 1/(ih) )·mc^{2}·(1/2)·t^{2}·u}

g(t) = e^{(-1)·( 1/(ih) )·mc^{2}·(1/2)·t^{2}·(u+v)}

h(t) = e^{( 1/(ih) )·mc^{2}·(1/2)·t^{2}·v}

Estructura de l'àtom:

( x_{k} = x || x_{k} = y || x_{k} = z )

Nucli de l'àtom:

Lley:

Protó x_{k}:

1 hexatró eléctric x_{k} = 1

3 quarks x_{k}

Proto-Neutró x_{k}

1 hexatró gravito-eléctric x_{k} = (-2)

3 quarks x_{k}

Neutró x_{k}:

1 hexatró gravitori x_{k} = 1

3 quarks x_{k}

Órbita de l'àtom:

Lley:

1 leptó x_{k} = (-1)

1 anti-leptó x_{k} = 1

Radio-activitat de l'àtom:

1 neutrí x_{k}

1 anti-neutrí x_{k}

Álgebra lineal y Geometría diferencial de Quaternions:

Teorema:

det( < 1,j >,< i,k > ) = 0

det( < 1,i >,< j,k > ) = 0

Teorema:

det( < 1,x^{n} >,< y^{n},z^{n} > ) = 0 <==> ...

... ( x = i^{(1/n)} & y = j^{(1/n)} & z = k^{(1/n)} )

det( < 1,y^{n} >,< x^{n},z^{n} > ) = 0 <==> ...

... ( x = i^{(1/n)} & y = j^{(1/n)} & z = k^{(1/n)} )

Teorema:

det( < (1+i),(k+(-j)) >,< (k+(-j)),(1+i) > ) = det( < (j+k),(1+(-i)) >,< (1+(-i)),(j+k) > )

Forma Fonamental escalar:

Definició:

< a,b > [o] < x,y > ) = ax+by

Teorema:

< 1,i > [o] < 1,i > = 0

Teorema:

< d_{u}[uv],d_{v}[i·uv] > [o] < d_{u}[uv],d_{v}[i·uv] > = 0

Teorema:

< k,j > [o] < k,j > = 0

Teorema:

< d_{u}[k·uv],d_{v}[j·uv] > [o] < d_{u}[k·uv],d_{v}[j·uv] > = 0

Definició:

< a,b,c,d > [o] < x,y,z,ct > ) = ax+by+cz+dct

Teorema:

< 1,i,k,j > [o] < 1,i,k,j > = 0

Teorema:

< 1,x^{n},y^{n},z^{n} > [o] < 1,x^{n},y^{n},z^{n} > = 0 <==> ...

... ( x = i^{(1/n)} & y = j^{(1/n)} & z = k^{(1/n)} )

Teorema:

< d_{x}[xyz·ct],d_{y}[i·xyz·ct],d_{z}[k·xyz·ct],d_{ct}[j·xyz·ct] > [o] ...

... d_{x}[xyz·ct],d_{y}[i·xyz·ct],d_{z}[k·xyz·ct],d_{ct}[j·xyz·ct] = 0

Forma Bilineal Quaterniónica de dimesió 3:

Definició:

< x,y,z > [-|o|-] < u,w,v > = (yv+(-1)·zw)+(xv+zu)+(xw+(-1)·yu) 

Teorema:

< a+x,b+y,c+z > [-|o|-] < u,w,v > = ...

... ((b+y)·v+(-1)·(c+z)·w)+((a+x)·v+(c+z)·u)+((a+x)·w+(-1)·(b+y)·u) = ...

... ( < a,b,c > [-|o|-] < u,w,v > )+( < x,y,z > [-|o|-] < u,w,v > )

Teorema:

< ax,ay,az > [-|o|-] < u,w,v > = ...

... (ayv+(-1)·azw)+(axv+azu)+(axw+(-1)·ayu) = a·( < x,y,z > [-|o|-] < u,w,v > )

Teorema:

< 1,i,1 > [-|o|-] < j,w,k > = 0

< (-1),i,(-1) > [-|o|-] < k,w,j > = 0

Teorema:

< x,y,z > [-|o|-] < u,w,v > = (yv+(-1)·zw)+(xv+zu)+(xw+(-1)·yu) = ...

... < x,y,z > o ( < 0,1,1 >,< (-1),0,1 >,< 1,(-1),0 > ) o < u,w,v >

Geometría Diferencial de Quaternions:

Forma Fonamental Quaterniónica de dimensió 3:

Teorema:

... < d_{x}[f(x,y,z)],d_{y}[g(x,y,z)],d_{z}[h(x,y,z)] > ...

... [-|o|-] ...

... < d_{x}[F(x,y,z)],d_{y}[G(x,y,z)],d_{z}[H(x,y,z)] > ...

... = ...

... < d_{x}[f(x,y,z)],d_{y}[g(x,y,z)],d_{z}[h(x,y,z)] > ...

... o ...

... ( < 0,d[y]d[x],d[z]d[x] >,< (-1)·d[x]d[y],0,d[z]d[y] >,< d[x]d[z],(-1)·d[y]d[z],0 > ) ...

... o ...

... < d_{x}[F(x,y,z)],d_{y}[G(x,y,z)],d_{z}[H(x,y,z)] >

Teorema:

< d_{x}[yxz],d_{y}[i·yzx],d_{z}[zyx] > [-|o|-] ...

... < d_{x}[j·xyz],d_{y}[w·xyz],d_{z}[k·zyx] > = 0

Teorema:

< d_{x}[(-1)·yxz],d_{y}[i·yzx],d_{z}[(-1)·zyx] > [-|o|-] ...

... < d_{x}[k·xyz],d_{y}[w·xyz],d_{z}[j·zyx] > = 0

Demostració:

int-int[ d_{y}[xyz]·d_{z}[xyz] ]d[y]d[z] = (1/4)·(xyz)^{2}

Forma Fonamental Binómica:

Definició:

< a,b > [-(2)-] < x,y > ) = (a+b)·(x+y)

Teorema:

< 1,(-1) > [-(2)-] < 1,(-1) > ) = 0

Teorema:

< d_{u}[uv],d_{v}[(-1)·uv] > [-(2)-] < d_{u}[uv],d_{v}[(-1)·uv] > = 0

Métrica de Minkowski invariant Lorentz-Newton-LaGrange:

Sistema de coordenades A:

Lley:

( < x,y,z > [o] < x,y,z > ) = (ct)^{2} <==> ...

... ( x = ct·cos(u)·cos(v) & y = ct·sin(u)·cos(v) & z = ct·sin(v) )

v = velocitat del sistema de coordenades.

Lley:

( 1/(1+(-1)·(v/c)^{2}) )·( < x,y,z,i·vt > [o] < x,y,z,i·vt > ) = ...

... ( 1/(1+(-1)·(v/c)^{2}) )·( x^{2}+y^{2}+z^{2}+(-1)·(vt)^{2} )

Sistema de coordenades B:

Lley:

( 1/(1+(-1)·(v/c)^{2}) )·( < x,y,z,i·vt > [o] < x,y,z,i·vt > )  = (ct)^{2} <==> ...

... ( x = ct·cos(u)·cos(v) & y = ct·sin(u)·cos(v) & z = ct·sin(v) )

Métrica de Minkowski invariant Lorentz-Hamilton:

Sistema de coordenades A:

Lley:

( < x,y,z > [o] < ct,ct,ct > ) = (ct)^{2} <==> ...

... ( x = ct·( cos(u) )^{2}·( cos(v) )^{2} & ...

... y = ct·( sin(u) )^{2}·( cos(v) )^{2} & z = ct·( sin(v) )^{2} )

v = velocitat del sistema de coordenades.

Lley:

( 1/(1+(-1)·(v/c)) )·( < x,y,z,i·vt > [o] < ct,ct,ct,i·ct > ) = ...

... ( 1/(1+(-1)·(v/c)) )·( x·ct+y·ct+z·ct+(-1)·(vt)·(ct) )

Sistema de coordenades B:

Lley:

( 1/(1+(-1)·(v/c)) )·( < x,y,z,i·vt > [o] < ct,ct,ct,i·ct > )  = (ct)^{2} <==> ...

... ( x = ct·( cos(u) )^{2}·( cos(v) )^{2} & ...

... y = ct·( sin(u) )^{2}·( cos(v) )^{2} & z = ct·( sin(v) )^{2} )

Métrica de Klein-Gordon invariant Lorentz-Newton-LaGrange:

Lley:

( d[x]d[x]+d[y]d[y]+d[z]d[z] ) = d[ct]d[ct] <==> ...

... ( x = ct·cos(u)·cos(v) & y = ct·sin(u)·cos(v) & z = ct·sin(v) )

Lley:

( 1/(1+(-1)·(v/c)^{2}) )·( d[x]d[x]+d[y]d[y]+d[z]d[z]+(-1)·d[vt]d[vt] ) = d[ct]d[ct] <==> ...

... ( x = ct·cos(u)·cos(v) & y = ct·sin(u)·cos(v) & z = ct·sin(v) )

Métrica de Dirac invariant Lorentz-Hamilton:

Lley:

( d[x]d[ct]+d[y]d[ct]+d[z]d[ct] ) = d[ct]d[ct] <==> ...

... ( x = ct·( cos(u) )^{2}·( cos(v) )^{2} & ...

... y = ct·( sin(u) )^{2}·( cos(v) )^{2} & z = ct·( sin(v) )^{2} )

Lley:

( 1/(1+(-1)·(v/c)) )·( d[x]d[ct]+d[y]d[ct]+d[z]d[ct]+(-1)·d[vt]d[ct] ) = d[ct]d[ct] <==> ...

... ( x = ct·( cos(u) )^{2}·( cos(v) )^{2} & ...

... y = ct·( sin(u) )^{2}·( cos(v) )^{2} & z = ct·( sin(v) )^{2} )

Ecuacions de Klein-Gordon invariants Lorentz:

Lley:

( int-int[ P[ 0 [< t [< oo ]·f(t) ]d[x]d[x]+...

... int-int[ P[ 0 [< t [< oo ]·f(t) ]d[y]d[y]+int-int[ P[ 0 [< t [< oo ]·f(t) ]d[z]d[z] ) = ...

... i·(h/m)·int[f(t)]d[t]

P[ 0 [< t [< oo ]·f(t)·( d_{t}[x]^{2}+d_{t}[y]^{2}+d_{t}[z]^{2} ) =  i·(h/m)·d_{t}[f(t)]

( x = ct·cos(u)·cos(v) & y = ct·sin(u)·cos(v) & z = ct·sin(v) )

f(t) = e^{(1/(ih))·( int[ P[ 0 [< t [< oo ] ]d[t] [o(t)o] mc^{2}·t )}

Lley:

( 1/(1+(-1)·(v/c)^{2}) )·( ...

... int-int[ P[ 0 [< t [< oo ]·f(t) ]d[x]d[x]+...

... int-int[ P[ 0 [< t [< oo ]·f(t) ]d[y]d[y]+int-int[ P[ 0 [< t [< oo ]·f(t) ]d[z]d[z]+...

... (-1)·int-int[ P[ 0 [< t [< oo ]·f(t) ]d[vt]d[vt] ) = i·(h/m)·int[f(t)]d[t]

( 1/(1+(-1)·(v/c)^{2}) )·( ...

... P[ 0 [< t [< oo ]·f(t)·( d_{t}[x]^{2}+d_{t}[y]^{2}+d_{t}[z]^{2}+(-1)·d_{t}[vt]^{2} ) = ...

... i·(h/m)·d_{t}[f(t)]

( x = ct·cos(u)·cos(v) & y = ct·sin(u)·cos(v) & z = ct·sin(v) )

f(t) = e^{(1/(ih))·( int[ P[ 0 [< t [< oo ] ]d[t] [o(t)o] mc^{2}·t )}

Ecuació de Klein-Gordon-Newton

Lley:

(2/pi)·( 1/(1+(a·r(t))^{2}) )·f(t)·( d_{t}[x]^{2}+d_{t}[y]^{2}+d_{t}[z]^{2} ) = ...

... i·(h/m)·d_{t}[f(t)]

... ( ...

... x = (-1)·pq·(g/m)·(1/2)·t^{2}·cos(u)·cos(v) & ...

... y = (-1)·pq·(g/m)·(1/2)·t^{2}·sin(u)·cos(v) & ...

... z = (-1)·pq·(g/m)·(1/2)·t^{2}·sin(v) ...

... )

f(t) = e^{(1/(ih))·m·(-1)·(1/a)^{2}·(2/pi)·( ...

... ( a·(-1)·pq·(g/m)·(1/2)·t^{2} ) [o(t)o] arc-tan(a·(-1)·pq·(g/m)·(1/2)·t^{2}) ...

...)}

Lley:

( 1/(1+(-1)·(v/c)^{2}) )·( ...

(2/pi)·( 1/(1+(a·r(t))^{2}) )·f(t)·( ...

... d_{t}[x]^{2}+d_{t}[y]^{2}+d_{t}[z]^{2}+(-1)·d_{2}[vt]^{2} ) = ...

... i·(h/m)·d_{t}[f(t)]

... ( ...

... x = (-1)·pq·(g/m)·(1/2)·t^{2}·cos(u)·cos(v) & ...

... y = (-1)·pq·(g/m)·(1/2)·t^{2}·sin(u)·cos(v) & ...

... z = (-1)·pq·(g/m)·(1/2)·t^{2}·sin(v) ...

... )

f(t) = e^{(1/(ih))·m·( 1/(1+(-1)·(v/c)^{2}) )·(2/pi)·( ...

... (-1)·(1/a)^{2}·( ...

... ( a·(-1)·pq·(g/m)·(1/2)·t^{2} ) [o(t)o] arc-tan(a·(-1)·pq·(g/m)·(1/2)·t^{2}) ...

... )+...

... (-1)·v^{2}·t [o(t)o] arc-tan(a·(-1)·pq·(g/m)·(1/2)·t^{2}) [o(t)o] ...

... ln(t) [o(t)o] (1/a)·(-1)·(1/(pq))·(m/g)·t

... )}

Ecuacions de Dirac invariants Lorentz:

Lley:

( int-int[ P[ 0 [< t [< oo ]·f(t) ]d[x]d[ct]+...

... int-int[ P[ 0 [< t [< oo ]·f(t) ]d[y]d[ct]+int-int[ P[ 0 [< t [< oo ]·f(t) ]d[z]d[ct] ) = ...

... i·(h/m)·int[f(t)]d[t]

P[ 0 [< t [< oo ]·f(t)·( d_{t}[x]·c+d_{t}[y]·c+d_{t}[z]·c ) =  i·(h/m)·d_{t}[f(t)]

( x = ct·( cos(u) )^{2}·( cos(v) )^{2} & y = ct·( sin(u) )^{2}·( cos(v) )^{2} & ...

... z = ct·( sin(v) )^{2} )

r(t) = x+y+z

f(t) = e^{(1/(ih))·( int[ P[ 0 [< t [< oo ] ]d[t] [o(t)o] mc^{2}·t )}

Lley:

( 1/(1+(-1)·(v/c)) )·( ...

... int-int[ P[ 0 [< t [< oo ]·f(t) ]d[x]d[ct]+...

... int-int[ P[ 0 [< t [< oo ]·f(t) ]d[y]d[ct]+int-int[ P[ 0 [< t [< oo ]·f(t) ]d[z]d[ct]+...

... (-1)·int-int[ P[ 0 [< t [< oo ]·f(t) ]d[vt]d[ct] ) = i·(h/m)·int[f(t)]d[t]

( 1/(1+(-1)·(v/c)) )·( ...

... P[ 0 [< t [< oo ]·f(t)·( d_{t}[x]·c+d_{t}[y]·c+d_{t}[z]·c+(-1)·vc ) = ...

... i·(h/m)·d_{t}[f(t)]

( x = ct·( cos(u) )^{2}·( cos(v) )^{2} & y = ct·( sin(u) )^{2}·( cos(v) )^{2} & ...

... z = ct·( sin(v) )^{2} )

r(t) = x+y+z

f(t) = e^{(1/(ih))·( int[ P[ 0 [< t [< oo ] ]d[t] [o(t)o] mc^{2}·t )}

Ecuació de Dirac-Hamilton

Lley:

( ((-d)/pi)·( 1/(1+(a·r(t))^{2}) )·f(t)·( d_{t}[x]·c+d_{t}[y]·c+d_{t}[z]·c ) = ...

... i·(h/m)·d_{t}[f(t)]

... ( ...

... x = x_{0}·e^{(-2)·( (pq·g)/(mc) )·t}·( cos(u) )^{2}·( cos(v) )^{2} & ...

... y = x_{0}·e^{(-2)·( (pq·g)/(mc) )·t}·( sin(u) )^{2}·( cos(v) )^{2} & ...

... z = x_{0}·e^{(-2)·( (pq·g)/(mc) )·t}·( sin(v) )^{2} ...

... )

r(t) = x+y+z

f(t) = e^{(1/(ih))·mc·(1/a)·((-d)/pi)·( ...

... arc-tan(a·x_{0}·e^{(-2)·( (pq·g)/(mc) )·t}) ...

... )}

Lley:

( 1/(1+(-1)·(v/c)) )·( ...

((-d)/pi)·( 1/(1+(a·r(t))^{2}) )·f(t)·( ...

... d_{t}[x]·c+d_{t}[y]·c+d_{t}[z]·c+(-1)·d_{t}[vt]c ) = ...

... i·(h/m)·d_{t}[f(t)]

... ( ...

... x = x_{0}·e^{(-2)·( (pq·g)/(mc) )·t}·( cos(u) )^{2}·( cos(v) )^{2} & ...

... y = x_{0}·e^{(-2)·( (pq·g)/(mc) )·t}·( sin(u) )^{2}·( cos(v) )^{2} & ...

... z = x_{0}·e^{(-2)·( (pq·g)/(mc) )·t}·( sin(v) )^{2} ...

... )

r(t) = x+y+z

f(t) = e^{(1/(ih))·m·( 1/(1+(-1)·(v/c)^{2}) )·((-d)/pi)·( ...

... (1/a)·c·( ...

... arc-tan(a·x_{0}·e^{(-2)·( (pq·g)/(mc) )·t}) ...

... )+...

... (-1)·v^{2}·t [o(t)o] arc-tan(a·x_{0}·e^{(-2)·( (pq·g)/(mc) )·t}) [o(t)o] ...

... (-1)·(1/4)·( 1/(a·x_{0}) )·e^{2·( (pq·g)/(mc) )·t} [o(t)o] ( (mc)/(pq·g) )^{2}·t

... )}

Mecàniques:

Newton-LaGrange:

Lley:

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

x(t) = ct·cos(u)·cos(v) & y(t) = ct·sin(u)·cos(v) & z(t) = ct·sin(v)

Métrica de Newton-LaGrange bilineal: 

d[r(t)]d[r(t)] = ...

... < d[x],d[y],d[z] > o ( < 1,0,0 >,< 0,1,0 >,< 0,0,1 > ) o < d[x],d[y],d[z] >

Hamilton:

Lley:

(m/2)·c·( d_{t}[x]+d_{t}[y]+d_{t}[z] ) = (1/2)·mc^{2}

x(t) = ct·( cos(u) )^{2}·( cos(v) )^{2} & ...

... y(t) = ct·( sin(u) )^{2}·( cos(v) )^{2} & z(t) = ct·( sin(v) )^{2}

Métrica de Hamilton lineal:

d[r(t)] = < 1,1,1 > o < d[x],d[y],d[z] >

No ser malvado o seguir al Diablo,

no es de deficiente mental,

porque toda-alguna gente no es y hay condenación según dice el Diablo.

Ser malvado y no seguir al Diablo,

es de deficiente mental,

aunque quizás toda-alguna gente no es y hay condenación según dice el Diablo.

Francisco chupa un Jalisco es ley del mundo,

porque es un chocho y se comete adulterio.

Francisca chupa una Jalisca es ley del mundo,

porque es una polla y se comete adulterio.

Matrius de Dirac:

s_{0} = ( < (-1),0,0,0 >,< 0,(-1),0,0 >,< 0,0,(-1),0 >,< 0,0,0,(-1) > )

s_{x} = ( < 0,0,0,1 >,< 0,0,1,0 >,< 0,1,0,0 >,< 1,0,0,0 > )

s_{y} = ( < 0,0,1,0 >,< 0,0,0,1 >,< 1,0,0,0 >,< 0,1,0,0 > )

s_{z} = ( < 0,1,0,0 >,< 1,0,0,0 >,< 0,0,0,1 >,< 0,0,1,0 > )

Ecuació de Klein-Gordon invariant Lorentz-Newton-LaGrange de funció d'ona 4 dimesional:

Lley:

sum[k = 1]-[3][ s_{k}·d_{t}[x_{k}]^{2} ] o ...

... ( < 1,1,1,1> (1/E)·E(x)·f(x),< 1,1,1,1 >·(1/E)·E(y)·f(y),< 1,1,1,1 >·(1/E)·E(z)·f(z),...

... < 1,1,1,1 >·f(t) > = ...

... i·(h/m)·...

... ( < 1,1,1,1> d_{t}[f(x)],< 1,1,1,1 >·d_{t}[f(y)],< 1,1,1,1 >·d_{t}[f(z)],...

... < 1,1,1,1 >·d_{t}[f(t)] >

Lley:

( 1/(1+(-1)·(v/c)^{2}) )·( s_{0}·v^{2}+sum[k = 1]-[3][ s_{k}·d_{t}[x_{k}]^{2} ] ) o ...

... ( < 1,1,1,1> (1/E)·E(x)·f(x),< 1,1,1,1 >·(1/E)·E(y)·f(y),< 1,1,1,1 >·(1/E)·E(z)·f(z),...

... < 1,1,1,1 >·f(t) > = ...

... i·(h/m)·...

... ( < 1,1,1,1> d_{t}[f(x)],< 1,1,1,1 >·d_{t}[f(y)],< 1,1,1,1 >·d_{t}[f(z)],...

... < 1,1,1,1 >·d_{t}[f(t)] >

Ecuació de Dirac invariant Lorentz-Hamilton de funció d'ona 4 dimesional:

Lley:

sum[k = 1]-[3][ s_{k}·d_{t}[x_{k}]·c ] o ...

... ( < 1,1,1,1> (1/E)·E(x)·f(x),< 1,1,1,1 >·(1/E)·E(y)·f(y),< 1,1,1,1 >·(1/E)·E(z)·f(z),...

... < 1,1,1,1 >·f(t) > = ...

... i·(h/m)·...

... ( < 1,1,1,1> d_{t}[f(x)],< 1,1,1,1 >·d_{t}[f(y)],< 1,1,1,1 >·d_{t}[f(z)],...

... < 1,1,1,1 >·d_{t}[f(t)] >

Lley:

( 1/(1+(-1)·(v/c)) )·( s_{0}·cv+sum[k = 1]-[3][ s_{k}·d_{t}[x_{k}]·c ] ) o ...

... ( < 1,1,1,1> (1/E)·E(x)·f(x),< 1,1,1,1 >·(1/E)·E(y)·f(y),< 1,1,1,1 >·(1/E)·E(z)·f(z),...

... < 1,1,1,1 >·f(t) > = ...

... i·(h/m)·...

... ( < 1,1,1,1> d_{t}[f(x)],< 1,1,1,1 >·d_{t}[f(y)],< 1,1,1,1 >·d_{t}[f(z)],...

... < 1,1,1,1 >·d_{t}[f(t)] >

Lley de Einstein-Newton-LaGrange:

Lley:

(m/2)·d_{t}[r]^{2} = mc^{2}·( 1/( 1+(-1)·(d_{t}[r]/c)^{2} )^{(1/2)} )

r(t) = (2/i)^{( 1/(2+(1/2)·]2[) )}·ct

Deducció:

(d_{t}[r]/c)^{2} = (2/i)·(d_{t}[r]/c)^{(-1)·(1/2)·]2[}

(d_{t}[r]/c)^{2+(1/2)·]2[} = (2/i)

Lley:

(2/i)^{( 1/(2+(1/2)·]2[) )} = a <==> (-4) = a^{6}+(-1)·a^{4}

a^{2} = b <==> (-4) = b^{3}+(-1)·b^{2}

b = y+(1/3)

y^{3}+y^{2}+(1/3)·y+(1/27)+(-1)·y^{2}+(-1)·(2/3)·y+(-1)·(1/9)+4 = 0

y^{3}+(-1)·(1/3)·y+(-1)·(2/27)+4 = 0

Lley de Einstein-Hamilton:

Lley:

(m/2)·c·d_{t}[r] = mc^{2}·( 1/( 1+(-1)·(d_{t}[r]/c) )^{(1/2)} )

r(t) = (2/i)^{( 1/(1+(1/2)·]1[) )}·ct

Deducció:

(d_{t}[r]/c) = (2/i)·(d_{t}[r]/c)^{(-1)·(1/2)·]1[}

(d_{t}[r]/c)^{1+(1/2)·]1[} = (2/i)

Lley:

(2/i)^{( 1/(1+(1/2)·]1[) )} = a <==> (-4) = a^{3}+(-1)·a^{2}

a = y+(1/3)

y^{3}+y^{2}+(1/3)·y+(1/27)+(-1)·y^{2}+(-1)·(2/3)·y+(-1)·(1/9)+4 = 0

y^{3}+(-1)·(1/3)·y+(-1)·(2/27)+4 = 0

Energía cinética y energía en repós de Einstein:

Lley:

E(t)+(-1)·mc^{2} = mc^{2}·( 1+(1/2)·(d_{t}[r]/c)^{2}+(-1) )

Lley:

E(t)+(-1)·mc^{2} = mc^{2}·( 1+(1/2)·(d_{t}[r]/c)+(-1) )

Força de Einstein:

Lley:

m·d_{tt}^{2}[r] = m·d_{tt}^{2}[r]·( 1/( 1+(-1)·(d_{t}[r]/c)^{2} )^{(3/2)} ) = 0

Lley:

(m/2)·c·( d_{tt}^{2}[r]/d_{t}[r] ) = ...

... (m/2)·c·( d_{tt}^{2}[r]/d_{t}[r] )·( 1/( 1+(-1)·(d_{t}[r]/c) )^{(3/2)} ) = 0

Moment de Einstein:

Lley:

m·d_{t}[r] = mc^{2}·( ( t/o(t)o/x ) [o(t)o] ( 1/( 1+(-1)·(d_{t}[r]/c)^{2} )^{(1/2)} ) )

Lley:

(m/2)·c·ln(d_{t}[r]) = mc^{2}·( ( t/o(t)o/x ) [o(t)o] ( 1/( 1+(-1)·(d_{t}[r]/c) )^{(1/2)} ) )

Caminad con la luz,

mientras tengáis luz,

para que vos sorprendan las tinieblas,

porque el que camina con la luz sin saber a donde vatchnar,

no le sorprenden las tinieblas.

Caminad con el sonido,

mientras tengáis sonido,

para que vos sorprenda el silencio,

porque el que camina con el sonido sin saber a donde vatchnar,

no le sorprende el silencio.

Caminad con la luz,

mientras tengáis luz,

para que vos sorprendan las tinieblas,

porque el que camina por las tinieblas,

no ve a donde va.

Caminad con el sonido,

mientras tengáis sonido,

para que vos sorprenda el silencio,

porque el que camina por el silencio,

no oye a donde va.

Relativitat ampliada:

Lley:

(m/2)·d_{t}[r]^{2} = i·mc^{2}·( 1+(-i)·(d_{t}[r]/c)^{2} )^{(1/2)}

r(t) = (2k)^{( 1/(2+(-1)·(1/2)[...(i)...[2]...(i)...]) )}·ct

Lley:

(m/2)·c·d_{t}[r] = i·mc^{2}·( 1+(-i)·(d_{t}[r]/c) )^{(1/2)}

r(t) = (2k)^{( 1/(1+(-1)·(1/2)[...(i)...[1]...(i)...]) )}·ct

Invariants Lorentz inversos:

Lley:

( 1+(-i)·(v/c)^{2} )·( 1/( < x,y,z,j·vt >[o]< x,y,z,j·vt > ) ) = (1/ct)^{2}

Lley:

( 1+(-i)·(v/c) )·( 1/( < x,y,z,j·vt >[o]< ct,ct,ct,j·ct > ) ) = (1/ct)^{2}

Los hombres con la polla grande,

si son hombres fieles,

se van a extinguir y no ver nunca más,

y tienen que andar con la luz sin saber a donde vatchnar,

porque Dios les está concediendo.

Los hombres fieles con la polla grande,

tienen el otro vector del par de vectores de centros del alma de hombre no renovado,

y tienen la polla como un hombre infiel,

en tener solo un vector de centros como un hombre infiel.

Las mujeres con el chocho grande,

si son mujeres fieles,

se van a extinguir y no oír nunca más,

y tienen que andar con el sonido sin saber a donde vatchnar,

porque Diosa les está concediendo.

Las mujeres fieles con el chocho grande,

tienen el otro vector del par de vectores de centros del alma de mujer no renovado,

y tienen el chocho como una mujer infiel,

en tener solo un vector de centros como una mujer infiel.

Teorema: [ de Poisson ]

int[x = (-oo)]-[oo][ ( 1/(2x) ) ]d[x] = (1/6)·pi^{2}

Demostració:

int[ ( 1/(2x) ) ]d[x]+(-1)·int[ ( 1/(2·(-x)) ) ]d[(-x)] = C

lim[x = oo][ x [o(x)o] ( ( x^{2} )^{[o(x)o](-1)}+...+( (x+(-k))^{2} )^{[o(x)o](-1)} )+...

(-x) [o(x)o] ( ( (-x)^{2} )^{[o(x)o](-1)}+...+( ((-x)+k)^{2} )^{[o(x)o](-1)} ) ] = ...

... (1/6)·pi^{2}·oo+(1/6)·pi^{2}·(-oo) = (1/6)·pi^{2}

Teorema: [ de Euler-Mascheroni ]

ln(oo)+(-1)·ln(oo) = ln(-1)+(1/3)·pi^{2}

Demostració:

int[x = (-oo)]-[oo][ ( 1/(2x) ) ]d[x] = (1/2)·( ln(oo)+(-1)·ln(-oo) ) = (1/6)·pi^{2}

Teorema:

ln(oo^{p})+(-1)·ln(oo^{p}) = p·( ln(-1)+(1/3)·pi^{2} )

Teorema:

ln(n) no és convergent

Demostració:

|ln(oo)+(-1)·ln(oo)| = |ln(-1)+(1/3)·pi^{2}| = |pi|·|i+(1/3)·pi| >] s

|a+bi| = |a|+(-1)·|b|

Teorema:

(ln(n)/n) és convergent

Demostració:

|(ln(oo)/oo)+(-1)·(ln(oo)/oo)| = (1/oo)·|ln(oo)+(-1)·ln(oo)| = (1/oo)·|ln(-1)+(1/3)·pi^{2}| = ...

... (1/oo)·|pi|·|i+(1/3)·pi| < s

Teoría de viatges en el temps:

Te dos dimensions el temps ( it & t ) = ( p(-t) || 1 )

(-t) [< 0 [< t

Lley:

¬p(t) = p(-t) <==> p(t) = ¬p(-t)

Lley:

( ( p(-t) || 1 ) & p(t) ) <==> p(t)

Lley:

( ( p(t) & ( q(-t) || 1 ) ) & ( ( p(t) & ( q(-t) || 1 ) ) ==> w(t) )

( q(-t) != ¬p(t) || q(-t) != p(-t) )

( No pot ser matar || No pot ser viure )

Lley:

( ( ( p(t) || p(t) està en el Pare ) & ( q(-t) || 1 ) ) & ...

... ( ( ( p(t) || p(t) està en el Pare ) & ( q(-t) || 1 ) ) ==> w(t) )

Lley:

a [< t [< b <==> (-b) [< (-t) [< (-a)

p(a) = p(-b) & p(-a) = p(b)

A star-trek 4 la tripulació del enteprise està en el Pare en el segle XX.

Les ulleres del capità Kirk es destrueishen cuant es fabriquen les ulleres del present.

L'arma del Pavel Checkov no funciona perque no pot matar.

L'arma del capità Kirk funciona només perque no mata.

La científica se'n pot vaitxnar al present,

perque el temps està bifurcat en it.

La bifurcació acaba cuant tornen al present.

Lley:

L(x,u,v,t) = ...

... pqk·(1/r)^{2}·r(u,v,t)+...

... (-h)·( (c/s)^{(1/3)}·( (3/2^{(1/2)})·V·t )^{(2/3)} )·( e^{iut}+e^{ivt} )

m·(c/s)^{(2/3)}·V^{2}·( (3/2^{(1/2)})·V·t )^{(-1)·(2/3)} = ...

... pqk·( ( pq·(k/m) )^{(1/2)}·t )^{(-1)·(2/3)}

Lley:

L(x,u,v,t) = ...

... (-1)·pqk·(1/r)^{2}·r(u,v,t)+...

... (-h)·( (c/s)^{(1/3)}·( (3/2^{(1/2)})·V·it )^{(2/3)} )·( e^{iut}+e^{ivt} )

m·(c/s)^{(2/3)}·V^{2}·( (3/2^{(1/2)})·V·it )^{(-1)·(2/3)} = ...

... pqk·( (3/2^{(1/2)})·( pq·(k/m) )^{(1/2)}·it )^{(-1)·(2/3)}

Viatge al passat:

e^{(1/3)·pi·i} || (-1) || e^{(-1)·(1/3)·pi·i}

Viatge al present:

e^{(2/3)·pi·i} || 1 || e^{(-1)·(2/3)·pi·i}

Matrius de Pauli:

s_{0} = ( < (-1),0 >,< 0,(-1)> )

s_{x} = ( < 0,1 >,< 1,0 > )

Matrius de Dirac-Pauli:

s_{0} = ( < (-1),0,0 >,< 0,(-1),0 >,< 0,0,(-1) > )

s_{x} = ( < 0,1,0 >,< 0,0,1 >,< 1,0,0 > )

s_{y} = ( < 0,0,1 >,< 1,0,0 >,< 0,1,0 > )

I havere-kate-maruto menjjet-yuto-yamed mutchet-muto,

and I not querere-kate-maruto smash-muto.

I havere-kate-maruto menjjet-yuto-yamed pocket-muto,

and I not querere-kate-maruto smensh-muto.

Kino-yute I vare-kate-maruto drinket-yuto-yam mutchet-muto.

Kino-yute I vare-kate-maruto drinket-yuto-yam pocket-muto.

Asa-yute I wil-kate-maruto drinket-yuto-yam mutchet-muto.

Asa-yute I wil-kate-maruto drinket-yuto-yam pocket-muto.

I querere-kate-maruto a cotet-yuto-yamed wizh miruku.

I querere-kate-maruto a cotet-yuto-yamed wizhwat miruku.

ingenieria técnica en llum y so y calor

1r curs de electrónica analógica

i^{2} = (-1)

q(t) = pe^{at} || q(t) = pe^{(-1)·at}

q(t) = pe^{i·at} || q(t) = pe^{(-i)·at}

2n curs de electrónica virtual

k^{2} = i

j^{2} = (-i)

q(t) = pe^{k·at} || q(t) = pe^{(-k)·at}

q(t) = pe^{j·at} || q(t) = pe^{(-j)·at}

Teoría matemàtica:

Teorema:

d_{t}[ f(t)+g(t) ] = d_{t}[f(t)]+d_{t}[g(t)]

d_{t}[ s·f(t) ] = s·d_{t}[f(t)]

Teorema:

d_{t}[g( f(t) )] = d_{f(t)}[g( f(t) )]·d_{t}[f(t)]

Teorema:

d_{t}[t] = 1

d_{t}[e^{t}] = e^{t}

Teorema:

d_{t}[e^{at}] = ae^{at}

d_{tt}^{2}[e^{at}] = a^{2}·e^{at}

Teorema:

d_{tt}^{2}[ f(t)+g(t) ] = d_{tt}^{2}[f(t)]+d_{tt}^{2}[g(t)]

Teorema:

int[s]d[t] = st

Teorema:

d_{t}[ ln(f(t)) ] = ( d_{t}[f(t)]/f(t) )

Teorema:

d_{t}[ f(t) [o(t)o] g(t) ] = d_{t}[f(t)]·d_{t}[g(t)]

Teoría física:

1r curs de electrónica analógica:

Osciladors:

Lley:

R·d_{t}[q(t)]+(-C)·q(t) = 0

q(t) = pe^{(C/R)·t}

R·d_{t}[q(t)]+C·q(t) = 0

q(t) = pe^{(-1)·(C/R)·t}

Lley:

R·d_{t}[q(t)]+i·(-C)·q(t) = 0

q(t) = pe^{i·(C/R)·t}

R·d_{t}[q(t)]+i·C·q(t) = 0

q(t) = pe^{(-i)·(C/R)·t}

Bifurcadors:

Lley:

L·d_{tt}^{2}[q(t)]+(-C)·q(t) = 0

q(t) = pe^{(C/L)^{(1/2)}·t} || q(t) = pe^{(-1)·(C/L)^{(1/2)}·t}

L·d_{tt}^{2}[q(t)]+C·q(t) = 0

q(t) = pe^{i·(C/L)^{(1/2)}·t} || q(t) = pe^{(-i)·(C/L)^{(1/2)}·t}

Lley:

L·d_{tt}^{2}[f(t)+g(t)]+(-C)·(f(t)+g(t)) = 0

f(t) = pe^{(C/L)^{(1/2)}·t} & g(t) = pe^{(-1)·(C/L)^{(1/2)}·t}

L·d_{tt}^{2}[f(t)+g(t)]+C·(f(t)+g(t)) = 0

f(t) = pe^{i·(C/L)^{(1/2)}·t} & g(t) = pe^{(-i)·(C/L)^{(1/2)}·t}

Distorsoniados:

Lley:

R·d_{t}[q(t)]+(-C)·q(t) = Ae^{st}

q(t) = A·( 1/(s·R+(-C)) )·e^{st}

R·d_{t}[q(t)]+C·q(t) = Ae^{(-1)·st}

q(t) = A·( 1/((-s)·R+C) )·e^{(-1)·st}

Lley:

R·d_{t}[q(t)]+i·(-C)·q(t) = Ae^{i·st}

q(t) = A·(1/i)·( 1/(s·R+(-C)) )·e^{i·st}

R·d_{t}[q(t)]+i·C·q(t) = Ae^{(-i)·st}

q(t) = A·(1/i)·( 1/((-s)·R+C) )·e^{(-i)·st}

Amplificadors:

Lley:

L·d_{tt}^{2}[q(t)]+(-C)·q(t) = Ae^{st}

q(t) = A·( 1/(s^{2}·L+(-C)) )·e^{st}

L·d_{tt}^{2}[q(t)]+(-C)·q(t) = Ae^{(-1)·st}

q(t) = A·( 1/(s^{2}·L+(-C)) )·e^{(-1)·st}

Lley:

L·d_{tt}^{2}[q(t)]+C·q(t) = Ae^{i·st}

q(t) = A·( 1/((-1)·s^{2}·L+C) )·e^{i·st}

L·d_{tt}^{2}[q(t)]+C·q(t) = Ae^{(-i)·st}

q(t) = A·( 1/((-1)·s^{2}·L+C) )·e^{(-i)·st}

Lley:

n resistencies en serie <==> R = ( R_{1}+...+R_{n} )

n resistencies en paralel <==> R = ( (1/R_{1})+...+(1/R_{n}) )^{(-1)}

Lley:

R = ( R_{1}+...+R_{n} )·( (1/R_{1})+...+(1/R_{m}) )·( R_{1}+...+R_{n} )

R = ( ( (1/R_{1})+...+(1/R_{n}) )·( R_{1}+...+R_{m} )·( (1/R_{1})+...+(1/R_{n}) ) )^{(-1)}

Principi:

E(x) = qk·(1/r^{2})·(x/r)

B(x) = (-1)·qk·(1/r^{2})·(d_{t}[x]/r)

Lley:

m·d_{tt}^{2}[h(t)] = p·( E( h(t) )+int[ B( h(t) ) ]d[t] ) = 0

h(t) = ct

(-1)·h(t) = (-c)·t

Microfons y Altavoxums mono:

Lley:

int[ c·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = h(t)

q(t) = pe^{(C/R)·t}

int[ (-c)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = (-1)·h(t)

q(t) = pe^{(C/R)·t}

Lley:

int[ (-c)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = h(t)

q(t) = pe^{(-1)·(C/R)·t}

int[ c·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = (-1)·h(t)

q(t) = pe^{(-1)·(C/R)·t}

Cámares y Pantalles mono:

Lley:

int[ c·(1/i)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = h(t)

q(t) = pe^{i·(C/R)·t}

int[ (-c)·(1/i)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = (-1)·h(t)

q(t) = pe^{i·(C/R)·t}

Lley:

int[ (-c)·(1/i)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = h(t)

q(t) = pe^{(-i)·(C/R)·t}

int[ c·(1/i)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = (-1)·h(t)

q(t) = pe^{(-i)·(C/R)·t}

Microfons y Altavoxums stereos:

Lley:

int[ c·(L/C)·( d_{tt}^{2}[q(t)]/q(t) ) ]d[t] = h(t)

q(t) = pe^{(C/L)^{(1/2)}·t} || q(t) = pe^{(-1)·(C/L)^{(1/2)}·t}

int[ (-c)·(L/C)·( d_{tt}^{2}[q(t)]/q(t) ) ]d[t] = (-1)·h(t)

q(t) = pe^{(C/L)^{(1/2)}·t} || q(t) = pe^{(-1)·(C/L)^{(1/2)}·t}

Lley:

int[ c·(L/C)·( d_{tt}^{2}[f(t)+g(t)]/(f(t)+g(t)) ) ]d[t] = h(t)

f(t) = pe^{(C/L)^{(1/2)}·t} & g(t) = pe^{(-1)·(C/L)^{(1/2)}·t}

int[ (-c)·(L/C)·( d_{tt}^{2}[f(t)+g(t)]/(f(t)+g(t)) ) ]d[t] = (-1)·h(t)

f(t) = pe^{(C/L)^{(1/2)}·t} & g(t) = pe^{(-1)·(C/L)^{(1/2)}·t}

Cámares y Pantalles stereos:

Lley:

int[ (-c)·(L/C)·( d_{tt}^{2}[q(t)]/q(t) ) ]d[t] = h(t)

q(t) = pe^{i·(C/L)^{(1/2)}·t} || q(t) = pe^{(-i)·(C/L)^{(1/2)}·t}

int[ c·(L/C)·( d_{tt}^{2}[q(t)]/q(t) ) ]d[t] = (-1)·h(t)

q(t) = pe^{i·(C/L)^{(1/2)}·t} || q(t) = pe^{(-i)·(C/L)^{(1/2)}·t}

Lley:

int[ (-c)·(L/C)·( d_{tt}^{2}[f(t)+g(t)]/(f(t)+g(t)) ) ]d[t] = h(t)

f(t) = pe^{i·(C/L)^{(1/2)}·t} & g(t) = pe^{(-i)·(C/L)^{(1/2)}·t}

int[ c·(L/C)·( d_{tt}^{2}[f(t)+g(t)]/(f(t)+g(t)) ) ]d[t] = (-1)·h(t)

f(t) = pe^{i·(C/L)^{(1/2)}·t} & g(t) = pe^{(-i)·(C/L)^{(1/2)}·t}

Reproductors de disc:

Lley:

h(t) = ( ln(1/p)+ln(q(t)) ) [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = (C/R)·r(t)

q(t) = pe^{(C/R)·t}

h(t) = ( ln(1/p)+ln(q(t)) ) [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = (-1)·(C/R)·r(t)

q(t) = pe^{(-1)·(C/R)·t}

Lley:

h(t) = ( ln(1/p)+ln(q(t)) ) [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = i·(C/R)·r(t)

q(t) = pe^{i·(C/R)·t}

h(t) = ( ln(1/p)+ln(q(t)) ) [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = (-i)·(C/R)·r(t)

q(t) = pe^{(-i)·(C/R)·t}

Reproductor de disc amb pitch:

Lley:

h(t) = int[ (C/L)^{(1/2)}·( ln(1/p)+ln(q(t)) ) ]d[t] [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = (C/L)·t·r(t)

d_{tt}^{2}[h(t)] = (C/L)·r(t)+(C/L)·t·d_{t}[r(t)]

q(t) = pe^{(C/L)^{(1/2)}·t}

h(t) = int[ (C/L)^{(1/2)}·( ln(1/p)+ln(q(t)) ) ]d[t] [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = (-1)·(C/L)·t·r(t)

d_{tt}^{2}[h(t)] = (-1)·(C/L)·r(t)+(-1)·(C/L)·t·d_{t}[r(t)]

q(t) = pe^{(-1)·(C/L)^{(1/2)}·t}

Lley:

h(t) = int[ (C/L)^{(1/2)}·( ln(1/p)+ln(q(t)) ) ]d[t] [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = i·(C/L)·t·r(t)

d_{tt}^{2}[h(t)] = i·(C/L)·r(t)+i·(C/L)·t·d_{t}[r(t)]

q(t) = pe^{i·(C/L)^{(1/2)}·t}

h(t) = int[ (C/L)^{(1/2)}·( ln(1/p)+ln(q(t)) ) ]d[t] [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = (-i)·(C/L)·t·r(t)

d_{tt}^{2}[h(t)] = (-i)·(C/L)·r(t)+(-i)·(C/L)·t·d_{t}[r(t)]

q(t) = pe^{(-i)·(C/L)^{(1/2)}·t}

Pitch:

Lley:

P = < R_{1},L_{1},...,R_{n},L_{n}>

Q = < L_{1},R_{1},...,L_{n},R_{n}>

2n curs de electrónica virtual:

Osciladors virtuals:

Lley:

R·d_{t}[q(t)]+k·(-C)·q(t) = 0

q(t) = pe^{k·(C/R)·t}

R·d_{t}[q(t)]+k·C·q(t) = 0

q(t) = pe^{(-k)·(C/R)·t}

Lley:

R·d_{t}[q(t)]+j·(-C)·q(t) = 0

q(t) = pe^{j·(C/R)·t}

R·d_{t}[q(t)]+j·C·q(t) = 0

q(t) = pe^{(-j)·(C/R)·t}

Bifurcadors virtuals:

Lley:

L·d_{tt}^{2}[q(t)]+i·(-C)·q(t) = 0

q(t) = pe^{k·(C/L)^{(1/2)}·t} || q(t) = pe^{(-k)·(C/L)^{(1/2)}·t}

L·d_{tt}^{2}[q(t)]+i·C·q(t) = 0

q(t) = pe^{j·(C/L)^{(1/2)}·t} || q(t) = pe^{(-j)·(C/L)^{(1/2)}·t}

Lley:

L·d_{tt}^{2}[f(t)+g(t)]+i·(-C)·(f(t)+g(t)) = 0

f(t) = pe^{k·(C/L)^{(1/2)}·t} & g(t) = pe^{(-k)·(C/L)^{(1/2)}·t}

L·d_{tt}^{2}[f(t)+g(t)]+i·C·(f(t)+g(t)) = 0

f(t) = pe^{j·(C/L)^{(1/2)}·t} & g(t) = pe^{(-j)·(C/L)^{(1/2)}·t}

Distorsoniados virtuals:

Lley:

R·d_{t}[q(t)]+k·(-C)·q(t) = Ae^{k·st}

q(t) = A·(1/k)·( 1/(s·R+(-C)) )·e^{k·st}

R·d_{t}[q(t)]+k·C·q(t) = Ae^{(-k)·st}

q(t) = A·(1/k)·( 1/((-s)·R+C) )·e^{(-k)·st}

Lley:

R·d_{t}[q(t)]+j·(-C)·q(t) = Ae^{j·st}

q(t) = A·(1/j)·( 1/(s·R+(-C)) )·e^{j·st}

R·d_{t}[q(t)]+j·C·q(t) = Ae^{(-j)·st}

q(t) = A·(1/j)·( 1/((-s)·R+C) )·e^{(-j)·st}

Amplificadors virtuals:

Lley:

L·d_{tt}^{2}[q(t)]+i·(-C)·q(t) = Ae^{k·st}

q(t) = A·(1/i)·( 1/(s^{2}·L+(-C)) )·e^{k·st}

L·d_{tt}^{2}[q(t)]+i·(-C)·q(t) = Ae^{(-k)·st}

q(t) = A·(1/i)·( 1/(s^{2}·L+(-C)) )·e^{(-k)·st}

Lley:

L·d_{tt}^{2}[q(t)]+i·C·q(t) = Ae^{j·st}

q(t) = A·(1/i)·( 1/((-1)·s^{2}·L+C) )·e^{j·st}

L·d_{tt}^{2}[q(t)]+i·C·q(t) = Ae^{(-j)·st}

q(t) = A·(1/i)·( 1/((-1)·s^{2}·L+C) )·e^{(-j)·st}

Microfons y Altavoxums virtuals mono:

Lley:

int[ c·(1/k)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = h(t)

q(t) = pe^{k·(C/R)·t}

int[ (-c)·(1/k)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = (-1)·h(t)

q(t) = pe^{k·(C/R)·t}

Lley:

int[ (-c)·(1/k)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = h(t)

q(t) = pe^{(-k)·(C/R)·t}

int[ c·(1/k)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = (-1)·h(t)

q(t) = pe^{(-k)·(C/R)·t}

Cámares y Pantalles virtuals mono:

Lley:

int[ c·(1/j)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = h(t)

q(t) = pe^{j·(C/R)·t}

int[ (-c)·(1/j)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = (-1)·h(t)

q(t) = pe^{j·(C/R)·t}

Lley:

int[ (-c)·(1/j)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = h(t)

q(t) = pe^{(-j)·(C/R)·t}

int[ c·(1/j)·(R/C)·( d_{t}[q(t)]/q(t) ) ]d[t] = (-1)·h(t)

q(t) = pe^{(-j)·(C/R)·t}

Microfons y Altavoxums virtuals stereos:

Lley:

int[ c·(1/i)·(L/C)·( d_{tt}^{2}[q(t)]/q(t) ) ]d[t] = h(t)

q(t) = pe^{k·(C/L)^{(1/2)}·t} || q(t) = pe^{(-k)·(C/L)^{(1/2)}·t}

int[ (-c)·(1/i)·(L/C)·( d_{tt}^{2}[q(t)]/q(t) ) ]d[t] = (-1)·h(t)

q(t) = pe^{k·(C/L)^{(1/2)}·t} || q(t) = pe^{(-k)·(C/L)^{(1/2)}·t}

Lley:

int[ c·(1/i)·(L/C)·( d_{tt}^{2}[f(t)+g(t)]/(f(t)+g(t)) ) ]d[t] = h(t)

f(t) = pe^{k·(C/L)^{(1/2)}·t} & g(t) = pe^{(-k)·(C/L)^{(1/2)}·t}

int[ (-c)·(1/i)·(L/C)·( d_{tt}^{2}[f(t)+g(t)]/(f(t)+g(t)) ) ]d[t] = (-1)·h(t)

f(t) = pe^{k·(C/L)^{(1/2)}·t} & g(t) = pe^{(-k)·(C/L)^{(1/2)}·t}

Cámares y Pantalles virtuals stereos:

Lley:

int[ (-c)·(1/i)·(L/C)·( d_{tt}^{2}[q(t)]/q(t) ) ]d[t] = h(t)

q(t) = pe^{j·(C/L)^{(1/2)}·t} || q(t) = pe^{(-j)·(C/L)^{(1/2)}·t}

int[ c·(1/i)·(L/C)·( d_{tt}^{2}[q(t)]/q(t) ) ]d[t] = (-1)·h(t)

q(t) = pe^{j·(C/L)^{(1/2)}·t} || q(t) = pe^{(-j)·(C/L)^{(1/2)}·t}

Lley:

int[ (-c)·(1/i)·(L/C)·( d_{tt}^{2}[f(t)+g(t)]/(f(t)+g(t)) ) ]d[t] = h(t)

f(t) = pe^{j·(C/L)^{(1/2)}·t} & g(t) = pe^{(-j)·(C/L)^{(1/2)}·t}

int[ c·(1/i)·(L/C)·( d_{tt}^{2}[f(t)+g(t)]/(f(t)+g(t)) ) ]d[t] = (-1)·h(t)

f(t) = pe^{j·(C/L)^{(1/2)}·t} & g(t) = pe^{(-j)·(C/L)^{(1/2)}·t}

Reproductors de disc virtuals:

Lley:

h(t) = ( ln(1/p)+ln(q(t)) ) [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = k·(C/R)·r(t)

q(t) = pe^{k·(C/R)·t}

h(t) = ( ln(1/p)+ln(q(t)) ) [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = (-k)·(C/R)·r(t)

q(t) = pe^{(-k)·(C/R)·t}

Lley:

h(t) = ( ln(1/p)+ln(q(t)) ) [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = j·(C/R)·r(t)

q(t) = pe^{j·(C/R)·t}

h(t) = ( ln(1/p)+ln(q(t)) ) [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = (-j)·(C/R)·r(t)

q(t) = pe^{(-j)·(C/R)·t}

Reproductor de disc virtuals amb pitch:

Lley:

h(t) = int[ (C/L)^{(1/2)}·( ln(1/p)+ln(q(t)) ) ]d[t] [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = k·(C/L)·t·r(t)

d_{tt}^{2}[h(t)] = k·(C/L)·r(t)+k·(C/L)·t·d_{t}[r(t)]

q(t) = pe^{k·(C/L)^{(1/2)}·t}

h(t) = int[ (C/L)^{(1/2)}·( ln(1/p)+ln(q(t)) ) ]d[t] [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = (-k)·(C/L)·t·r(t)

d_{tt}^{2}[h(t)] = (-k)·(C/L)·r(t)+(-k)·(C/L)·t·d_{t}[r(t)]

q(t) = pe^{(-k)·(C/L)^{(1/2)}·t}

Lley:

h(t) = int[ (C/L)^{(1/2)}·( ln(1/p)+ln(q(t)) ) ]d[t] [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = j·(C/L)·t·r(t)

d_{tt}^{2}[h(t)] = j·(C/L)·r(t)+j·(C/L)·t·d_{t}[r(t)]

q(t) = pe^{j·(C/L)^{(1/2)}·t}

h(t) = int[ (C/L)^{(1/2)}·( ln(1/p)+ln(q(t)) ) ]d[t] [o(t)o] int[ r(t) ]d[t]

d_{t}[h(t)] = (-j)·(C/L)·t·r(t)

d_{tt}^{2}[h(t)] = (-j)·(C/L)·r(t)+(-j)·(C/L)·t·d_{t}[r(t)]

q(t) = pe^{(-j)·(C/L)^{(1/2)}·t}

3r curs de tecnología del calor:

T(x) = (R·q)(x)

T(x) = (P+(-Q))(x)

Increment de temperatura <==> T(x) >] 0

Decrement de temperatura <==> T(x) [< 0

Lley:

v·d_{x}[T(x)]+(-u)·T(x) = 0

T(x) = we^{(u/v)·x}

v·d_{x}[T(x)]+u·T(x) = 0

T(x) = we^{(-1)·(u/v)·x}

Lley:

v·d_{x}[T(x)]+i·(-u)·T(x) = 0

T(x) = we^{i·(u/v)·x}

v·d_{x}[T(x)]+i·u·T(x) = 0

T(x) = we^{(-i)·(u/v)·x}

Lley:

(h/m)·d_{xx}^{2}[T(x)]+(-u)·T(x) = 0

T(x) = we^{( u·(m/h) )^{(1/2)}·x} || T(x) = we^{(-1)·( u·(m/h) )^{(1/2)}·x}

(h/m)·d_{xx}^{2}[T(x)]+u·T(x) = 0

T(x) = we^{i·( u·(m/h) )^{(1/2)}·x} || T(x) = we^{(-i)·( u·(m/h) )^{(1/2)}·x}

Lley:

(h/m)·d_{xx}^{2}[f(x)+g(x)]+(-u)·(f(x)+g(x)) = 0

f(x) = we^{( u·(m/h) )^{(1/2)}·x} & g(x) = we^{(-1)·( u·(m/h) )^{(1/2)}·x}

(h/m)·d_{xx}^{2}[f(x)+g(x)]+u·(f(x)+g(x)) = 0

f(x) = we^{i·( u·(m/h) )^{(1/2)}·x} & g(x) = we^{(-i)·( u·(m/h) )^{(1/2)}·x}

Lley:

v·d_{x}[T(x)]+(-u)·T(x) = Ae^{ax}

T(x) = A·( 1/(av+(-u)) )·e^{ax}

v·d_{x}[T(x)]+u·T(x) = Ae^{(-1)·ax}

T(x) = A·( 1/((-a)·v+u) )·e^{(-1)·ax}

Lley:

v·d_{x}[T(x)]+i·(-u)·T(x) = Ae^{i·ax}

T(x) = A·(1/i)·( 1/(av+(-u)) )·e^{i·ax}

v·d_{x}[T(x)]+i·u·T(x) = Ae^{(-i)·ax}

T(x) = A·(1/i)·( 1/((-a)·v+u) )·e^{(-i)·ax}

Lley:

(h/m)·d_{xx}^{2}[T(x)]+(-u)·T(x) = Ae^{ax}

T(x) = A·( 1/(a^{2}·(h/m)+(-u)) )·e^{ax}

(h/m)·d_{xx}^{2}[T(x)]+(-u)·T(x) = Ae^{(-1)·ax}

T(x) = A·( 1/(a^{2}·(h/m)+(-u)) )·e^{(-1)·ax}

Lley:

(h/m)·d_{xx}^{2}[T(x)]+u·T(x) = Ae^{i·ax}

T(x) = A·( 1/((-1)·a^{2}·(h/m)+u) )·e^{i·ax}

(h/m)·d_{xx}^{2}[T(x)]+u·T(x) = Ae^{(-i)·ax}

T(x) = A·( 1/((-1)·a^{2}·(h/m)+u) )·e^{(-i)·ax}

Lley:

int[ c·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = h(t)

T(x) = we^{(u/v)·x}

int[ (-c)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = (-1)·h(t)

T(x) = we^{(u/v)·x}

Lley:

int[ (-c)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = h(t)

T(x) = we^{(-1)·(u/v)·x}

int[ c·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = (-1)·h(t)

T(x) = we^{(-1)·(u/v)·x}

Lley:

int[ c·(1/i)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = h(t)

T(x) = we^{i·(u/v)·x}

int[ (-c)·(1/i)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = (-1)·h(t)

T(x) = we^{i·(u/v)·x}

Lley:

int[ (-c)·(1/i)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = h(t)

T(x) = we^{(-i)·(u/v)·x}

int[ c·(1/i)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = (-1)·h(t)

T(x) = we^{(-i)·(u/v)·x}

4r curs de tecnología virtual del calor:

Lley:

v·d_{x}[T(x)]+k·(-u)·T(x) = 0

T(x) = we^{k·(u/v)·x}

v·d_{x}[T(x)]+k·u·T(x) = 0

T(x) = we^{(-k)·(u/v)·x}

Lley:

v·d_{x}[T(x)]+j·(-u)·T(x) = 0

T(x) = we^{j·(u/v)·x}

v·d_{x}[T(x)]+j·u·T(x) = 0

T(x) = we^{(-j)·(u/v)·x}

Lley:

(h/m)·d_{xx}^{2}[T(x)]+i·(-u)·T(x) = 0

T(x) = we^{k·( u·(m/h) )^{(1/2)}·x} || T(x) = we^{(-k)·( u·(m/h) )^{(1/2)}·x}

(h/m)·d_{xx}^{2}[T(x)]+i·u·T(x) = 0

T(x) = we^{j·( u·(m/h) )^{(1/2)}·x} || T(x) = we^{(-j)·( u·(m/h) )^{(1/2)}·x}

Lley:

(h/m)·d_{xx}^{2}[f(x)+g(x)]+i·(-u)·(f(x)+g(x)) = 0

f(x) = we^{k·( u·(m/h) )^{(1/2)}·x} & g(x) = we^{(-k)·( u·(m/h) )^{(1/2)}·x}

(h/m)·d_{xx}^{2}[f(x)+g(x)]+i·u·(f(x)+g(x)) = 0

f(x) = we^{j·( u·(m/h) )^{(1/2)}·x} & g(x) = we^{(-j)·( u·(m/h) )^{(1/2)}·x}

Lley:

v·d_{x}[T(x)]+k·(-u)·T(x) = Ae^{k·ax}

T(x) = A·(1/k)·( 1/(av+(-u)) )·e^{k·ax}

v·d_{x}[T(x)]+k·u·T(x) = Ae^{(-k)·ax}

T(x) = A·(1/k)·( 1/((-a)·v+u) )·e^{(-k)·ax}

Lley:

v·d_{x}[T(x)]+j·(-u)·T(x) = Ae^{j·ax}

T(x) = A·(1/j)·( 1/(av+(-u)) )·e^{j·ax}

v·d_{x}[T(x)]+j·u·T(x) = Ae^{(-j)·ax}

T(x) = A·(1/j)·( 1/((-a)·v+u) )·e^{(-j)·ax}

Lley:

(h/m)·d_{xx}^{2}[T(x)]+i·(-u)·T(x) = Ae^{k·ax}

T(x) = A·(1/i)·( 1/(a^{2}·(h/m)+(-u)) )·e^{k·ax}

(h/m)·d_{xx}^{2}[T(x)]+i·(-u)·T(x) = Ae^{(-k)·ax}

T(x) = A·(1/i)·( 1/(a^{2}·(h/m)+(-u)) )·e^{(-k)·ax}

Lley:

(h/m)·d_{xx}^{2}[T(x)]+i·u·T(x) = Ae^{j·ax}

T(x) = A·(1/i)·( 1/((-1)·a^{2}·(h/m)+u) )·e^{j·ax}

(h/m)·d_{xx}^{2}[T(x)]+i·u·T(x) = Ae^{(-j)·ax}

T(x) = A·(1/i)·( 1/((-1)·a^{2}·(h/m)+u) )·e^{(-j)·ax}

Lley:

int[ c·(1/k)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = h(t)

T(x) = we^{k·(u/v)·x}

int[ (-c)·(1/k)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = (-1)·h(t)

T(x) = we^{k·(u/v)·x}

Lley:

int[ (-c)·(1/k)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = h(t)

T(x) = we^{(-k)·(u/v)·x}

int[ c·(1/k)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = (-1)·h(t)

T(x) = we^{(-k)·(u/v)·x}

Lley:

int[ c·(1/j)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = h(t)

T(x) = we^{j·(u/v)·x}

int[ (-c)·(1/j)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = (-1)·h(t)

T(x) = we^{j·(u/v)·x}

Lley:

int[ (-c)·(1/j)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = h(t)

T(x) = we^{(-j)·(u/v)·x}

int[ c·(1/j)·(v/u)·( d_{x}[T(x)]/T(x) ) ]d[t] = (-1)·h(t)

T(x) = we^{(-j)·(u/v)·x}

ecuacions de Maxwell

rot[ E(x,y,z) ] = ...

... < ...

... (1/a^{2})·( d_{yz}^{2}[E_{y}·a^{3}xyz]+(-1)·d_{zy}^{2}[E_{z}·a^{3}xyz] ) , ...

... (1/a^{2})·( d_{zx}^{2}[E_{z}·a^{3}yzx]+(-1)·d_{xz}^{2}[E_{x}·a^{3}yzx] ) , ...

... (1/a^{2})·( d_{xy}^{2}[E_{x}·a^{3}zxy]+(-1)·d_{yx}^{2}[E_{y}·a^{3}zxy] ) ...

... >

anti-rot[ E(x,y,z) ] = ...

... < ...

... (1/a)·( d_{x}[E_{y}·a^{3}xyz]+(-1)·d_{x}[E_{z}·a^{3}xyz] ) , ...

... (1/a)·( d_{y}[E_{z}·a^{3}yzx]+(-1)·d_{y}[E_{x}·a^{3}yzx] ) , ...

... (1/a)·( d_{z}[E_{x}·a^{3}zxy]+(-1)·d_{z}[E_{y}·a^{3}zxy] ) ...

... >

Principi:

E(x,y,z) = qk·(1/r^{2})·( < x,y,z >/r )

B(x,y,z) = (-1)·qk·(1/r^{2})·( < d_{t}[x],d_{t}[y],d_{t}[z] >/r )

Lley:

Sigui ( x = r & y = r & z = r ) ==> ( Maxwell-Ampere & Maxwell-Faraday )

Lley de Maxwell-Ampere en forma integral:

anti-potencial[ rot[ E(x,y,z) ] ] = ...

... qk+(1/3)·anti-potencial[ int[B(x,y,z)]d[t] ]

anti-potencial[ rot[ B(x,y,z) ] ] = ...

... d_{t}[q(t)]·k+(-1)·(1/3)·anti-potencial[ d_{t}[E(x,y,z,q(t))]+B(x,y,z,q(t)) ]

Lley de Maxwell-Faraday en forma integral:

potencial[ anti-rot[ E(x,y,z) ] ] = ...

... q·(k/r)+(2/3)·potencial[ int[B(x,y,z)]d[t] ]

potencial[ anti-rot[ B(x,y,z) ] ] = ...

... d_{t}[q(t)]·(k/r)+(-1)·(2/3)·potencial[ d_{t}[E(x,y,z,q(t))]+B(x,y,z,q(t)) ]

Lley:

Sigui ( x = r & y = r & z = r ) ==> ( Maxwell-Ampere & Maxwell-Faraday )

Lley de Maxwell-Ampere en forma diferencial:

rot[ E(x,y,z) ] = H(x,y,z)+(1/3)·int[B(x,y,z)]d[t]

rot[ B(x,y,z) ] = J(x,y,z,q(t))+(-1)·(1/3)·( d_{t}[E(x,y,z,q(t))]+B(x,y,z,q(t)) )

Lley de Maxwell-Faraday en forma diferencial:

anti-rot[ E(x,y,z) ] = P(x,y,z)+(2/3)·int[B(x,y,z)]d[t]

anti-rot[ B(x,y,z) ] = Q(x,y,z,q(t))+(-1)·(2/3)·( d_{t}[E(x,y,z,q(t))]+B(x,y,z,q(t)) )

Lley:

H(x,y,z) = qk·(1/r^{2})·...

... ( < 2axy+(-2)·azx+(1/3)·r,2ayz+(-2)·axy+(1/3)·r,2azx+(-2)·ayz+(1/3)·r >/r )

J(x,y,z) = (-1)·q·k·(1/r^{2})·...

... ( < (1/d_{t}[y])·d_{t}[ d_{t}[y]·ayx ]+(-1)·(1/d_{t}[z])·d_{t}[ d_{t}[z]·azx ], ...

... (1/d_{t}[z])·d_{t}[ d_{t}[z]·azy ]+(-1)·(1/d_{t}[x])·d_{t}[ d_{t}[x]·axy ], ...

... (1/d_{t}[x])·d_{t}[ d_{t}[x]·axz ]+(-1)·(1/d_{t}[y])·d_{t}[ d_{t}[y]·ayz ] >/r )+...

... (1/3)·d_{t}[q]·k·(1/r^{2})·( < r,r,r >/r )

Lley:

P(x,y,z) = qk·(1/r^{2})·...

... ( < a^{2}y^{2}z+(-1)·a^{2}yz^{2}+(2/3)·r, ...

... a^{2}z^{2}x+(-1)·a^{2}zx^{2}+(2/3)·r, ...

... a^{2}x^{2}y+(-1)·a^{2}xy^{2}+(2/3)·r >/r )

Q(x,y,z) = (-1)·q·k·(1/r^{2})·...

... ( < d_{t}[y]·a^{2}yz+(-1)·d_{t}[z]·a^{2}zy, ...

... d_{t}[z]·a^{2}zx+(-1)·d_{t}[x]·a^{2}xz, ...

... d_{t}[x]·a^{2}xy+(-1)·d_{t}[y]·a^{2}yx >/r )+...

... (2/3)·d_{t}[q]·k·(1/r^{2})·( < r,r,r >/r )

Principi:

E(x,y,z) = qk·(1/r^{2})·...

... ( f(br) )^{(-3)}·( < x·f(bx),y·f(by),z·f(bz) >/r )

B(x,y,z) = (-1)·qk·(1/r^{2})·...

... ( f(br) )^{(-3)}·( < d_{t}[x·f(bx)],d_{t}[y·f(by)],d_{t}[z·f(bz)] >/r )

Lley:

Sigui ( x = r & y = r & z = r ) ==> ( Maxwell-Ampere & Maxwell-Faraday )

Lley de Maxwell-Ampere en forma integral:

anti-potencial[ rot[ E(x,y,z) ] ] = ...

... qk+(1/3)·anti-potencial[ int[B(x,y,z)]d[t] ]

anti-potencial[ rot[ B(x,y,z) ] ] = ...

... d_{t}[q(t)]·k+(-1)·(1/3)·anti-potencial[ d_{t}[E(x,y,z,q(t))]+B(x,y,z,q(t)) ]

Lley de Maxwell-Faraday en forma integral:

potencial[ anti-rot[ E(x,y,z) ] ] = ...

... q·(k/r)·(1/f(br))+(2/3)·potencial[ int[B(x,y,z)]d[t] ]

potencial[ anti-rot[ B(x,y,z) ] ] = ...

... d_{t}[q(t)]·(k/r)·(1/f(br))+(-1)·(2/3)·potencial[ d_{t}[E(x,y,z,q(t))]+B(x,y,z,q(t)) ]

f(br) = 1

Principi: [ d'un planeta amb dia y nit ]

E(x,y,z) = qk·(1/r^{2})·...

... e^{(-3)·br}·( < x·e^{bx},y·e^{by},z·e^{bz} >/r )

B(x,y,z) = (-1)·qk·(1/r^{2})·...

... e^{(-3)·br}·( < d_{t}[x·e^{bx}],d_{t}[y·e^{by}],d_{t}[z·e^{bz}] >/r )

b = ( (2pi·i)/r )

Principi: [ de propulsió d'un coet ]

E(x,y,z) = qk·(1/r^{2})·...

... ( ln(br) )^{(-3)}·( < x·ln(bx),y·ln(by),z·ln(bz) >/r )

B(x,y,z) = (-1)·qk·(1/r^{2})·...

... ( ln(br) )^{(-3)}·( < d_{t}[x·ln(bx)],d_{t}[y·ln(by)],d_{t}[z·ln(bz)] >/r )

b = ( e/r )

Principi: [ d'ona de volum cosinosoidal ]

E(x,y,z) = qk·(1/r^{2})·...

... ( cos(br) )^{(-3)}·( < x·cos(bx),y·cos(by),z·cos(bz) >/r )

B(x,y,z) = (-1)·qk·(1/r^{2})·...

... ( cos(br) )^{(-3)}·( < d_{t}[x·cos(bx)],d_{t}[y·cos(by)],d_{t}[z·cos(bz)] >/r )

b = ( (2pi)/r )

Principi: [ d'ona de volum sinosoidal ]

E(x,y,z) = qk·(1/r^{2})·...

... ( sin(br) )^{(-3)}·( < x·sin(bx),y·sin(by),z·sin(bz) >/r )

B(x,y,z) = (-1)·qk·(1/r^{2})·...

... ( sin(br) )^{(-3)}·( < d_{t}[x·sin(bx)],d_{t}[y·sin(by)],d_{t}[z·sin(bz)] >/r )

b = ( pi/(2r) )

Ecuacións de variables estocástiques.

Teorema:

0 [< x [< oo

f(x) = (1/2)·e^{(1/2)·(-x)}

0 [< y [< oo

g(y) = (1/2)·e^{(1/2)·(-y)}

z = x+y

x = (z/2) & y = (z/2)

h(z) = p·(1/4)·e^{(1/4)·(-z)}·e^{(1/4)·(-z)} = (1/2)·e^{(1/2)·(-z)} & p = 2

Teorema:

0 [< x [< oo

f(x) = (1/3)·e^{(1/3)·(-x)}

0 [< y [< oo

g(y) = (2/3)·e^{(2/3)·(-y)}

z = x+y

x = (z/2) & y = (z/2)

h(z) = p·(2/9)·e^{(1/6)·(-z)}·e^{(2/6)·(-z)} = (1/2)·e^{(1/2)·(-z)} & p = (9/4)

Teorema:

( cos(x) )^{2}+( sin(x) )^{2} = 1

Demostració:

a^{2}+b^{2} = h^{2}

(a/h)^{2}+(b/h)^{2} = (h/h)^{2} = 1

Teorema:

( 1/sin(x) )^{2}·( 1+cos(x) )·( 1+(-1)·cos(x) ) = 1

( 1/cos(x) )^{2}·( 1+sin(x) )·( 1+(-1)·sin(x) ) = 1

Teorema:

( 1+cos(x) )·( 1+cos(x) )+( sin(x) )^{2} = 2

( 1+sin(x) )·( 1+sin(x) )+( cos(x) )^{2} = 2

Teorema:

( sin(x) )^{2}·( ( 1/(1+cos(x)) )+( 1/(1+(-1)·cos(x)) ) ) = 2

( cos(x) )^{2}·( ( 1/(1+sin(x)) )+( 1/(1+(-1)·sin(x)) ) ) = 2

Teorema:

( sin(x) )^{2}·( 1+( cot(x) )^{2} ) = 1

( cos(x) )^{2}·( 1+( tan(x) )^{2} ) = 1

Teorema:

( cos(x)+sin(x) )^{2}+(-1)·sin(2x) = 1

( cos(x)+(-1)·sin(x) )^{2}+sin(2x) = 1

Teorema:

( 1/( cos(x) )^{2} )·( cos(2x)+( sin(x) )^{2} ) = 1

( 1/( sin(x) )^{2} )·( (-1)·cos(2x)+( cos(x) )^{2} ) = 1

cálcul diferencial y integral

< m,n = f(m) > <==> mx^{n}

< n,m = g(n) > <==> nx^{m}

[Eh][ < n,h(n) > = < n,n > || < m,h(m) > = < m,m > ]

Teoría:

Teorema:

d_{x}[ f(x)+g(x) ] = d_{x}[f(x)]+d_{x}[g(x)]

d_{x}[ s·f(x) ] = s·d_{x}[f(x)]

Teorema:

d_{x}[g( f(x) )] = d_{f(x)}[g( f(x) )]·d_{x}[f(x)]

d_{x}[ ( f(x) )^{n} ] = n·( f(x) )^{n+(-1)}·d_{x}[f(x)]

d_{x}[ ln(f(x)) ] = (1/f(x))·d_{x}[f(x)]

Teorema:

d_{x}[ f_{1}(x) [o(x)o] ...(n)... [o(x)o] f_{n}(x) ] = ...

... d_{x}[f_{1}(x)]·...(n)...·d_{x}[f_{n}(x)]

Problemes:

Teorema:

d_{x}[ ( 2x^{2}+1 )^{n} ] = ...

... 4n·( 2x^{2}+1 )^{n+(-1)}·x

int[ ( 2x^{2}+1 )^{n} ]d[x] = ...

... ( 1/(n+1) )·( 2x^{2}+1 )^{n+1} [o(x)o] ln(4x) [o(x)o] (1/4)·x

Teorema:

d_{x}[ ( x^{3}+3x+2 )^{n} ] = ...

... 3n·( x^{3}+3x+2 )^{n+(-1)}·(x^{2}+1)

int[ ( x^{3}+3x+2 )^{n} ]d[x] = ...

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

... ln(3x^{2}+3) [o(x)o] ln(6x) [o(x)o] (1/6)·x

Teorema:

d_{x}[ ( 2x^{3}+3x^{2}+1 )^{n} ] = ...

... 6n·( 2x^{3}+3x^{2}+1 )^{n+(-1)}·(x^{2}+x)

int[ ( 2x^{3}+3x^{2}+1 )^{n} ]d[x] = ...

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

... ln(6x^{2}+6x) [o(x)o] ln(12x+6) [o(x)o] (1/12)·x

Teoría:

Teorema:

d_{x}[ f(x)·g(x) ] = d_{x}[f(x)]·g(x)+f(x)·d_{x}[g(x)]

Teorema: [ fonamental del producte integral ]

d_{x}[ G( f(x) ) [o(x)o] H( f(x) ) ] = d_{f(x)}[ G( f(x) ) ]·d_{f(x)}[ H( f(x) ) ]·d_{x}[f(x)]

Problemes

Teorema:

d_{x}[ ( xe^{x}+c )^{n} ] = ...

... n·( xe^{x}+c )^{n+(-1)}·( e^{x}+xe^{x} )

int[ ( xe^{x}+c )^{n} ]d[x] = ...

... ( 1/(n+1) )·( xe^{x}+c )^{n+1} [o(x)o] (-1)·e^{(-x)} [o(x)o] ln(1+x)

Teorema:

d_{x}[ ( xe^{(-x)}+c )^{n} ] = ...

... n·( xe^{(-x)}+c )^{n+(-1)}·( e^{(-x)}+(-x)·e^{(-x)} )

int[ ( xe^{(-x)}+c )^{n} ]d[x] = ...

... ( 1/(n+1) )·( xe^{(-x)}+c )^{n+1} [o(x)o] e^{x} [o(x)o] (-1)·ln(1+(-x))

Teorema:

d_{x}[ ( x^{2}·e^{x}+c )^{n} ] = ...

... n·( x^{2}·e^{x}+c )^{n+(-1)}·( 2x·e^{x}+x^{2}·e^{x} )

int[ ( x^{2}·e^{x}+c )^{n} ]d[x] = ...

... ( 1/(n+1) )·( x^{2}·e^{x}+c )^{n+1} [o(x)o] (-1)·e^{(-x)} [o(x)o] ln(x) [o(x)o] ln(2+x)

Teorema:

d_{x}[ ( x^{2}·e^{(-x)}+c )^{n} ] = ...

... n·( x^{2}·e^{(-x)}+c )^{n+(-1)}·( 2x·e^{(-x)}+(-1)·x^{2}·e^{(-x)} )

int[ ( x^{2}·e^{(-x)}+c )^{n} ]d[x] = ...

... ( 1/(n+1) )·( x^{2}·e^{(-x)}+c )^{n+1} [o(x)o] e^{x} [o(x)o] ln(x) [o(x)o] (-1)·ln(2+(-x))

Teorema:

d_{x}[ ( x^{p}·e^{x}+c )^{n} ] = ...

... n·( x^{p}·e^{x}+c )^{n+(-1)}·( px^{p+(-1)}·e^{x}+x^{p}·e^{x} )

int[ ( x^{p}·e^{x}+c )^{n} ]d[x] = ...

... ( 1/(n+1) )·( x^{p}·e^{x}+c )^{n+1} [o(x)o] ...

... (-1)·e^{(-x)} [o(x)o] ( 1/((-p)+2) )·x^{(-p)+2} [o(x)o] ln(p+x)

Teorema:

d_{x}[ ( x^{p}·e^{(-x)}+c )^{n} ] = ...

... n·( x^{p}·e^{(-x)}+c )^{n+(-1)}·( px^{p+(-1)}·e^{(-x)}+(-1)·x^{p}·e^{(-x)} )

int[ ( x^{p}·e^{(-x)}+c )^{n} ]d[x] = ...

... ( 1/(n+1) )·( x^{p}·e^{(-x)}+c )^{n+1} [o(x)o] ...

... e^{x} [o(x)o] ( 1/((-p)+2) )·x^{(-p)+2} [o(x)o] (-1)·ln(p+(-x))

Teorema:

sin(2x) = 2·sin(x)·cos(x)

cos(2x) = ( cos(x) )^{2}+(-1)·( sin(x) )^{2}

Teorema:

d_{x}[ ( sin(x)·e^{x} )^{n} ] = ...

... n·( sin(x)·e^{x} )^{n+(-1)}·( cos(x)·e^{x}+sin(x)·e^{x} )

int[ ( sin(x)·e^{x} )^{n} ]d[x] = ...

... ( 1/(n+1) )·( sin(x)·e^{x} )^{n+1} [o(x)o] ln( sin(x)·e^{x} ) [o(x)o] ...

... ( ln(cos(x))+x ) [o(x)o] (-1)·(1/4)·ln(cos(2x))

Teorema:

d_{x}[ ( cos(x)·e^{x} )^{n} ] = ...

... n·( cos(x)·e^{x} )^{n+(-1)}·( (-1)·sin(x)·e^{x}+cos(x)·e^{x} )

int[ ( cos(x)·e^{x} )^{n} ]d[x] = ...

... ( 1/(n+1) )·( cos(x)·e^{x} )^{n+1} [o(x)o] ln( cos(x)·e^{x} ) [o(x)o] ...

... ( ln(sin(x))+x ) [o(x)o] (-1)·(1/4)·ln(cos(2x))

Teorema:

d_{x}[ ( sin(x)·e^{(-x)} )^{n} ] = ...

... n·( sin(x)·e^{(-x)} )^{n+(-1)}·( cos(x)·e^{(-x)}+(-1)·sin(x)·e^{(-x)} )

int[ ( sin(x)·e^{(-x)} )^{n} ]d[x] = ...

... ( 1/(n+1) )·( sin(x)·e^{(-x)} )^{n+1} [o(x)o] ln( sin(x)·e^{(-x)} ) [o(x)o] ...

... ( ln(cos(x))+(-x) ) [o(x)o] (1/4)·ln(cos(2x))

Teorema:

d_{x}[ ( cos(x)·e^{(-x)} )^{n} ] = ...

... n·( cos(x)·e^{(-x)} )^{n+(-1)}·( (-1)·sin(x)·e^{(-x)}+(-1)·cos(x)·e^{(-x)} )

int[ ( cos(x)·e^{(-x)} )^{n} ]d[x] = ...

... ( 1/(n+1) )·( cos(x)·e^{(-x)} )^{n+1} [o(x)o] ln( cos(x)·e^{(-x)} ) [o(x)o] ...

... ( ln(sin(x))+(-x) ) [o(x)o] (1/4)·ln(cos(2x))

Teorema:

d_{x}[ ( sinh(x)·e^{x} )^{n} ] = ...

... n·( sinh(x)·e^{x} )^{n+(-1)}·( cosh(x)·e^{x}+sinh(x)·e^{x} )

int[ ( sinh(x)·e^{x} )^{n} ]d[x] = ...

... ( 1/(n+1) )·( sinh(x)·e^{x} )^{n+1} [o(x)o] ln( sinh(x)·e^{x} ) [o(x)o] ...

... ( (-1)·ln(cosh(x))+x ) [o(x)o] (1/2)·( sinh(x) )^{2}

Teorema:

d_{x}[ ( cosh(x)·e^{x} )^{n} ] = ...

... n·( cosh(x)·e^{x} )^{n+(-1)}·( sinh(x)·e^{x}+cosh(x)·e^{x} )

int[ ( cosh(x)·e^{x} )^{n} ]d[x] = ...

... ( 1/(n+1) )·( cosh(x)·e^{x} )^{n+1} [o(x)o] ln( cosh(x)·e^{x} ) [o(x)o] ...

... ( (-1)·ln(sinh(x))+x ) [o(x)o] (-1)·(1/2)·( cosh(x) )^{2}

Teorema:

d_{x}[ ( sinh(x)·e^{(-x)} )^{n} ] = ...

... n·( sinh(x)·e^{(-x)} )^{n+(-1)}·( cosh(x)·e^{(-x)}+(-1)·sinh(x)·e^{(-x)} )

int[ ( sinh(x)·e^{(-x)} )^{n} ]d[x] = ...

... ( 1/(n+1) )·( sinh(x)·e^{(-x)} )^{n+1} [o(x)o] ln( sinh(x)·e^{(-x)} ) [o(x)o] ...

... ( ln(cosh(x))+x ) [o(x)o] (1/2)·( sinh(x) )^{2}

Teorema:

d_{x}[ ( cosh(x)·e^{(-x)} )^{n} ] = ...

... n·( cosh(x)·e^{(-x)} )^{n+(-1)}·( sinh(x)·e^{(-x)}+(-1)·cosh(x)·e^{(-x)} )

int[ ( cosh(x)·e^{(-x)} )^{n} ]d[x] = ...

... ( 1/(n+1) )·( cosh(x)·e^{(-x)} )^{n+1} [o(x)o] ln( cosh(x)·e^{(-x)} ) [o(x)o] ...

... ( ln(sinh(x))+x ) [o(x)o] (-1)·(1/2)·( cosh(x) )^{2}

Si me hubiese inventado la radiación estaría muerto del Xeplion,

era real la radiación y estoy vivo.

No se puede inventar ninguien una enfermedad psiquiátrica,

porque la medicación lo mata.

Esto solo tiene sentido para fieles,

que no son pecadores:

Se tiene que andar y llegar al Nirvana,

porque se tiene que renovar un centro de los pares de centros.

Solo se puede vivir dos veces sin renovar,

gastando el máximo de energía disponible.

fachere

fectered

feintered

dechire

dictered

dientered

yo havere-po dictered la veritatsone.

yo havere-po dictered la veritatsorum.

yo havere-po-mitzli dictered-sam la veritatsokitx.

yo havere-proika dictered-prom la veritatsoki.

Italiano-latín:

-one [o] -orum

Euskera-Bascotzok:

-koak [o] -koaikek

-una-tat-koashek [o] -orum-tat-koashek

-utna [o] -oprum

No nos podemos saltar el derecho internacional constitucional,

y sabemos que hay condenación si te saltas la ley,

y lo sabéis de la Meloni y de Puigdemont.

Si la verdad,

vos hace libres,

libres seréis,

porque hace cumplir la ley,

y se puede salir de cualquier imperio.

Si la falsedad,

no vos hace libres,

no libres seréis,

porque no hace cumplir la ley,

y no se puede salir de cualquier imperio.

I havere-kate-maruto drinket-yuto-yamed smash-muto that yu-maruto.

I havere-kate-maruto drinket-yuto-yamed smensh-muto that yu-maruto.

I havere-kate-tai-tai drinket-yung-yangued smash-tai-mung that yu-tai-tai.

I havere-kate-tai-tai drinket-yung-yangued smensh-tai-mung that yu-tai-tai.

Don Corleone sere-po matxe poderoso que la Meloni.

La Meloni sere-po ménotxe poderosa que Don Corleone.

Don Corleone vatchnare-po por amonto de la Meloni.

La Meloni vatchnare-po por avallo de Don Corleone.

Don Corleone estare-po adalto de la Meloni.

La Meloni estare-po abaisho de Don Corleone.

Don Corleone sere-po molto poderoso comparato con la Meloni.

La Meloni sere-po poca poderosa comparata con Don Corleone.

El mundo es consistente,

ninguien se salta el buey del prójimo,

y se sigue el derecho internacional constitucional.

Todos siguen el ama al próximo como a ti mismo.

Distribucions continues:

1 [< x [< oo

F(x) = (4/pi)·int[ ( 1/(1+x^{2}) ) ]d[x]

G(x) = int[ ( 1/x^{2} ) ]d[x]

Esperança[x·f(x)] = (2/pi)·ln(1+x^{2})

Esperança[x·g(x)] = ln(x)

Distribucions del Hamiltonià de Heisenberg.

(-oo) [< x [< oo

ihc·d_{x}[f(x)] = pqgx·(1/pi)·( 1/(1+(ax)^{2}) )·f(x)

f(x) = e^{( 1/(ihc) )·pqg·(1/a)^{2}·(1/(2pi))·( arc-tan(ax) [o(ax)o] (1/2)·(ax)^{2} )}

(-oo) [< x [< oo

ihc·d_{x}[f(x)] = (-k)·(1/2)·x^{2}·(1/pi)·( 1/(1+(ax)^{2}) )·f(x)

f(x) = e^{( 1/(ihc) )·(-k)·(1/2)·(1/a)^{3}·(1/(4pi))·( arc-tan(ax) [o(ax)o] (1/3)·(ax)^{3} )}

Distribucions del Hamiltonià de Srôdinguer

0 [< t [< oo

ih·d_{t}[f(t)] = (1/m)·(pqg)^{2}·(1/2)·t^{2}·...

... (4/pi)·( 1/(1+( ( a·( (pqg)/(2m) ) )^{(1/2)}·t )^{2}) )·f(t)

f(t) = e^{( 1/(ih) )·(1/a)·(pqg)·( (1/a)·( (2m)/(pqg) ) )^{(1/2)}·(1/(4pi))·...

... ( ...

... arc-tan( ( a·( (pqg)/(2m) ) )^{(1/2)}·t ) [o( ( a·( (pqg)/(2m) ) )^{(1/2)}·t )o] ...

... (1/3)·( ( a·( (pqg)/(2m) ) )^{(1/2)}·t )^{3} ...

... )}

0 [< t [< oo

ih·d_{t}[f(t)] = (1/2)·(-k)·( x_{0}e^{(k/m)^{(1/2)}(-i)·t} )^{2}·...

... (-1)·( 1/ln(1+ax_{0}) )·...

... ( ax_{0}e^{(k/m)^{(1/2)}(-i)·t}/( 1+ax_{0}e^{(k/m)^{(1/2)}(-i)·t} ) )·f(t)

f(t) = e^{( 1/(ih) )·(1/2)·(-k)·(m/k)^{(1/2)}·(1/i)·...

... ( ...

... (1/ln(1+ax_{0}))·( ln(1+ax_{0}e^{(k/m)^{(1/2)}(-i)·t}) [o( (k/m)^{(1/2)}·(-i)·t )o] ...

... (1/2)·( x_{0}·e^{(k/m)^{(1/2)}(-i)·t} )} )^{2} ...

... )}

Respiración = [16e]:

Pulmonía o corona-virus:

Error en la destrucción del agua.

2·( 4·H_{2}O <==> 4·H_{2}+O_{4} )

[4·H_{2}O]·[4e] <==> [4·H_{2}]·[O_{4}]

Bronquitis de pulmón:

Error en la construcción del carburo-metano.

C_{4}+8·H_{2} <==> 4·CH_{4}

[C_{4}]·[8·H_{2}] <==> [8e]·[4·CH_{4}]

Hidróxido de carbono:

4·( CH_{4}+O_{4} <==> C(OH)_{4} )

[CH_{4}]·[O_{4}] <==> [4e]·[C(OH)_{4}]

Teorema:

x^{n+1}+(-1) = (x+(-1))·(1+x+...+x^{n})

Teorema:

lim[x = 1][ ( (x^{n}+(-1))/(x^{m}+(-1)) ) ] = (n/m)

lim[x = 1][ ( 1/(x+(-1)) )·( sum[k = 1]-[n][ x^{k} ]+(-n) ) ] = ...

... (1/2)·( n(n+1) )

lim[x = 1][ ( 1/(x+(-1))^{2} )·( sum[k = 1]-[n][ x^{2k}+(-2)·x^{k} ]+n ) ] = ...

... (1/6)·( n(n+1)(2n+1) )

lim[x = 1][ ( 1/(x+(-1))^{n} )·( prod[k = 1]-[n][ ( x^{k}+(-1) ) ] ) ] = n!

Teorema:

a_{n} és convergent <==> a_{n} és de Cauchy.

Demostració:

[==>]

Sigui s > 0 ==>

Sigui u = (s/2) & v = (s/2) ==>

Es defienish k_{0} > max{n_{0},m_{0}} ==>

|a_{n}+(-1)·a_{m}| [< |a_{n}+(-l)|+|a_{m}+(-l)| < u+v = s

[<==]

Sigui s > 0 ==>

Es defienish n_{0} > k_{0} ==>

|a_{n}+(-1)·a_{m}| < s

a_{n} = a_{m}

|i(a_{n}+(-1)·a_{m})| = (-0)

|a_{n}+(-l)| [< |a_{n}+(-1)·a_{m}|+|a_{m}+(-l)|

(|1|+|i|)·|a_{n}+(-l)| [< (|1|+|i|)·|a_{n}+(-1)·a_{m}| < (|1|+|i|)·s

|a_{n}+(-l)| < s

350 Italia en Cygnus-Kepler:

150 Córcega-y-Sardeña-y-Sicilia:

Latín con u. -urum.

100 Estatereds-Pontificatereds-y-Nápoles:

Latín con o. -orum

100 Génova-Calabria:

Italiano.

350 Reino Stowed en Cygnus-Kepler:

75 Welsh-y-Cornikland:

Stowed Gaelical British

100 Ireland:

Stowed Gaelical Irish

75 Scotland:

Stowed Scotish

100 England:

Stowed English

550 Asamblea Nacional

350 Reino Stehed en Cygnus-Kepler:

75 Bretaña:

Stehed Gaelical Irish

100 Normandia:

Stehed Gaelical British

75 Bélgica:

Stehed English

100 Holanda:

Stehed Scotish

200 Francia en Cygnus-Kepler:

100 Occitania:

Occità

100 Estatu-dom Françé:

Françé de le Patuá

350 España en Cygnus-Kepler:

105 Cáteldor:

Català:

80 Euskal-Herria:

Euskera-Bascotzok

20 Astur-Cantabria:

Euskera-Bascotzok Cantabri-koashek

105 Castilla-Madrid:

Castellano

20 Galicia:

Gallego

20 Andalucía:

Andaluz

100 Portugal en Cygnus-Kepler:

50 Oporto:

Portugueshe-y

50 Coimbra:

Portuguehe-y

200 Yugoslavia en Cygnus-Kepler

100 Croacia:

Serbio-croata con u

100 Serbia:

Serbio-croata con o

300 Troika-Yugoslavia en Cygnus-Kepler:

100 Grecia:

Greco-Romano con o

100 Bulgaria

Greco-Romano con u

100 Rumania

Rumano

Las administraciones de estos países:

Tienen que pagar pensiones a infieles,

porque están apuntados en el paro,

y pueden robar al gobierno.

No tienen que pagar pensiones a fieles,

porque no están apuntados en el paro,

y no pueden robar al gobierno.

Adjudicar proyectos de construcción.

Adjudicar proyectos de destrucción.

Cobrar el impuesto de contribución-patrimonio,

de alquiler al gobierno de casa vacía.

f(n) = (n!·n)€

Cobrar el impuesto de contribución-patrimonio,

de alquiler al gobierno de casa ocupada.

g(n,k) = ( (n+(-k))!·(n+(-k)) )€

Cobrar el impuesto socialista de la utilidad del agua.

Cobrar el impuesto social-demócrata de la utilidad del agua.

h = ( (n+m)/k )

Cobrar el impuesto socialista de la utilidad del taxi.

Cobrar el impuesto social-demócrata de la utilidad del taxi.

h = ( (n+(-m))/k )

Ecuaciones de núcleos integrales estocásticos:

Si ( F(x) = int[f(x)]d[x] = 1 & G(y) = int[g(y)]d[y] = 1 ) ==>

P(x) = p·int[ H(x)·f(x)·g(y) ]d[x] = 1 & y = u(x)

Q(y) = q·int[ J(y)·f(x)·g(y) ]d[y] = 1 & x = v(y)

Teorema:

0 [< x [< oo

f(x) = e^{(-x)}

0 [< y [< oo

f(y) = e^{(-y)}

y = x^{2}+a

y = (-x)

x^{2}+x+a = 0 [< x [< oo

f(x) = (2x+1)·e^{(-1)·( x^{2}+x+a )}

x = ( y+(-a) )^{(1/2)}

y = (-x)

y+( y+(-a) )^{(1/2)} = 0 [< y [< oo

f(y) = ( 1+(1/2)·( y+(-a) )^{(-1)·(1/2)} )·e^{(-1)·( y+( y+(-a) )^{(1/2)} )}

Lema:

2n+1 [< e^{n}

2n+3 [< e^{n}+e^{n} = 2e^{n} [< e^{n+1}

Teorema:

1 [< x [< oo

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

1 [< y [< oo

f(y) = (1/y^{2})

y = x^{2}+a

x^{2}+a = e [< x [< e^{oo}

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

x^{2} = ( y+(-a) )

y+(-a) = e [< y [< e^{oo}

f(y) = (e+a)·( 1/(y+(-a)) )·( 1/y^{2} )

Doctorats de stroniken

Guifré del Bergadà:

Doctorat en análisis matemátic.

Capítol I:

Teorema:

[Ek][ k >] 2 & cos((1/pi)·i) [< ( k/(k+(-1)) ) ]

[Ek][ k >] 2 & sin((1/pi)·i) [< ( i/(k+(-1)) ) ]

Desmostració:

Destrocter ponens:

[Ap][ (1/(2p)!)·(1/pi)^{2p} > 1 ]

Destrocter ponens:

[Ap][ (1/(2p+1)!)·(1/pi)^{2p+1} > (1/k) ]

Teorema:

[Ek][ k >] 2 & cosh(1/pi) [< ( k/(k+(-1)) ) ]

[Ek][ k >] 2 & sinh(1/pi) [< ( 1/(k+(-1)) ) ]

Teorema:

(1/3) [< e^{(-1)·(1/pi)} [< 1

1 [< e^{(1/pi)} [< 3

Teorema:

( sin(x) & cos(x) ) convergeish la serie a [0i,i]_{C}

( sinh(x) & cosh(x) ) convergeish la serie a [0,1]_{C}

Capítol II:

Teorema:

[Ek][ k >] 2 & cos((1/pi)·i) >] ( k/(k+1) ) ]

[Ek][ k >] 2 & sin((1/pi)·i) >] ( i/(k+1) ) ]

Desmostració:

Destrocter ponens:

[Ap][ (1/(2p)!)·(1/pi)^{2p} < (1/(2p)!)·(1/pi)^{2p}( (-1)·(1/k) )^{p} ]

[Ap][ (1/(2p)!)·(1/pi)^{2p}·( (-1)·(1/k) )^{p} < ( (-1)·(1/k) )^{p} ]

Destrocter ponens:

[Ap][ (1/(2p+1)!)·(1/pi)^{2p+1} < (1/(2p+1)!)·(1/pi)^{2p+1}·(1/k)·( (-1)·(1/k) )^{p} ]

[Ap][ (1/(2p+1)!)·(1/pi)^{2p+1}·(1/k)·( (-1)·(1/k) )^{p} < (1/k)·( (-1)·(1/k) )^{p} ]

Teorema:

[Ek][ k >] 2 & cosh(1/pi) >] ( k/(k+1) ) ]

[Ek][ k >] 2 & sinh(1/pi) >] ( 1/(k+1) ) ]

Teorema:

(1/3) [< e^{(-1)·(1/pi)} [< 1

1 [< e^{(1/pi)} [< 3

Teorema:

( sin(x) & cos(x) ) convergeish la serie a [0i,i]_{C}

( sinh(x) & cosh(x) ) convergeish la serie a [0,1]_{C}

Hugo de Portugal:

Doctorat en lógica algebraica.

[p(x)] = Binari concret.

]q(x)[ = Borrós semblant-abstracte.

Teorema:

min{[p(x)],]q(x)[} = [p(x)] <==> max{[p(x)],]q(x)[} = ]q(x)[

max{¬[p(x)],¬]q(x)[} = ¬[p(x)] <==> min{¬[p(x)],¬]q(x)[} = ¬]q(x)[

Teorema:

min{[f(1)],]f(n)[} = [f(1)] <==> max{[f(1)],]f(n)[} = ]f(n)[

max{[f(-1)],]f(-n)[} = [f(-1)] <==> min{[f(-1)],]f(-n)[} = ]f(-n)[

Don Casasayas de Euskal-Herria:

Doctorat en análisis matemátic.

Capítol I:

Teorema:

Si a [< b ==> [Au][Eq][En][ a [< q+(u/n) [< b ]

Demostració:

a [< ( (a+(-u))+(b+u) )/2 [< b

q = ( (a+(-u)+b)/2 ) & n = 2

Teorema:

Si a [< b ==> [Au][Av][Eq][En][Em][ a [< q+(u/n)+(v/m) [< b ]

Demostració:

a [< ( (5a+(-5)·u+(-2)·v)+(5b+5u+2v) )/10 [< b

q = ( (5a+(-5)·u+(-2)·v+5b)/10 ) & n = 2 & m = 5

Teorema:

[Ax][Ea_{n}][Eb_{n}][ a_{n} [< x [< b_{n} ...

... & [Eq][ b_{n}+(-1)·a_{n} = q ] & lim[a_{n}] = lim[b_{n}] = x ]

Demostració:

a_{n} = x+(-1)·(1/n)

b_{n} = x+(1/n)

q = (2/n)

Teorema:

[Ax][Ay][Ea_{n}][Eb_{n}][ x [< a_{n}+b_{n} [< y...

... & [Eq][ b_{n}+(-1)·a_{n} = q ] & lim[a_{n}] = lim[b_{n}] ]

Demostració:

a_{n} = ( (x+y)/4 )+(-1)·(1/n)

b_{n} = ( (x+y)/4 )+(1/n)

q = (2/n)

Capítol II:

Teorema:

max{x,y} = ( ( (x+y)+|y+(-x)| )/2 )

min{x,y} = ( ( (x+y)+|i(y+(-x))| )/2 )

Demostració:

x [< y <==> 0 [< y+(-x)

x >] y <==> 0 >] y+(-x)

Teorema:

x^{2} = ( ( x+|x| )/2 )^{2}+( ( x+(-1)·|x| )/2 )^{2}

x^{2} = ( ( x+|ix| )/2 )^{2}+( ( x+(-1)·|ix| )/2 )^{2}

Teorema:

|x_{1}+...+x_{n}| [< |x_{1}|+...+|x_{n}|

|i(x_{1}+...+x_{n})| >] |ix_{1}|+...+|ix_{n}|

Pla d'estudis de la universitat de Stroniken:

Nota de tall = 7.50

1r semestre:

Guifré del Bergadà:

Análisis matemátic I

Análisis matemátic III

Don Casasayas:

Álgebra

Probabilitats

Hugo de Portugal:

Lógica

Topología

Jûan Garriga:

Informática

Especies combinatories

2n semestre:

Guifré del Bergadà:

Análisis matemátic II

Análisis matemátic IV

Don Casasayas:

Ecuacions Diferencials

Análisis Complex y Borrós

Hugo de Portugal:

Teoria de conjunts

Lógica algebraica y Dualogía

Jûan Garriga:

Álgebra lineal y geometría lineal

Geometría Diferencial

Hidrogen verd:

Aigua:

4·H_{2}+O_{4} <==> 4·H_{2}O

[4·H_{2}]·[O_{4}] <==> [4e]·[4·H_{2}O]

Aigua oxigenada:

2·H_{2}+O_{6} <==> 2·H_{2}O_{3}

[2·H_{2}]·[O_{6}] <==> [2e]·[2·H_{2}O_{3}]

Oxigen:

2·O_{4}+O_{4} <==> 2·O_{6}

[2·O_{4}]·[O_{4}] <==> [2e]·[2·O_{6}]

Ley que no es del mundo:

Si no es tu dinero:

Si enseñas el DNI en el banco robas.

Si no enseñas el DNI en el banco no robas.

Si es tu dinero:

Si enseñas el DNI en el banco no te roban.

Si no enseñas el DNI en el banco te roban.

menjar [o] menjjar [o] menjjate [o] menjjet-kazhe

pujar [o] pujjar [o] pujjate [o] pujjet-kazhe

bajar [o] baishar [o] bashate  [o] bashet-kazhe

dejar [o] deishar [o] deshate  [o] deshet-kazhe

yo havere-po encontratered una miravilem demostraciorum,

apud en el marginis non sere-po capered la demostraciorum.

A + B = A [ || ] B & ¬A + ¬B = ¬A [&] ¬B

A = < {a_{1},...(n)...,a_{n}},{a_{1}} > & S[A] = (n+1)·x^{n}

¬A = < }a_{1},...(n)...,a_{n}{,}a_{1}{ > & S[A] = ((-n)+(-1))·x^{n}

A = {a_{1},...(n)...,a_{n}} [&] {a_{1},...,a_{k}} & S[A] = kx^{k}

¬A = }a_{1},...(n)...,a_{n}{ [&] }a_{1},...,a_{k}{ & S[A] = (-k)·x^{k}

A = }a_{1},...(n)...,a_{n}{ [ \ ] }a_{1},...,a_{k}{  & S[A] = ((-n)+k)·x^{k}

¬A = {a_{1},...(n)...,a_{n}} [ \ ] {a_{1},...,a_{k}}  & S[A] = (n+(-k))·x^{k}

Teoría de ingeniería y de economía:

Definició:

[ n // k ]+[ n // (k+1) ] = [ (n+1) // (k+1) ]

sum[k = 0]-[n][ [ n // k ] ] = 2^{n}

[ (-n) // k ]+[ (-n) // (k+1) ] = [ ((-n)+1) // (k+1) ]

sum[k = 0]-[n][ [ (-n) // k ] ] = 2^{(-n)}

Teorema:

[ (-2) // 0 ] = 1 & [ (-2) // 1 ] = (-2) & [ (-2) // 2 ] = (5/4)

[ (-3) // 0 ] = 1 & [ (-3) // 1 ] = (-3) & [ (-3) // 2 ] = (17/4) & [ (-3) // 3 ] = (-1)·(17/8)

Si k >] 2 ==> [ (-n) // k ] = (-1)^{k}·( F(n,k)/2^{k} )

Binomis:

Teorema:

(x+x)^{n} = sum[k = 0]-[n][ [ n // k ]·x^{n+(-k)}·x^{k} ]

Teorema:

(x+x)^{(-n)} = sum[k = 0]-[n][ [ (-n) // k ]·x^{(-n)+(-k)}·x^{k} ]

Teorema:

lim[h = 0][ (x+h)^{n} ] = ...

... lim[h = 0][ sum[k = 0]-[n][ [ n // k ]·x^{n+(-k)}·h^{k} ] ] = x^{n}

Teorema:

lim[h = 0][ (x+h)^{(-n)} ] = ...

... lim[h = 0][ sum[k = 0]-[n][ [ (-n) // k ]·x^{(-n)+(-k)}·h^{k} ] ] = x^{(-n)}

Demostració:

[ (-n) // k ]·x^{(-n)+(-k)}·h^{k}·(x+h) = ...

... [ (-n) // k ]·x^{(-n)+1+(-1)·(k+1)}·h^{k+1}+[ (-n) // p ]·x^{(-n)+1+(-p)}·h^{p}

Distribucions:

f(k) = [ n // k ]·2^{(-n)}

g(k) = [ (-n) // k ]·2^{n}

E[k·f(k)] = (n/2)

E[k·g(k)] = (-n)+sum[k = 2]-[n][ (-1)^{k}·k·( F(n,k)/2^{k} ) ]

H(n) = sum[k = 1]-[n][ (1/k)·[ (n+(-1)) // (k+(-1)) ] ] = (1/n)·2^{n}

Derivada:

d_{x}[x^{n}] = lim[h = 0][ ( ( (x+h)^{n}+(-1)·x^{n} )/h ) ] = nx^{n+(-1)}

Integral:

int[x^{n}]d[x] = ( 1/(n+1) )·lim[h = 0][ int[ (x+h)^{n}·(x+h)+(-1)·x^{n}·x ] ] = ...

... ( 1/(n+1) )·int[ d[x^{n+1}] ] = ( 1/(n+1) )·x^{n+1}

int[x^{n}]d[x] = ( 1/(n+1) )·int[ (n+1)·x^{n} ]d[x]

Derivada:

d_{x}[x^{(-n)}] = lim[h = 0][ ( ( (x+h)^{(-n)}+(-1)·x^{(-n)} )/h ) ] = (-n)·x^{(-n)+(-1)}

Integral:

int[x^{(-n)}]d[x] = ( 1/((-n)+1) )·lim[h = 0][ int[ (x+h)^{(-n)}·(x+h)+(-1)·x^{(-n)}·x ] ] = ...

... ( 1/((-n)+1) )·int[ d[x^{(-n)+1}] ] = ( 1/((-n)+1) )·x^{(-n)+1}

int[x^{(-n)}]d[x] = ( 1/((-n)+1) )·int[ ((-n)+1)·x^{(-n)} ]d[x]

Derivada:

d_{x}[e^{x}] = lim[h = 0][ ( ( e^{x+h}+(-1)·e^{x} )/h ) ] = e^{x}

Integral:

int[e^{x}]d[x] = lim[h = 0][ int[ e^{x+h}·(x+h)+(-1)·e^{x}·x ] ] = ...

... lim[h = 0][ int[ e^{x}·(x+h)+(-1)·e^{x}·x ] ] = ...

... int[ e^{x} ]d[x] = int[ d_{x}[e^{x}] ]d[x] = e^{x}

Derivada:

d_{x}[ln(x)] = lim[h = 0][ ( ( ln(x+h)+(-1)·ln(x) )/h ) ] = (1/x)

Integral:

int[ (1/x) ]d[x] = lim[h = 0][ int[ ( 1/(x+h) )·(x+h)+(-1)·(1/x)·x ] ] = ...

... lim[h = 0][ int[ (1/x)·(x+h)+(-1)·(1/x)·x ] ] = ...

... int[ (1/x) ]d[x] = int[ d_{x}[ln(x)] ]d[x] = ln(x)

economia

n = habitaciones

m = lavabos

k = precio del agua

h = Impuesto del agua

F(x,y) = nx+my+(-h)·10·( px+qy+(-k) )

F(1,1) = n+m

G(x,y) = nx+my+(-h)·10·( px+qy )

G(1,1) = 0

h = ( (n+m)/(10k) )

( n = 1 & m = 1 )

k = ( 2.20+0.30 )

h = (2/25) = 0.04€

( n = 2 & m = 1 )

k = ( 2.20+0.30 )

h = (3/25) = 0.12€

( n = 3 & m = 1 )

k = ( 2.20+0.30 )

h = (4/25) = 0.16€

( n = 4 & m = 1 )

k = ( 2.20+0.30 )

h = (1/5) = 0.20€

( n = 4 & m = 2 )

k = ( 2.20+0.30 )

h = (6/25) = 0.24€

( n = 4 & m = 3 )

k = ( 2.20+0.30 )

h = (7/25) = 0.28€

n = conductor + copilotos

m = viajeros

k = precio de la gasolina

h = impuesto de circulación

F(x,y) = (n+(-1))+(m+(-1))+x^{n}+y^{m}+(-h)·10·( px+qy+(-k) )

F(1,1) = n+m

G(x,y) = (n+(-1))+(m+(-1))+x^{n}+y^{m}+(-h)·10·( px+qy )

G(1,1) = 0

h = ( (n+m)/(10k) )

n = 2

m = 3

k = ( 0.85+0.15 )

h = (1/2) = 0.50€

n = 1

m = 1

k = ( 0.85+0.15 )

h = (1/5) = 0.20€

El taxi y el transportista no pagan impuesto de circulación.

Está completamente loco el que habla en la mente y mira,

lo va a escuchar y mirar el mundo,

y como siga algún mandamiento el mundo lo joderá.

No puede masturbar-se, ni poner la polla en un chocho,

porque van a cometer adulterio con él.

No puede no embozar el váter,

porque se le van a cagar encima.

No puede fumar,

porque le harán un análisis de sangre.

Como no mate teniendo pistola,

el mundo lo matará.

No puede Pixle molestar-se porque le mirase el pene cuando se masturbaba,

porque cometí adulterio mirando,

y el no cometió adulterio masturbando-se.

No puede decir-le al mundo,

que le de o da rabia que le miren el pene,

cuando mirando se comete adulterio.

Decir-le al mundo que no apesta el chocho de Danila es de loco,

honrar al padre y a la madre.

Decir-le al mundo que mi madre no me sigue es de loco,

un infiel cristiano amará al próximo como a él mismo,

Un infiel cristiano siempre sigue al señor,

y va a misa a adorar al señor tu Dios tu Padre.

Escalera de 8 tonos: 2^{(1/8)}

[00+01][00+03][00+05][00+07] = 16k = 2·2·2·2·k

[00+05][00+07][08+01][08+03] = 32k = 2·2·2·2·2·k

[00+05][00+07][08+04][00+07] = 31k

[08+01][08+03][08+08][08+03] = 47k

Capellà home.

Capellana muller.

El senyor estigui amb nosaltres,

nosaltres estiguem amb el senyor.

El senyora estigui amb nosaltres,

nosaltres estiguem amb el senyora.

Lectura del evangeli segons Sant Mateu,

lectura del evangeli segons Sant Matea.

Gràcies Déu, senyor,

gràcies Déa, senyora.

Diáquen home.

Diáquen muller.

En aquell temps el senyor els hi digué:

Dona-li al que et demani,

si feu o fa alguna cosa para tú,

o et dona alguna cosa a canvi.

Treballàs sis dies y al séptim descansaràs.

En aquell temps la senyora els hi digué:

Reb del que t'ofereshi,

si feus o fas alguna cosa para ell,

o li dones alguna cosa a canvi.

Descansaràs sis dies y al séptim treballaràs.

Capellà home:

Capellana muller:

L'evangeli d'avui ens invita a treballar y a vendre,

y ens recorda la importancia de rebre diners.

No té sentit robar la materia, no tenint energía

perque aleshores si es roba aleshores es perd la vida de la materia

si no es té energía perque no es reb la vida de la materia robant.

L'evangeli d'avui ens invita a descansar y a comprar,

y ens recorda la importancia de donar diners.

Té sentit robar la materia, tenint energía

encara que potser aleshores si es roba aleshores es perd la vida de la materia

si no es té energía perque no es reb la vida de la materia robant.

Diáquen home:

Diáquen muller:

Cuant deyuneu,

que és no voler menjar, tenint menjar a l'abast,

vos-perfumeu la boca, bebent begudes energétiques,

para que la gent no se'n anadoni, de que esteu deyunant,

y estigueu contents.

Mentres passeu gana,

que és voler menjar, no tenint menjar a l'abast,

no vos-perfumeu la boca, no bebent begudes energétiques,

para que la gent se'n anadoni, de que esteu passant gana,

y estigueu tristos.

Capellà home:

Capellana nuller:

El evangeli de avui en invita a donar el que sobra.

No té sentit posar-se suero, no havent passat gana,

perque no s'ha de guanyar pes.

El evangeli de avui ens invita a rebre el que falta.

Té sentit posar-se suero, havent passat gana,

perque s'ha de guanyar pes.

Derecho internacional:

Anexión por referéndum del mismo territorio geográfico.

Des-Anexión por referéndum del mismo territorio geográfico.

Derecho internacional constitucional:

No se puede ser prójimo del mismo territorio geográfico.

No se puede ser próximo de diferente territorio geográfico.

En la Tierra cercanías es gratis,

pero aquí en Cygnus-Kepler tan solo no se pagan impuestos.

1 zona 1.10€ de 2.20 = (0.11)·10+1.10 Socialista Bolivariano.

2 zonas 2.20€ de 4.40 = (0.22)·10+2.20 Socialista Bolivariano.

3 zonas 3.30€ de 6.60 = (0.33)·10+3.30 Socialista Bolivariano.

Honré al padre y a la madre en televisión con el Guille,

y me tocó el Rafa la cara con semen,

y al Guille la Elisenda le tiró mierda por la cabeza.

Estos dos son del mundo.

Teorema:

[Ax][ x€R <==> [Ep][Eq][En][Em][ x = (p/q)^{(n/m)} ] ]

Demostración

x€Q <==> [Ek][ n = mk ]

x€I <==> [Ak][ n != mk ]

Teorema:

[Ax][Ak][ ( x€R & k€N ) ==> [Es][ x = k+s ] ]

[Ax][Ak][ ( x€R & k€N ) ==> [Es][ x = (-k)+s ] ]

Demostración

Sea x = (p/q)^{m/n} ==>

Se define s = (p/q)^{m/n}+(-k)

Teorema:

[Ax][Ak][ ( x€R & k€N ) ==> [Es][ x = k·s ] ]

[Ax][Ak][ ( x€R & k€N ) ==> [Es][ x = (1/k)·s ] ]

Teorema:

[Ax][Aa][Ab][ x€R ==> [Es][ x = (a/b)+(s/b) ] ]

[Ax][Aa][Ab][ x€R ==> [Es][ x = (-1)·(a/b)+(s/b) ] ]

Teorema:

#Q = oo

#R = oo^{oo}

Demostración:

0 = (1/oo)

0^{0} = (1/oo)^{(1/oo)}

Teorema:

(2/3) = [0,1,2] = [1,(-3)]

(3/4) = [0,1,3] = [1,(-4)]

Teorema:

( (kn+1)/n ) = [k,n]

( (kn+(-1))/n ) = [k,(-n)]

Teorema:

( (n^{2}+1)/n ) = [n,n]

( (n^{2}+(-1))/n ) = [n,(-n)]

No respeta el derecho internacional constitucional,

el 25% de castellano en las escuelas.

Es próximo de diferente territorio geográfico.

No tiene sentido hablar un idioma de meseta,

en un ortogonal de mar y cordillera montañosa.

No me digáis homosexual que lo dicen por mirar una polla,

y es cometer adulterio mirar, y vos va a violar el mundo.

No tiene sentido ser policía y saltar-se el derecho internacional,

la luz te mata si no vas armado con destructor porque quieres independencia con guerra.

Pero si cierras a un fiel el mundo en algún momento te mirará,

y si vas armado tendrás que vatchnar matando porque sinó el mundo te matará.

Como vas a seguir a un hombre casado con hijos,

y honrar al padre y a la madre en el mundo.

Te conviertes en un basurero de toda substancia.

huir [o] fugir

huigo [o] fugeishû

huyes [o] fugeishes

huye [o] fugeish

oir [o] ogir

oigo [o] ogeshû

oyes [o] ogeishes

oye [o] ogeish

Teorema:

x^{2}+y^{2}+z^{2} >] xy+yz+zx

x^{2}+y^{2}+u^{2}+v^{2} >] (x+y)·(u+v)

Demostración:

( x+(-y) )^{2} >] 0

campo diferencial y campo integral:

< a·d_{x}[ ],b·d_{y}[ ] >o< f(x,y),g(x,y) > =  0

f(x,y) = (x/a)

g(x,y) = (-1)·(y/b)

< a·int[ ]d[x],b·int[ ]d[y] >o< f(x,y),g(x,y) > =  0

f(x,y) = (y/a)

g(x,y) = (-1)·(x/b)

< (1/y)·d_{x}[ ],(1/x)·d_{y}[ ] >o< f(x,y),g(x,y) > =  0

f(x,y) = xy

g(x,y) = (-1)·yx

< (1/x)·int[ ]d[x],(1/y)·int[ ]d[y] >o< f(x,y),g(x,y) > =  0

f(x,y) = 2xy

g(x,y) = (-2)·yx

< e^{(-y)}·d_{x}[ ],e^{(-x)}·d_{y}[ ] >o< f(x,y),g(x,y) > =  0

f(x,y) = xe^{y}

g(x,y) = (-1)·ye^{x}

< (1/x)·e^{(-y)}·int[ ]d[x],(1/y)·e^{(-x)}·int[ ]d[y] >o< f(x,y),g(x,y) > =  0

f(x,y) = e^{y}

g(x,y) = (-1)·e^{x}

4xy+2x^{2}·d_{x}[y] = c

4xy·d[x]d[y]+2x^{2}·d[y]d[y] = c·d[x]d[y]

y(x) = (c/2)·(1/x)

(1/x)·(1/y)+(-1)·ln(x)·(1/y)^{2}·d_{x}[y] = c

y(x) = anti-pow[(-1)]-ln-( (c/2)·(x/ln(x)) )

Arte:

[Ec][Ex][Ey][ (1/x)·(1/y) = (c/2)·(1/ln(x))·(1/ln(y)) ]

c = (2/e^{2})

x = e & y = e

Arte:

[Ex][Ey][ (1/ln(x))·( (ln(1/x)+1)/(ln(1/y)+1) ) = 2+(-1)·(1/ln(x))·(1/ln(y)) ]

x = e & y = e

(1/ln(e))·( (ln(1/e)+1)/(ln(1/e)+1) ) = 2+(-1)·(1/ln(e))·(1/ln(e))

yo me havere-po fumatered un biturbi-sorum.

yo me havere-po fumatered una ele-sorum.

Doctorado del Guifré:

Teorema:

[Ak][ k >] 2 ==> cos(pi·i) >] (-1)·( k/(k+(-1))) ]

Demostración:

cos(pi·i) >] 1+(1/2)·pi^{2}·(1/k)+(1/4!)·pi^{4}·(1/k)^{2}+...

... ( (-1)^{p}/(2p)! )·(pi·i)^{2p}·(1/k)^{p} >] (-1)·( k/(k+(-1)) )

Teorema:

[Ak][ k >] 2 ==> sin(pi·i) >] (-1)·( i/(k+(-1))) ]

Demostración:

sin(pi·i) >] i·pi·(1/k)+i·(1/3!)·pi^{3}·(1/k)^{2}+...

... ( (-1)^{p}/(2p+1)! )·(pi·i)^{2p+1}·(1/k)^{p+1} >] (-1)·(i/k)·( k/(k+(-1)) )

Ruski y Françé-de-le-Patuá

Teorema:

sum[k = 1]-[n][ k ] = (1/2)·n+O(e^{n})

Demostración:

n^{2} [< e^{n}

(n+1)^{2} [< e^{n}+2n+1 [< e^{n+1}

Teorema:

prod[k = 2]-[n][ ( 1+(-1)·(1/k) ) ] = O(1)

prod[k = 2]-[n][ ( k+(-1) ) ] = O(n!)

Demostración:

( (n+(-1))!/n! ) = (1/n)

Teorema:

sum[k = 1]-[n][ ln(k) ] = O(n!)

Demostración:

0 [< ( ln(n!)/n! ) [< (1/2)

hat-rush-telat <==> hat-make

det-rush-telat <==> det-make

narash-kivat <==> constroctetch-tate

rat-rash-kivat <==> destroctetch-tate

puted-bir-mishkat

pusted-bir-mishkat

rat-cot-mush-temat <==> make

rat-sot-mush-temat <==> smanke

rat-smush-temat <==> smoke

rat-tendush-telat <==> tendrake

rat-prondush-telat <==> prendrake

I rat-entendush-telat the guzhenish Ruski,

when not rat-cot-prush-temat the guzhenish people puted-bir-mishkat-me.

I not rat-entendush-telat the guzhenish Ruski,

when rat-cot-prush-temat the guzhenish people puted-bir-mishkat-me.

I intrate-rush-temat to the guzhenish High-Way.

I exited-bir-mishkat from the guzhenish High-Way.

Integral de Lebesgue:

m(ah) = 0 <==> (ah/h) [< 0 <==> int[ f(x) ]d[x] = 0

int[ x^{2} ]d[x] = int[ ( (2x+h)^{2}/4 ) ]·h = ...

... (1/3)·int[ (x^{3}+3x^{2}h+3xh^{2}+h^{3})+(-1)·x^{3} ]+(-1)·(1/12)·h^{3} = ...

... (1/3)·x^{3}

Arte:

[En][ sum[k = 1]-[n][ ( 1/(2k) ) ] = (n/2) ]

Exposición:

n = 1

f(1/(2k)) = (1/2)

Arte:

[En][ sum[k = 1]-[n][ ( 1/(2k+1) ) ] = (n/3) ]

Exposición:

n = 1

f(1/(2k+1)) = (1/3)

d_{x}[y(x)]^{n}·H( d_{x}[y(x)] ) = f(x)

y(x) = int[ anti-pow[(-n)]-H( f(x) ) ]d[x]

d_{x}[y(x)]^{n}·H( d_{xx}^{2}[y(x)] ) = f(x)

y(x) = int-int[ anti-d_{x}[-pow[(-n)]-]-H( f(x) ) ]d[x]d[x]

d_{xx}^{2}[y(x)]^{n}·H( d_{x}[y(x)] ) = f(x)

y(x) = int[ anti-int[-pow[(-n)]-]d[x]-H( f(x) ) ]d[x]

Escaños de España:

Euskaldor:

Euskal-Herria:

36 PNV

44 EH-Bildu

Astur-Cantabria:

10 PRC

6 PNV

4 EH-Bildu

Cáteldor:

Catalunya-y-Països-Catalans

74 ERC

40 Junts

11 CUP

Cásteldor:

Castilla-Madrid:

53 PP

31 PSOE

21 Más-País

Galicia

6 PP

4 BNG

Andalucía:

6 PP

4 PSOE

Escaños de Francia:

Occitania:

60 ERO

40 Front-Nacional Occità

Breton-Land:

30 Breton Gaelical Sin-Fein

20 Breton Nacional-Front  

Normand-Land:

30 Normand Gaelical Sin-Fein.

20 Normand Nacional-Front  

Estatu-dom Françé:

100 Estatu-dom Françé in Martx

50 Front-Nacionel del Estatu-dom Françé

Aquità-Gasconiá:

entreshkû-puá a la-tha-eneth autopista.

ishkû-puá de la-tha-eneth autopista.

Tolosenc

entretxkû-puá a la-tha-eneth autopista.

surtitxkû-puá de la-tha-eneth autopista.

Provençal:

entrû-puá a la-tha-eneth autopista.

surtû-puá de la-tha-eneth autopista.

vuloire-dom:

ye vuke ye-de-muá

tú vuke tú-de-tuá

vuke pont-de-suá

vuloms

vuloz

vulen pont-de-suá

pudoire-dom:

ye puke ye-de-muá

tú puke tú-de-tuá

puke pont-de-suá

pudoms

pudoz

puden pont-de-suá

becboire-dom:

ye becbe ye-de-muá

tú becbe tú-de-tuá

becbe pont-de-suá

beboms

beboz

becben pont-de-suá

decboire-dom:

ye decbe ye-de-muá

tú decbe tú-de-tuá

decbe pont-de-suá

deboms

deboz

decben pont-de-suá

havoire-dom:

ye have ye-de-muá

tú have tú-de-tuá

have pont-de-suá

havoms

havoz

haven pont-de-suá

Pasatu-dom

ye vare ye-de-muá

tú vare tú-de-tuá

vare pont-de-suá

varoms

varoz

varen pont-de-suá

Teorema:

x^{n} =[p]= a <==> x = ( pk+a )^{(1/n)}

Teorema:

x^{n}+x^{m} =[p]= a <==> x = ( pk+a )^{( 1/(m+[n+(-m)]) )}

El que tú vuke tú-de-tuá,

és-pois becboire-dom de la Font avec ye-de-muá?

El que ye vuke ye-de-muá,

és-pois becboire-dom de la Font avec tú-de-tuá.

sere-dom

suy-pois

ets-pois

és-pois

soms

soz

son-pois

stare-dom

estuy-pois

estás-pois

está-pois

estoms

estoz

están-pois

creyere-dom

ye creigue ye-de-muá

tú creigue tú-de-tuá

creigue pont-de-suá

creyoms

creyoz

creiguen pont-de-suá

cayere-dom

ye caigue ye-de-muá

tú caigue tú-de-tuá

caigue pont-de-suá

cayoms

cayoz

caiguen pont-de-suá

ye creigue ye-de-muá de-le-dans Le-Déu.

ye creigue ye-de-muá de-le-dans La-Déa.

No entiendo porque se saltan,

el buey del prójimo hablando,

porque se destruyen.

No entiendo porque no siguen,

el buey del próximo hablando,

porque se construyen.

No se puede amar más a las tinieblas de infiel,

que a la luz de fiel,

es este mundo del universo negro,

donde los fieles son de constructor.

No se puede amar más a la luz de infiel,

que a las tinieblas de fiel,

es ese mundo del universo blanco,

donde los fieles son de destructor.

Amar la vida en este mundo tiene alternativa.

Odiar la vida en ese mundo tiene alternativa.

Amar más a las tinieblas que a la luz no tiene alternativa,

y es la condenación de este mundo.

Ama más a la luz que a las tinieblas no tiene alternativa,

y es la condenación de ese mundo.

Para que te necesita la voz de la mente si es un dios,

solo te necesita para destruir-te rezando a Dios.

Ni un dios del bien te necesita para nada,

tiene constructor y hace pagar condenación.

Mi hermana es ingeniera informática de verdad,

no es falso su título y sabe ofimática,

porque tiene mis prácticas en Turbo-C y en NASM de ensamblador.

Asignaturas aprobadas por mis prácticas:

Memoria Dinámica

Cálculo Numérico

Grafos

Combinatoria

Software Gráfico

Software Musical

Ensamblador