óptica-física y psico-neurología-extraterrestre y arte-matemático y análisis-matemático y termodinámica y filosofía y congruencias

Ley:

d_{rw}[f(w,x)]+d_{x}[f(w,x)] = a·( sin(2arw)+(-1)·(1/(ax))^{n} )

f(w,x) = ( sin(arw) )^{2}+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

d_{rw}[g(w,x)]+d_{x}[g(w,x)] = a·( (-1)·sin(2arw)+(1/(ax))^{n} )

g(w,x) = ( cos(arw) )^{2}+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

( f(w,x)+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) )·...

... ( g(w,x)+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ) = (1/4) <==> ...

... w = (1/(ar))·(pi/4)

( f(w,x)+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) )·...

... ( g(w,x)+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ) = (3/16) <==> ...

... ( w = (1/(ar))·(pi/3) || w = (1/(ar))·(pi/6) )

Deducción:

( sin(arw) )^{2}·( cos(arw) )^{2} = (1/4)

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

( sin(arw) )^{4}+(-1)·( sin(arw) )^{2}+(1/4) = 0

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

arw = arc-sin( (1/2)^{(1/2)} ) = (pi/4)

Ley:

d_{rw}[f(w,x)]+d_{x}[f(w,x)] = a·( ( sin(arw) )^{2}+(-1)·(1/(ax))^{n} )

f(w,x) = (1/2)·arw+(-1)·(1/4)·sin(2arw) )+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

d_{rw}[g(w,x)]+d_{x}[g(w,x)] = a·( ( cos(arw) )^{2}+(1/(ax))^{n} )

g(w,x) = (1/2)·arw+(1/4)·sin(2arw) )+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

int[ f(w,x)+g(w,x) ]d[arw] = 2pi^{2} <==> w = (1/(ar))·2pi

Deducción:

int[ arw ]d[arw] = (1/2)·(arw)^{2} = 2pi^{2}

(arw)^{2} = 4pi^{2} = (2pi)^{2}

Principio: [ de la primera directriz ]

Hay contacto extraterrestre,

con motor de curvatura,

siendo el próximo,

pudiendo ir a su planeta.

No hay contacto extraterrestre,

sin motor de curvatura,

siendo el prójimo,

no pudiendo ir a su planeta.

Ley:

No puede haber contacto extraterrestre,

saltando-te la primera directriz,

porque te crees un dios del universo.

Puede haber contacto extraterrestre,

no saltando-te la primera directriz,

porque no te crees un dios del universo.

Ley:

Pensamiento peligroso:

Te crees un dios del universo 

y entonces también te crees que caminas solo sin estar allí.

Pensamiento seguro:

Quizás te cree un dios del universo

pero no te crees que caminas solo sin estar allí.

Principio: [ de la segunda directriz ]

No puede haber contacto extraterrestre des-ascendido,

con un mundo ascendido,

porque no se puede estar en un mundo des-ascendido,

con testimonio del evangelio,

siendo el prójimo de ti el mundo des-ascendido.

Puede haber contacto extraterrestre des-ascendido,

con un mundo des-ascendido, 

porque se puede estar en un mundo des-ascendido,

sin testimonio del evangelio,

siendo el próximo de ti el mundo des-ascendido.

Ley:

Todos los hombres que se creen dioses del universo,

son de la Tierra,

y no de Cygnus-Kepler,

porque se han saltado la segunda directriz.

Todos los hombres que no se creen dioses del universo,

son de Cygnus-Kepler,

y no de la Tierra,

porque no se han saltado la segunda directriz.

Análisis matemático 2:

Arte:

Sea Z(s) = sum[n = 1]-[oo][ (1/n)^{s} ] ==>

[Es][ sum[n = 1]-[oo][ (s+(-1))·(1/n)^{s} ] = ( Z(s)/Z(s+(-1)) ) ]

Exposición:

s = 1 

( Z(s)/Z(s+(-1)) ) = ln(2)

f(s+(-1)) = ( 1/(s+(-1)) )

Id(s+(-1)) = ( 1/(s+(-1)) ) <==> s = 2

g( h(s+(-1)) ) = Z(s+(-1))

Id( h(s+(-1)) ) = Z(s+(-1)) <==> h = Z

sum[n = 1]-[oo][ (s+(-1))·(1/n)^{s} ] = (s+(-1))·sum[n = 1]-[oo][ (1/n)^{s} ] = ...

.... (s+(-1))·Z(s) = f(s+(-1))·Z(s) = ( 1/(s+(-1)) )·Z(s) = ...

... ( 1/(g o h)(s+(-1)) ) )·Z(s) = ( 1/g( h(s+(-1)) ) )·Z(s) = ( Z(s)/Z(s+(-1)) )

Arte:

Sea H(s) = sum[n = 1]-[oo][ (1+(1/n))^{s} ] ==>

[Es][ sum[n = 1]-[oo][ 0s·(1+(1/n))^{s} ] = ( H(s)/H(s+(-1)) ) ]

Exposición:

s = 1

( H(s)/H(s+(-1)) ) = 1+ln(2)

Arte:

Sea Z(s) = sum[n = 1]-[oo][ (1/n)^{s} ] ==>

[Es][ sum[n = 1]-[oo][ 0·[ n // s ]·(1/n)^{s} ] = (s+(-1))·Z(s+(-1)) ]

Exposición:

s = 1

u(s) = 1

v(1) = s

sum[n = 1]-[oo][ 0·[ n // s ]·(1/n)^{s} ] = sum[n = 1]-[oo][ 0·[ n // u(s) ]·(1/n)^{u(s)} ] = ...

... sum[n = 1]-[oo][ 0·[ n // 1 ]·(1/n) ] = sum[n = 1]-[oo][ 0n·(1/n) ] = sum[n = 1]-[oo][ 0 ] = 1 = ...

... 0·oo = 0·Z(0) = (1+(-1))·Z(1+(-1)) = (v(1)+(-1))·Z(v(1)+(-1)) = (s+(-1))·Z(s+(-1))

Arte:

Sea Z(s) = sum[n = 1]-[oo][ (1/n)^{s} ] ==>

[Es][ sum[n = 1]-[oo][ (1/2)^{n+(-1)}·[ n // s ]·(1/n)^{s} ] = 2s·(s+(-1))·Z(s+(-1)) ]

Exposición:

s = 1

u(s) = 1

v(1) = s

sum[n = 1]-[oo][ (1/2)^{n+(-1)}·[ n // s ]·(1/n)^{s} ] = ...

... sum[n = 1]-[oo][ (1/2)^{n+(-1)}·[ n // u(s) ]·(1/n)^{u(s)} ] = ...

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

... sum[n = 1]-[oo][ (1/2)^{n+(-1)} ] = 2 = 2·0·oo = 2·0·Z(0) = (1+1)·(1+(-1))·Z(1+(-1)) = ...

... (v(1)+v(1))·(v(1)+(-1))·Z(v(1)+(-1)) = (s+s)·(s+(-1))·Z(s+(-1)) = 2s·(s+(-1))·Z(s+(-1))

Análisis matemático 1:

[%] Derivación

Continuidad

Cuerpos ordenados

Sucesiones

Análisis matemático 2:

[%] Integración y producto integral

Integral definida

Euler Falsus Infinitorum

Teoremas y Artes de series

Análisis matemático 3:

[%] Derivadas parciales

[%] Optimización

Continuidad

Análisis matemático 4:

[%] Integrales múltiples

[%] Integrales de línea

Integrales impropias

Análisis matemático 5:

Sucesiones de funciones

Integral de Lebesgue

Series de potencies

Análisis matemático 6:

Transformada integral exponencial

Arte método de Euler

Arte series de Laurent

Teorema:

Sea d_{x}[F(x)] = f(x) ==>

F(x) es continua <==> f(x) es continua

Demostración:

Sea s > 0 ==>

Sea d < (s/2) ==>

| F(x+h)+(-1)·F(x) | < d

| F(x+h)+(-1)·F(x) | = 0

| f(x+h)+(-1)·f(x) | = 0^{2} = 2·0 < 2d < s

Sea d > 0 ==>

Sea s > 0 ==>

| f(x+h)+(-1)·f(x) | < s < 2s

| f(x+h)+(-1)·f(x) | = 2·0 = 0^{2}

| F(x+h)+(-1)·F(x) | = 0

| F(x+h)+(-1)·F(x) | < d

Análisis matemático 2:

Teorema:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{0}·(b+(-a))·(1/n) ] ] = b+(-a)

Demostración:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{0}·(b+(-a))·(1/n) ] ] = ...

... lim[n = oo][ sum[k = 1]-[n][ (b+(-a))·(1/n) ] ] = lim[n = oo][ (b+(-a))·(n/n) ] = b+(-a)

Teorema:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )·(b+(-a))·(1/n) ] ] = (1/2)·b^{2}+(-1)·(1/2)·a^{2}

Demostración:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )·(b+(-a))·(1/n) ] ] = ...

... lim[n = oo][ a·(b+(-a))·(n/n)+(1/2)·n·(n+1)·(b+(-a))^{2}·(1/n)^{2} ] = ...

... ab+(-1)·a^{2}+(1/2)·b^{2}+(-1)·ab+(1/2)·a^{2} = (1/2)·b^{2}+(-1)·(1/2)·a^{2}

Teorema:

lim[n = oo][ sum[k = 1]-[n][ e^{a+(k/n)·(b+(-a))}·(b+(-a))·(1/n) ] ] = e^{b}+(-1)·e^{a}

Demostración:

lim[n = oo][ sum[k = 1]-[n][ e^{a+(k/n)·(b+(-a))}·(b+(-a))·(1/n) ] ] = ...

... lim[n = oo][ e^{a}·( ( e^{((1/n)+1)·(b+(-a))}+(-1) )/( e^{(1/n)·(b+(-a))}+(-1) ) )·(b+(-a))·(1/n) ] = ...

... e^{b}+(-1)·e^{a}

Teorema:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{2}·(b+(-a))·(1/n) ] ] = (1/3)·b^{3}+(-1)·(1/3)·a^{3}

Demostración:

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

... lim[n = oo][ ( a^{2}·(n/n)+2·(1/2)·n·(n+1)·a·(b+(-a))·(1/n)^{2}+...

... (1/6)·n·(n+1)·(2n+1)·(b+(-a))^{2}·(1/n)^{3} )·(b+(-a)) ] = ...

... ab·(b+(-a))+(1/3)·b^{3}+(-1)·ab·(b+(-a))+(-1)·(1/3)·a^{3} = (1/3)·b^{3}+(-1)·(1/3)·a^{3}

Teorema:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{3}·(b+(-a))·(1/n) ] ] = (1/4)·b^{4}+(-1)·(1/4)·a^{4}

Demostración:

lim[n = oo][ sum[k = 1]-[n][ ( a+(k/n)·(b+(-a)) )^{3}·(b+(-a))·(1/n) ] ] = ...

... lim[n = oo][ ( a^{3}·(n/n)+(3/2)·n·(n+1)·a^{2}·(b+(-a))·(1/n)^{2}+...

... (1/2)·n·(n+1)·(2n+1)·a·(b+(-a))^{2}·(1/n)^{3}+...

... (1/4)·n^{2}·(n^{2}+2n+1)·(b+(-a))^{3}·(1/n)^{4} )·(b+(-a)) ] = (1/4)·b^{4}+(-1)·(1/4)·a^{4}

(-1)·a^{4}+(3/2)·a^{4}+(-1)·a^{4}+(1/4)·a^{4} = (-1)·(1/4)·a^{4}

(3/2)·(ab)^{2}+(-3)·(ab)^{2}+(3/2)·(ab)^{2} = 0

a^{3}b+(-3)·a^{3}b+3a^{3}b+(-1)·a^{3}b = 0

ab^{3}+(-1)·ab^{3} = 0

Teorema:

lim[n = oo][ sum[k = 1]-[n][ (k/n)·(1/n) ] ] = (1/2)

Demostración:

lim[n = oo][ sum[k = 1]-[n][ (k/n)·(1/n) ] ] = ...

... lim[n = oo][ (1/2)·n·(n+1)·(1/n)^{2} ] = (1/2) = (1/2)·1^{2}+(-1)·(1/2)·0^{2}

Teorema:

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

Demostración:

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

... lim[n = oo][ ( (e^{(1/n)+1}+(-1))/(e^{(1/n)}+(-1)) )·(1/n) ] = e+(-1) = e^{1}+(-1)·e^{0}

Definición:

lim[n = oo][ sum[k = 1]-[n][ f(k/n)·(1/n) ] ] = int[x = 0]-[1][ f(x) ]d[x]

Teorema:

lim[n = oo][ sum[k = 1]-[n][ f(k/n)·(1/n) ] ] = F(1)+(-1)·F(0)

Demostración:

lim[n = oo][ sum[k = 1]-[n][ f(k/n)·(1/n) ] ] = int[x = 0]-[1][ f(x) ]d[x] = F(1)+(-1)·F(0)

Teorema:

lim[n = oo][ sum[k = 1]-[n][ (p+1)·k^{p}·f( (k/n)^{p+1} )·(1/n)^{p+1} ] ] = F(1)+(-1)·F(0)

Demostración:

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

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

... int[x = 0]-[1][ (p+1)·x^{p}·f(x^{p+1}) ]d[x] = [ F(x^{p+1}) ]_{x = 0}^{x = 1} = ...

... F(1)+(-1)·F(0)

Teorema:

lim[n = oo][ sum[k = 1]-[n][ ( 1/(n^{p}+k^{p}) )·pk^{p+(-1)} ] ] = ln(2)

Teorema:

lim[n = oo][ sum[k = 1]-[n][ (npk^{p+(-1)}+k^{p})·e^{(k/n)}·(1/n)^{p+1} ] ] = e

Teorema:

int[x = 0]-[1][ x^{p}·e^{x} ]d[x] = p!·( e+(-1) )

Demostración:

int[x = 0]-[1][ x^{p}·e^{x} ]d[x] = (1/(p+1))·x^{p+1} [o(x)o] e^{x}

Teorema:

int[x = 0]-[1][ x^{p}·e^{(-x)} ]d[x] = p!·( 1+(-1)·(1/e) )

Demostración:

int[x = 0]-[1][ x^{p}·e^{(-x)} ]d[x] = (1/(p+1))·x^{p+1} [o(x)o] (-1)·e^{(-x)}

Teorema:

int[x = 0]-[1][ x^{p}·e^{x} ]d[x] = p!·( e+(-1) )

Demostración: [ por inducción ]

int[x = 0]-[1][ x^{p+1}·e^{x} ]d[x] = ...

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

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

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

Teorema:

int[x = 0]-[1][ x^{p}·e^{(-x)} ]d[x] = p!·( 1+(-1)·(1/e) )

Demostración: [ por inducción ]

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

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

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

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

... (-1)·(p+1)!·int[x = 1]-[0][ e^{(-x)} ]d[x] = (p+1)!·( 1+(-1)·(1/e) )

Teorema:

int[x = (-oo)]-[0][ x^{p}·e^{x} ]d[x] = p!

Demostración:

int[x = (-oo)]-[0][ x^{p}·e^{x} ]d[x] = (1/(p+1))·x^{p+1} [o(x)o] e^{x}

Teorema:

int[x = 0]-[oo][ x^{p}·e^{(-x)} ]d[x] = p!

Demostración:

int[x = 0]-[oo][ x^{p}·e^{(-x)} ]d[x] = (1/(p+1))·x^{p+1} [o(x)o] (-1)·e^{(-x)}

Teorema:

int[x = (-oo)]-[0][ x^{p}·e^{x} ]d[x] = p!

Demostración: [ por inducción ]

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

... [ x^{p+1}·e^{x} ]_{x = 0}^{x = 0}+(-1)·(p+1)·int[x = 0]-[(-oo)][ x^{p}·e^{x} ]d[x] = ...

... [ x^{p+1}·e^{x} ]_{x = 0}^{x = 0}+(p+1)·int[x = (-oo)]-[0][ x^{p}·e^{x} ]d[x] = ...

... (-1)·(p+1)·p!·int[x = 0]-[(-oo)][ e^{x} ]d[x] = (-1)·(p+1)!·int[x = 0]-[(-oo)][ e^{x} ]d[x] = (p+1)!

Teorema:

int[x = 0]-[oo][ x^{p}·e^{(-x)} ]d[x] = p!

Demostración: [ por inducción ]

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

... [ (-1)·x^{p+1}·e^{(-x)} ]_{x = 0}^{x = 0}+(p+1)·int[x = oo]-[0][ x^{p}·e^{(-x)} ]d[x] = ...

... [ (-1)·x^{p+1}·e^{(-x)} ]_{x = 0}^{x = 0}+(-1)·(p+1)·int[x = 0]-[oo][ x^{p}·e^{(-x)} ]d[x] = ...

... (-1)·(p+1)·p!·int[x = oo]-[0][ e^{(-x)} ]d[x] = (-1)·(p+1)!·int[x = oo]-[0][ e^{(-x)} ]d[x] = (p+1)!

Teorema: [ de Hôpital-Garriga ]

Si f(x) = 1 ==> f(x) = d_{x}[f(x)] en una indeterminación

Demostración:

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

Teorema: [ de Hôpital-Garriga ]

Si f(x) = (-1) ==> f(x) = d_{x}[f(x)] en una indeterminación

Demostración:

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

Teorema: [ de Hôpital-Garriga ]

Si f(x) = 0^{n} ==> f(x) = d_{x}[f(x)] en una indeterminación

Demostración:

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

Teorema: [ de Hôpital-Garriga ]

Si f(x) = oo^{n} ==> f(x) = d_{x}[f(x)] en una indeterminación

Demostración:

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

... (1/0)·oo^{n+(-1)} = oo^{n} = f(x)

Ley: [ de ejemplo de teoría ]

Si d_{V}[P_{0}]·V^{2}+PV+(-1)·d_{P}[k]·TP = 0 ==>

V_{min} = (-1)·(1/2)·( 1/d_{V}[P_{0}] )·P

(1/4)·( 1/d_{V}[P_{0}] )·P^{2}+d_{P}[k]·TP = 0

P_{min} = (-1)·2·d_{P}[k]·T·d_{V}[P_{0}]

(PV)_{min} = d_{P}[k]·TP

d_{P}[T(P)]·p = qR <==> p = qR·( 1/(PV)_{min} )·d_{P}[k]·(-1)·P^{2}

Deducción:

d_{V}[ d_{V}[P_{0}]·V^{2}+PV+(-1)·d_{P}[k]·TP ] = ...

... d_{V}[d_{V}[P_{0}]·V^{2}]+d_{V}[PV]+d_{V}[ (-1)·d_{P}[k]·TP ] = ...

... d_{V}[d_{V}[P_{0}]·V^{2}]+d_{V}[PV]+0 = d_{V}[d_{V}[P_{0}]·V^{2}]+d_{V}[PV] = ...

... d_{V}[P_{0}]·d_{V}[V^{2}]+P·d_{V}[V] = d_{V}[P_{0}]·2V+P

d_{V}[P_{0}]·2V+P = 0

d_{V}[P_{0}]·2V = d_{V}[P_{0}]·2V+0 = d_{V}[P_{0}]·2V+(P+(-P)) = ...

... ( d_{V}[P_{0}]·2V+P )+(-P) = 0+(-P) = (-P)·

V = ( (1/2)·(1/d_{V}[P_{0}])·(d_{V}[P_{0}]·2) )·V = ...

... (1/2)·(1/d_{V}[P_{0}])·( (d_{V}[P_{0}]·2)·V ) = (-1)·(1/2)·(1/d_{V}[P_{0}])·P

d_{P}[T(P)] = (PV)_{min}·(1/d_{P}[k])·(-1)·(1/P)^{2}

Ley:

Si ( P+d_{xyz}^{3}[q(x,y,z)]·gh )·V = kT ==>

q(x,y,z) = kT·(1/(gh))·(1/V)·xyz+(-1)·P·(1/(gh))·xyz

Ley:

Si ( P+d_{xy}^{2}[q(x,y)]·g )·V = kT ==>

q(x,y) = kT·(1/g)·(1/V)·xy+(-1)·P·(1/g)·xy

Ley:

Si ( P+d_{xy}^{2}[q(x,y)]·g )·V = kT·xya^{2} ==>

q(x,y) = kT·(1/g)·(1/V)·(1/4)·(axy)^{2}+(-1)·P·(1/g)·xy

Ley:

Si ( P+d_{x}[m(x)]·u^{2} )·V = kT ==>

m(x) = kT·(1/u)^{2}·(1/V)·x+(-1)·P·(1/u)^{2}·x

Rezo al Mal:

Los hombres no tienen motor de curvatura,

y no pueden ir a ver a su mujer,

pero no son maricones.

Los extraterrestres tienen motor de curvatura,

y pueden ir a ver a su mujer,

pero son maricones.

Definición:

er-h[p](x) = sum[k = 0]-[oo][ (1/k!)·(1/(p+1))·x^{k [o(+)o] p+1} ]

er-h[p](x) = sum[k = 0]-[oo][ (1/(p+1))·x^{p+1} [o(x)o] (1/k!)·x^{k} ] = ...

... (1/(p+1))·x^{p+1} [o(x)o] e^{x}

er-h[p](-x) = sum[k = 0]-[oo][ (-1)^{k}·(1/k!)·(1/(p+1))·x^{k [o(+)o] p+1} ]

er-h[p](-x) = sum[k = 0]-[oo][ (1/(p+1))·x^{p+1} [o(x)o] (-1)^{k}·(1/k!)·x^{k} ] = ...

... sum[k = 0]-[oo][ (1/(p+1))·x^{p+1} [o(x)o] (1/k!)·(-x)^{k} ] = (1/(p+1))·x^{p+1} [o(x)o] e^{(-x)}

Teorema:

int[ x^{p}·e^{x} ]d[x] = er-h[p](x)

int[ x^{p}·e^{(-x)} ]d[x] = (-1)·er-h[p](-x)

Teorema:

er-h[p](1) = p!·e

er-h[p](0) = p!

er-h[p](-1) = p!·(1/e)

Demostración:

er-h[p](x) = sum[j = 0]-[oo][ (1/k!)·(1/(p+1))·x^{k [o(+)o] p+1} ] = ...

... sum[j = 0]-[oo][ (1/(p+1))·x^{p+1} [o(x)o] (1/k!)·x^{k} ] = p!·sum[j = 0]-[oo][ (1/k!)·x^{k} ]

Teorema:

d_{x}[er-h[p](-x)] = (-1)·x^{p}·e^{(-x)}

Demostración:

j = k+(-1)

d_{x}[er-h[p](-x)] = sum[k = 0]-[oo][ (-1)^{k}·(1/(k+(-1))!)·x^{(k+(-1))+p} ] = ...

... sum[k = 0]-[oo][ (-1)^{j+1}·(1/j!)·x^{j+p} ] = ...

... (-1)·x^{p}·sum[k = 0]-[oo][ (-1)^{j}·(1/j!)·x^{j} ] = ...

... (-1)·x^{p}·sum[k = 0]-[oo][ (1/j!)·(-x)^{j} ] = (-1)·x^{p}·e^{x}

Principio:

El que es,

es.

El que no es,

no es.

Ley:

Afirmación Verdadera:

El fiel es,

y el infiel no es.

Negación Falsa:

El fiel no es,

y el infiel es.

Ley:

Afirmación Verdadera:

No es ninguien,

no siendo los infieles,

estando todo fiel muerto.

Negación Falsa:

Es toto-hoimbre,

siendo los fieles,

estando todo-algún fiel vivo.

Anexo

Esta falsedad no es de Cygnus-Kepler,

porque hay fieles ascendidos,

y no lo puede decir el Mal.

Rezo al Mal desde Cygnus-Kepler:

Yo que soy hombre,

no soy,

amando al próximo,

no como a mi mismo.

Él que es extraterrestre,

es,

amando al prójimo,

como a mi mismo.

Teorema:

p^{m} =[m]= p

Demostración: [ por inducción ]

(p+1)^{m} = p^{m}+mk+1 =[m]= p^{m}+1 =[m]= p+1

Teorema:

p^{m} =[m]= mp

Demostración: [ por inducción ]

(p+1)^{m} = p^{m}+mk+1 =[m]= p^{m}+1 =[m]= mp+1

Definición:

f(a) = b <==> a =[m]= b

Teorema:

f(1) = 1

Demostración:

1 =[m]= 1

Teorema:

f(a+b) = f(a)+f(b)

Demostración:

a+b =[m]= a+b

f(a+b) = a+b

a =[m]= a & b =[m]= b

f(a+b) = a+b = f(a)+f(b)

Teorema:

f(ab) = f(a)·f(b)

Demostración:

ab =[m]= ab

f(ab) = ab

a =[m]= a & b =[m]= b

f(ab) = ab = f(a)·f(b)

Teorema:

Si a =[m]= 1 ==> sum[r = 0]-[m+(-1)][ f(a) ] = m+(-1)

Demostración:

a =[m]= 1

f(a) = 1

Teorema:

Si a =[m]= p^{m+(-1)} ==> sum[r = 0]-[m+(-1)][ f(a) ] = m+(-1)

Demostración:

a =[m]= p^{m+(-1)} =[m]= 1

f(a) = 1

Teorema:

Si a =[2]= 0 ==>

x^{2}+ax =[2]= p <==> x =[2]= p

Demostración:

a =[2]= 0

f(a) = 0

x+ax =[2]= x^{2}+ax =[2]= p

f(x) = f(x)+f(a)·f(x) = f(x)+f(ax) = f(x+ax) = p

x =[2]= p

Teorema:

Si a =[2]= 1 ==>

x^{2}+ax =[2]= p <==> x =[2]= p

Demostración:

a =[2]= 1

f(a) = 1

ax =[2]= 2x+ax =[2]= x^{2}+ax =[2]= p

f(x) = f(a)·f(x) = f(ax) = p

x =[2]= p

Definición: [ de función de Euler ]

H(ab) = a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]·b·Prod[q | b][ (2+(-1)·(1/q)) ]

Teorema:

H(1) = 1

Demostración:

H(1) = H(1·1) = 1·Prod[p | 1][ ( 2+(-1)·(1/p) ) ]·1·Prod[q | 1][ (2+(-1)·(1/q)) ] = 1

Teorema:

H(a) = a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]

Demostración:

H(a) = H(a·1) = a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]·1·Prod[q | 1][ (2+(-1)·(1/q)) ] = ...

... a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]·1

Teorema:

H(ab) = H(a)·H(b)

Demostración:

H(a·b) = a·Prod[p | a][ ( 2+(-1)·(1/p) ) ]·b·Prod[q | b][ (2+(-1)·(1/q)) ] = H(a)·H(b)

Teorema:

H(p^{m}) = 2p^{m}+(-1)·p^{m+(-1)}

Teorema:

H(p) = 2p+(-1)

Teorema:

Sea p =[m]= n ==>

p^{m} =[m]= 2n+(-1) <==> p =[m]= n =[m]= 1

Demostración:

p^{m}·(2p+(-1)) =[m]= (2n+(-1))·(2p+(-1))

H(p^{m+1}) =[m]= H(n)·H(p) = H(np)

p^{m+1} =[m]= np

p^{m} =[m]= n

2n+(-1) =[m]= p^{m} =[m]= n

n =[m]= 1

p =[m]= n =[m]= 1

Teorema:

3^{2} =[2]= 5 <==> 3 =[2]= 1

Demostración:

9+(-5) = 4 = 2·2 

3+(-1) = 2

Teorema:

4^{3} =[3]= 7 <==> 4 =[3]= 1

Demostración:

64+(-7) = 57 = 3·19

4+(-1) = 3

Teorema:

5^{4} =[4]= 9 <==> 5 =[4]= 1

Demostración:

625+(-9) = 616 = 4·154

5+(-1) = 4

Teorema:

8^{7} =[7]= 15 <==> 8 =[7]= 1

Demostración:

2,097,152+(-15) = 2,097,137 = 7·299,591

8+(-1) = 7

Teorema:

9^{8} =[8]= 17 <==> 9 =[8]= 1

Demostración:

43,046,721+(-17) = 43,046,704 = 8·5,380,838

9+(-1) = 8

Teorema:

x^{2} =[2]= a <==> x =[2]= a

Demostración:

Sea x = y+a ==>

(y+a)^{2} = y^{2}+2ya+a^{2} =[2]= y+a 

y+a =[2]= a

x+(-a) = y =[2]= 0

Teorema:

x^{2} =[2]= 2k <==> x =[2]= 2k

Demostración:

4k^{2}+(-2)·k = 2·( 2k^{2}+(-k) )

Teorema:

x^{2} =[2]= 2k+1 <==> x =[2]= 2k+1

Demostración:

4k^{2}+4k+1+(-2)·k+(-1) = 2·( 2k^{2}+k )

Teorema:

x^{3} =[3]= a <==> x =[3]= a

Demostración:

Sea x = y+a ==>

(y+a)^{3} = y^{3}+3y^{2}a+3ya^{2}+a^{3} =[3]= y+a 

y+a =[3]= a

x+(-a) = y =[3]= 0

Teorema:

x^{3} =[3]= 3k <==> x =[3]= 3k

Demostración:

27k^{3}+(-3)·k = 3·( 9k^{3}+(-k) )

Teorema:

x^{3} =[3]= 3k+1 <==> x =[3]= 3k+1

Demostración:

27k^{3}+27k^{2}+9k+1+(-3)·k+(-1) = 3·( 9k^{3}+9k^{2}+2k )

Teorema:

x^{3} =[3]= 3k+2 <==> x =[3]= 3k+2

Demostración:

27k^{3}+54k^{2}+36k+8+(-3)·k+(-2) = 3·( 9k^{3}+18k^{2}+11k+2 )

Teorema:

a^{2} =[4]= 2a

Demostración: 

a = 2k 

Teorema:

a =[4]= 1

Demostración:

a = 4k+1

Teorema:

x^{4} =[4]= a <==> ( 2x =[4]= a || 2x+1 =[4]= 3a )

Demostración:

Sea x = y+a ==>

(y+a)^{4} = y^{4}+4y^{3}a+6·(ya)^{2}+4ya^{3}+a^{4} =[4]= ( y^{2}+a^{2} )^{2} =[4]= ...

...  2y^{2}+2a^{2} =[4]= 2y+2a 

2y+2a =[4]= a

2x+(-a) = 2y+a =[4]= 0

2y^{2}+2a^{2} =[4]= 2y+1 =[4]= a

2x+1 =[4]= 3a

Teorema:

x^{4} =[4]= 4k <==> x =[4]= 2k

Demostración:

16k^{4}+(-4)·k = 4·( 4k^{4}+(-k) )

Teorema:

x^{4} =[4]= 4k+1 <==> x =[4]= 2k+1 =[4]= 6k+1

Demostración:

1,296k^{4}+864k^{3}+216k^{2}+24k+1+(-4)·k+-1 = 4·( 324k^{4}+216k^{2}+54k^{2}+5k )

electro-magnetismo y mecánica-ingeniería y ecuaciones-en-derivadas-parciales y mecánica-física y análisis-matemático-6 y medicina

Examen de electro-magnetismo:

Principio:

E(x,y,z) = qk·(1/r)^{3}·a·< x^{2},y^{2},z^{2} >

E(yz,zx,xy) = qk·(1/r)^{4}·a^{2}·< (yz)^{2},(zx)^{2},(xy)^{2} >

Ley:

div[ E(x,y,z) ] = ?

Anti-div[ E(yz,zx,xy) ] = ?

Ley:

Anti-Potencial[ E(x,y,z) ] = ?

Potencial[ E(yz,zx,xy) ] = ?

Ley: [ de corrección del examen ]

div[ E(x,y,z) ] = d_{x(yz)}^{2}[ Anti-Potencial[ E(x,y,z) ] ]

Anti-div[ E(yz,zx,xy) ] = d_{x(yz)}^{2}[ Potencial[ E(yz,zx,xy) ] ]

Ley:

R·d_{t}[q(t)]+(-C)·p(t) = W·f(ut)·e^{ut}

p(t) = W·( 1/(uR·d_{ut}[f(ut)]+(-C)·f(ut)) )·f(ut)·e^{ut}

q(t) = W·( ut /o(ut)o/ (uR·f(ut)+(-C)·int[ f(ut) ]d[ut]) ) [o(ut)o] f(ut) [o(ut)o] e^{ut}

Ley:

R·d_{t}[q(t)]+C·p(t) = W·f(ut)·e^{(-1)·ut}

p(t) = W·( 1/((-u)·R·d_{ut}[f(ut)]+C·f(ut)) )·f(ut)·e^{(-1)·ut}

q(t) = W·( ut /o(ut)o/ ((-u)·R·f(ut)+C·int[ f(ut) ]d[ut]) ) [o(ut)o] f(ut) [o(ut)o] e^{(-1)·ut}

Ley:

Sea ( d_{t}[ I_{cx} ] = 0 & d_{t}[ I_{cy} ] = 0 ) ==>

Si d[M_{1}(t)] = (1/2)·mgx·(1/s)^{2}·cos(nw)·d[w] ==>

M_{1}(t) = (1/2)·mg·(x/n)·(1/s)^{2}·sin(nw)

Si d[ d[M_{2}(t)] ] = mg·(1/s)^{2}·sin(nw)·cos(nw)·d[y]d[w] ==>

M_{2}(t) = mg·(y/n)·(1/s)^{2}·(1/2)·( sin(nw) )^{2}

M_{1}(t) = M_{2}(t) <==> ( w(t) = (1/n)·arc-sin( I_{cx}/I_{cy} ) & I_{cx} [< I_{cy} )

Ley:

Sea d_{t}[ I_{c} ] = 0 ==>

Si d[M_{1}(t)] = (1/2)·I_{c}·u^{2}·cos(nw)·d[w] ==>

M_{1}(t) = (1/2)·I_{c}·u^{2}·(1/n)·sin(nw)

Si d[ d[M_{2}(t)] ] = I_{c}·u^{2}·(1/x)·sin(nw)·cos(nw)·d[x]d[w] ==>

M_{2}(t) = I_{c}·u^{2}·ln(ax)·(1/n)·(1/2)·( sin(nw) )^{2}

M_{1}(t) = M_{2}(t) <==> ( w(t) = (1/n)·arc-sin( ( 1/ln( aI_{c}·(1/(md)) ) ) ) & aI_{c} >] md·e )

Ley: [ del calor electro-magnético ]

div[ E_{e}(x,y,t) ] = (-2)·(1/c)·B_{e}(x,y,t)

Deducción:

E_{e}(x,y,t)+int[ B_{e}(x,y,t) ]d[t] = 0 = m·d_{tt}^{2}[ < x,y > ]

x(t) = ct·( cos(w) )^{2}

y(t) = ct·( sin(w) )^{2}

div[ E_{e}(x,y,t) ]+div[ inr[ B_{e}(x,y,t) ]d[t] ] = 0^{2}

div[ int[ B_{e}(x,y,t) ]d[t] ] = ( 1/(d[x]+d[y]) )·(d[x]+d[y]) [o] div[ int[ B_{e}(x,y,t) ]d[t] ]

div[ E_{e}(x,y,t) ]+2·(1/c)·B_{e}(x,y,t) = 0^{2}

div[ E_{e}(x,y,t) ] = (-2)·(1/c)·B_{e}(x,y,t)

Ley: [ del calor gravito-magnético ]

div[ E_{g}(x,y,t) ] = (-2)·(1/c)·B_{g}(x,y,t)

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = (-2)·(1/c)·d_{t}[u(x,y,t)]

u(x,y,0) = H(ax,ay)

u(x,y,(1/u)) = K(ax,ay)

u(x,y,t) = ( (1+(-1)·ut)·H(ax,ay)+ut·K(ax,ay) || 1 )·e^{ax+ay+(-1)·act || 0}

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = 2·(1/c)·d_{t}[u(x,y,t)]

u(x,y,0) = H(ax,ay)

u(x,y,(1/u)) = K(ax,ay)

u(x,y,t) = ( (1+(-1)·ut)·H(ax,ay)+ut·K(ax,ay) || 1 )·e^{ax+ay+act || 0}

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = (-2)·(1/c)·d_{t}[u(x,y,t)]

u(0,0,t) = f(ut)

u(p,q,t) = g(ut)

u(x,y,t) = ...

... ( (1/2)·( (1+(-1)·(x/p))·f(ut)+(1+(-1)·(y/q))·f(ut) )+(1/2)·( (x/p)·g(ut)+(y/q)·g(ut) ) || 1 )·...

... e^{ax+ay+(-1)·act || 0}

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = 2·(1/c)·d_{t}[u(x,y,t)]

u(0,0,t) = f(ut)

u(p,q,t) = g(ut)

u(x,y,t) = ...

... ( (1/2)·( (1+(-1)·(x/p))·f(ut)+(1+(-1)·(y/q))·f(ut) )+(1/2)·( (x/p)·g(ut)+(y/q)·g(ut) ) || 1 )·...

... e^{ax+ay+act || 0}

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = (-2)·(1/c)·d_{t}[u(x,y,t)]

u(0,q,t) = f(ut)

u(p,0,t) = g(ut)

u(x,y,t) = ?

Teorema:

d_{x}[u(x,y,t)]+d_{y}[u(x,y,t)] = 2·(1/c)·d_{t}[u(x,y,t)]

u(0,q,t) = f(ut)

u(p,0,t) = g(ut)

u(x,y,t) = ?

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = H(ax,ay)

d_{t}[u(x,y,0)] = 0

u(x,y,t) = ...

... (1/2)·( e^{ax+ay+ac·it || ln( H(ax,ay) )+act}+e^{ax+ay+ac·it || ln( H(ax,ay) )+(-1)·act} )

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = H(ax,ay)

d_{t}[u(x,y,0)] = 0

u(x,y,t) = ...

... (1/2)·( e^{ax+ay+act || ln( H(ax,ay) )+act}+e^{ax+ay+act || ln( H(ax,ay) )+(-1)·act} )

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(0,y,0) = F(ay)

u(r,y,0) = G(ay)

d_{t}[u(x,y,0)] = 0

u(x,y,t) = ?

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(0,y,0) = F(ay)

u(r,y,0) = G(ay)

d_{t}[u(x,y,0)] = 0

u(x,y,t) = ?

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = 0

d_{t}[u(x,y,0)] = h(ax,ay)

u(x,y,t) = (1/2)·sum[k = 1]-[oo][ ...

... int[h(ax,ay)+(-1)·act·0 || (4t)^{(1/2)}]-[h(ax,ay)+act·0 || (4t)^{(1/2)}][ w ]d[w] ]·e^{ax+ay+ac·it || 0}

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = 0

d_{t}[u(x,y,0)] = h(ax,ay)

u(x,y,t) = (1/2)·sum[k = 1]-[oo][ ...

... int[h(ax,ay)+(-1)·act·0 || (4t)^{(1/2)}]-[h(ax,ay)+act·0 || (4t)^{(1/2)}][ w ]d[w] ]·e^{ax+ay+act || 0}

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = (-2)·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = 0

d_{t}[u(0,y,0)] = ac·f(ay)

d_{t}[u(r,y,0)] = ac·g(ay)

u(x,y,t) = ?

Teorema:

d_{xx}^{2}[u(x,y,t)]+d_{yy}^{2}[u(x,y,t)] = 2·(1/c)^{2}·d_{tt}^{2}[u(x,y,t)]

u(x,y,0) = 0

d_{t}[u(0,y,0)] = ac·f(ay)

d_{t}[u(r,y,0)] = ac·g(ay)

u(x,y,t) = ?

Motores a combustión de explosión acotada:

Ley:

Sea d[I_{c}] = (1/s)^{2}·Mrv·d[t] ==>

Si (I_{c}/2)·d_{t}[w]^{2} = qgh·cos(ut) ==>

x(t) = (M/(md))·(1/s)^{2}·rvt

w(t) = (1/u)·( 2qgh·(1/(Mrv))·us^{2}·( ln(ut) [o(ut)o] sin(ut) ) )^{[o(ut)o] (1/2)}

(1/u) [< t [< (pi/u)

Ley:

Sea d[I_{c}] = (1/s)^{2}·Mrgt·d[t] ==>

Si (I_{c}/2)·d_{t}[w]^{2} = qgh·sin(ut) ==>

x(t) = (M/(md))·(1/s)^{2}·rg·(1/2)·t^{2}

w(t) = (1/u)·( 4qgh·(1/(Mrg))·(us)^{2}·( (1/(ut)) [o(ut)o] cos(ut) ) )^{[o(ut)o] (1/2)}

(1/u) [< t [< (pi/(2u))

Teorema:

( cos(w) )^{4}+(-1)·( sin(w) )^{4}+i·sin(2w) = e^{2iw}

Teorema:

( cos(w) )^{4}+( sin(w) )^{4}+(1/2)·( sin(2w) )^{2} = 1

Ley:

Sea ( d_{t}[ I_{cx} ] = 0 & d_{t}[ I_{cy} ] = 0 ) ==>

Si d[ d[M(t)] ] = qg·(1/s)^{2}·sin(nw)·cos(nw)·d[x]d[w] ==>

M(t) = qg·(x/n)·(1/s)^{2}·(1/2)·( sin(nw) )^{2}

(I_{c}/2)·d_{t}[w]^{2} = qgx·(1/(ns))^{2}·(1/4)·( nw+(-1)·(1/2)·sin(2nw) )

x(t) = I_{c}·(1/(md))

w(t) = (1/n)·Anti-[ ( s /o(s)o/ ( (1/4)·s^{2}+(1/8)·cos(2s) ) )^{[o(s)o](1/2)}]-( ...

... ( (1/(md))·qg )^{(1/2)}·(1/s)·t )

Ley:

Sea d_{t}[ I_{c} ] = 0 ==>

Si d[ d[M(t)] ] = I_{c}·u^{2}·(1/x)·sin(nw)·cos(nw)·d[x]d[w] ==>

M(t) = I_{c}·u^{2}·ln(ax)·(1/n)·(1/2)·( sin(nw) )^{2}

(I_{c}/2)·d_{t}[w]^{2} = I_{c}·u^{2}·ln(ax)·(1/n)^{2}·(1/4)·( nw+(-1)·(1/2)·sin(2nw) )

x(t) = I_{c}·(1/(md))

w(t) = (1/n)·Anti-[ ( s /o(s)o/ ( (1/4)·s^{2}+(1/8)·cos(2s) ) )^{[o(s)o](1/2)}]-( ...

... ( ln( aI_{c}·(1/md) ) )^{(1/2)}·ut )

Ecuaciones de densidades:

Leyes de agua y aceite:

Ley: 

d_{x}[u(x,y)]+d_{y}[u(x,y)] = (m/V)·xy

u(0,y) = m·F(ay)

u(r,y) = m·G(ay)

u(x,y) = ( (1+(-1)·(x/r))·F(ay)+(x/r)·G(ay) || 1 )·( (m/(4V))·yx^{2} || (m/(4V))·xy^{2} || m )

Ley:

d_{x}[u(x,y)]+d_{y}[u(x,y)] = (-V)·m·( 1/(xy) )^{2}

u(x,0) = m·F(ax)

u(x,r) = m·G(ax)

u(x,y) = ( (1+(-1)·(y/r))·F(ax)+(y/r)·G(ax) || 1 )·( (V/2)·( m/(xy^{2}) ) || (V/2)·( m/(yx^{2}) ) || m )

Ley: [ de ola de mar ]

d_{x}[u(x,y)]+d_{y}[u(x,y)] = m·(1/a)·(1/(xy))

u(0,y) = m·F(ay)

u(r,y) = m·G(ay)

u(x,y) = ( (1+(-1)·(x/r))·F(ay)+(x/r)·G(ay) || 1 )·( (1/2)·(m/(ay))·ln(ax) || (1/2)·(m/(ax))·ln(ay) || m )

Ley: 

d_{x}[u(x,y)]+d_{y}[u(x,y)]+a·u(x,y) = (m/V)·xy

u(0,y) = m·F(ay)

u(r,y) = m·G(ay)

u(x,y) = ( (1+(-1)·(x/r))·F(ay)+(x/r)·G(ay) || 1 )·....

... ( (m/(6V))·yx^{2} || (m/(6V))·xy^{2} || (1/(3V))·(m/a)·xy || m )

Ley:

d_{x}[u(x,y)]+d_{y}[u(x,y)]+a·u(x,y) = (-V)·m·( 1/(xy) )^{2}

u(x,0) = m·F(ax)

u(x,r) = m·G(ax)

u(x,y) = ( (1+(-1)·(y/r))·F(ax)+(y/r)·G(ax) || 1 )·...

... ( (V/3)·( m/(xy^{2}) ) || (V/3)·( m/(yx^{2}) ) || (-1)·(V/3)·(m/a)·( 1/(xy) )^{2} || m )

Arte:

Sea u(x) = e^{(-x)} ==>

[Ax][ f(a)·(1/u)^{0} = f(a) ]

[Ex][ (-1)^{k}·(k+(-1))!·d_{a...a}^{k}[f(a)]·(1/u)^{k} = d_{a...a}^{k}[f(a)] ]

Exposición:

x = (-1)·(1/k)·ln( (-1)^{k}·(k+(-1))! )

Sea z(x) = e^{(-x)}+a ==>

Sea u(x) = e^{(-x)} ==>

d[u] = d[z]

s(u) = 1

d[u] = d[s(u)] = d[1] ==>

Caso 1:

int[x = 0]-[1][ f(a)/(a+(-z)) ]d[z] = int-int[ (-1)·d_{a}[f(a)]·(1/u) ]d[u]d[a] = f(a)

int[ (-1)·d_{a}[f(a)]·(1/u) ]d[u] = d_{a}[f(a)]

(-1)·d_{a}[f(a)]·(1/z) = d_{a}[f(a)]

Caso 2:

int-int[x = 0]-[1][ f(a)/(a+(-z))^{2} ]d[z]d[z] = ...

... int-int-int-int[ d_{aa}^{2}[f(a)]·(1/u)^{2} ]d[u]d[u]d[a]d[a] = f(a)

int-int[ d_{aa}^{2}[f(a)]·(1/u)^{2} ]d[u]d[u] = d_{aa}^{2}[f(a)]

d_{aa}^{2}[f(a)]·(1/z)^{2} = d_{aa}^{2}[f(a)]

Caso 3:

int-int-int[x = 0]-[1][ 2·f(a)/(a+(-z))^{3} ]d[z]d[z]d[z] = ...

... int-int-int-int-int-int[ (-1)·2·d_{aaa}^{2}[f(a)]·(1/u)^{3} ]d[u]d[u]d[u]d[a]d[a]d[a] = f(a)

int-int-int[ (-1)·2·d_{aaa}^{3}[f(a)]·(1/u)^{3} ]d[u]d[u]d[u] = d_{aaa}^{3}[f(a)]

(-1)·2·d_{aaa}^{3}[f(a)]·(1/u)^{3} = d_{aaa}^{3}[f(a)]

Artes: [ de series de Laurent ]

Sea z(x) = e^{(-x)} ==>

Exposición:

x = 0

Arte:

[Ex][ e^{x} = 1+sum[k = 1]-[oo][ (-1)^{k}·(1/k)·( xe^{x} )^{k} ] ]

[Ex][ e^{(-x)} = 1+sum[k = 1]-[oo][ (1/k)·( xe^{(-x)} )^{k} ] ]

Arte:

[Ex][ ( 1/(1+(-x)) ) = 1+sum[k = 1]-[oo][ k!·(1/k)·( xe^{(-x)} )^{k} ] ]

[Ex][ (-1)·( 1/(1+(-x))^{2} ) = (-1)+sum[k = 1]-[oo][ (-1)^{k+1}·(k+1)!·(1/k)·( xe^{(-x)} )^{k} ] ]

Arte:

[Ex][ e-pos[m](x) = m+sum[k = 1]-[oo][ (-1)^{k}·( 1+m·(1/k) )·( xe^{x} )^{k} ] ]

[Ex][ e-neg[m](x) = (-m)+sum[k = 1]-[oo][ (-1)^{k}·( 1+(-m)·(1/k) )·( xe^{x} )^{k} ] ]

Arte:

[Ex][ octopus(x) = 1+sum[k = 1]-[oo][ (-1)^{k}·(k+1)!·(1/k)·( xe^{x} )^{k} ] ]

[Ex][ d_{x}[ octopus(x) ] = 2+sum[k = 1]-[oo][ (-1)^{k}·(k+2)!·(1/k)·( xe^{x} )^{k} ] ]

Arte:

[Ex][ ln(1+x) = (-x)·e^{x}+sum[k = 2]-[oo][ (-1)·k!·(1/k)^{2}·( xe^{x} )^{k} ] ]

[Ex][ ln(1+(-x)) = xe^{(-x)}+sum[k = 2]-[oo][ (-1)^{k+1}·k!·(1/k)^{2}·( xe^{(-x)} )^{k} ] ]

(-0) = 0 = ln(1+0) = ln(1)

Enfermedad de centro de dos mandamientos duales a densidad de carga constante:

Ley:

d_{x}[f(x)] = qaie^{axi}

d_{x}[g(x)] = (-1)·qaie^{(-1)·ayi}

s(y) = x

Robar la intimidad,

sin conexión de luz eléctrica:

No puede duchar-se con cortina opaca.

Ley:

d_{x}[f(x)] = iqa·cos(ax)

d_{x}[g(x)] = (-1)·qa·sin(ax)

f(x)+g(x) = qe^{axi}

Robar la libertad,

sin conexión de luz eléctrica:

No puede salir lloviendo o nublado.

Ley:

d_{x}[f(x)] = (-i)·qa·cos(ax)

d_{x}[g(x)] = (-1)·qa·sin(ax)

f(x)+g(x) = qe^{(-1)·axi}

Terapia con constructor:

Ley:

d_{x}[f(x)] = qae^{ax}

d_{x}[g(x)] = (-1)·qae^{(-1)·ay}

s(y) = x

No robar la intimidad,

con visita de algoritmo interno:

Ley:

d_{x}[f(x)] = qa·cosh(ax)

d_{x}[g(x)] = qa·sinh(ax)

f(x)+g(x) = qe^{ax}

No robar la libertad,

con visita de algoritmo externo:

Ley:

d_{x}[f(x)] = (-1)·qa·cosh(ax)

d_{x}[g(x)] = qa·sinh(ax)

f(x)+g(x) = qe^{(-1)·ax}

Enfermedad de centro de dos mandamientos duales a densidad de carga variable:

Ley:

d_{x}[f(x)] = d_{x}[q(x)]·ie^{axi}

d_{x}[g(x)] = (-1)·d_{x}[q(x)]·ie^{(-1)·ayi}

s(y) = x

Deducción:

int[ d_{x}[q(x)] ]d[x] [o(x)o] int[ ie^{axi} ]d[x] = int[ d_{x}[q(x)] ]d[x] [o(ax)o] int[ ie^{axi} ]d[ax]

Ley:

d_{x}[f(x)] = i·d_{x}[q(x)]·cos(ax)

d_{x}[g(x)] = (-1)·d_{x}[q(x)]·sin(ax)

f(x)+g(x) = q(x) [o(ax)o] e^{axi}

Ley:

d_{x}[f(x)] = (-i)·d_{x}[q(x)]·cos(ax)

d_{x}[g(x)] = (-1)·d_{x}[q(x)]·sin(ax)

f(x)+g(x) = q(x) [o(ax)o] e^{(-1)·axi}

Terapia con constructor:

Ley:

d_{x}[f(x)] = d_{x}[q(x)]·e^{ax}

d_{x}[g(x)] = (-1)·d_{x}[q(x)]·e^{(-1)·ay}

s(y) = x

Ley:

d_{x}[f(x)] = d_{x}[q(x)]·cosh(ax)

d_{x}[g(x)] = d_{x}[q(x)]·sinh(ax)

f(x)+g(x) = q(x) [o(ax)o] e^{ax}

Ley:

d_{x}[f(x)] = (-1)·d_{x}[q(x)]·cosh(ax)

d_{x}[g(x)] = d_{x}[q(x)]·sinh(ax)

f(x)+g(x) = q(x) [o(ax)o] e^{(-1)·ax}

Principio: [ de oftalmología de imagen y sonido ]

Vista sana:

d_{x}[q( (pi/(2a)) )]·d_{y}[p( (-1)·(pi/(2a)) )]+d_{x}[p( (pi/a) )]·d_{y}[q( (0/a) )] = pqa^{2}

Oída sana:

d_{x}[q( (pi/(2a))·i )]·d_{y}[p( (-1)·(pi/(2a))·i )]+d_{x}[p( (pi/a)·i )]·d_{y}[q( (0/a)·i )] = pqa^{2}

Principio: [ de definición de lentes ]

Lentes de Miopía:

f(ax) = (-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

Lentes de Hipermetropía:

g(ay) = ( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

Ley: [ de gafas de miopía ]

q(x) = qe^{(-1)·(1/(n+1))·(ax)^{n+1} [o(ax)o] sin(ax) [o(ax)o] f(ax)} = qe^{sin(ax)}

p(x) = pe^{(-1)·(1/(n+1))·(ax)^{n+1} [o(ax)o] cos(ax) [o(ax)o] f(ax)} = pe^{cos(ax)}

Ley: [ de gafas de hipermetropía ]

p(y) = pe^{(1/(n+1))·(ay)^{n+1} [o(ay)o] sin(ay) [o(ay)o] g(ay)} = pe^{sin(ay)}

q(y) = qe^{(1/(n+1))·(ay)^{n+1} [o(ay)o] cos(ay) [o(ay)o] g(ay)} = qe^{cos(ay)}

Ley: [ de sonotone de miopía ]

q(x) = qe^{(-1)·(1/(n+1))·(ax)^{n+1} [o(ax)o] sinh(ax) [o(ax)o] f(ax)} = qe^{sinh(ax)}

p(x) = pe^{(-1)·(1/(n+1))·(ax)^{n+1} [o(ax)o] i·cosh(ax) [o(ax)o] f(ax)} = pe^{i·cosh(ax)}

Ley: [ de sonotone de hipermetropía ]

p(y) = pe^{(1/(n+1))·(ay)^{n+1} [o(ay)o] sinh(ay) [o(ay)o] g(ay)} = pe^{sinh(ay)}

q(y) = qe^{(1/(n+1))·(ay)^{n+1} [o(ay)o] i·cosh(ay) [o(ay)o] g(ay)} = qe^{i·cosh(ay)}

Principio: [ de ecuación de la lente ]

Miopía:

d_{z}[f(z,x)]+d_{x}[f(z,x)] = d_{z}[p(z)]+a·(-1)·(1/(ax))^{n}

f(z,x) = p(z)+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

Hipermetropía:

d_{z}[g(z,y)]+d_{y}[g(z,y)] = d_{z}[q(z)]+a·(1/(ay))^{n}

g(z,y) = q(z)+( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

Ley:

d_{z}[f(z,x)]+d_{x}[f(z,x)] = a·( 1+(-1)·(1/(ax))^{n} )

f(z,x) = az+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

d_{z}[g(z,x)]+d_{x}[g(z,x)] = a·( 1+(1/(ax))^{n} )

g(z,x) = az+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

f(z,x)+g(z,x) = n·(n+1) <==> z = (1/(2a))·n·(n+1)

Si n = 2k ==> (1/2)·n·(n+1) € N

Si n = 2k+1 ==> (1/2)·n·(n+1) € N

Deducción:

d_{z}[f(z,x)] = d_{z}[ az+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... d_{z}[ az ]+d_{z}[ (-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... d_{z}[az]+0 = d_{z}[az] = a·d_{z}[z] = a

d_{x}[f(z,x)] = d_{x}[ az+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... d_{x}[ az ]+d_{x}[ (-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... 0+d_{x}[ (-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... d_{x}[ (-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... a·d_{ax}[ (-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = ...

... a·(-1)·d_{ax}[ ( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} ) ] = a·(-1)·(1/(ax))^{n}

Ley:

d_{z}[f(z,y)]+d_{y}[f(z,y)] = a·( 2+(-1)·(1/(ay))^{n} )

f(z,y) = 2az+(-1)·( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

d_{z}[g(z,y)]+d_{y}[g(z,y)] = a·( 2+(1/(ay))^{n} )

g(z,y) = 2az+( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

( f(z,y)+g(z,y) )^{(1/2)} = n·(n+1) <==> z = (1/(4a))·n^{2}·(n^{2}+2n+1)

Si n = 2k ==> (1/4)·n^{2}·(n^{2}+2n+1) € N

Si n = 2k+1 ==> (1/4)·n^{2}·(n^{2}+2n+1) € N

Deducción:

Si n = 2k+1 ==>

(n^{2}+2n+1) = (n+1)^{2} = (2k+2)^{2} = 4k^{2}+4k+4 = 4·(k^{2}+k+1)

Ley:

d_{z}[f(z,x)]+d_{x}[f(z,x)] = a·( (1/(az))+(-1)·(1/(ax))^{n} )

f(z,x) = ln(az)+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

d_{z}[g(z,x)]+d_{x}[g(z,x)] = a·( (-1)·( 1/(1+(-1)·(az)) )+(-1)·(1/(ax))^{n} )

g(z,x) = ln(1+(-1)·(az))+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

f(z,x) = g(z,x) <==> z = (1/(2a))

Deducción:

ln(az) = ln(1+(-1)·(az))

az = 1+(-1)·(az)

2az = 1

z = (1/(2a))

Ley:

d_{z}[f(z,y)]+d_{y}[f(z,y)] = a·( (1/2)·(1/(az))+(1/(ay))^{n} )

f(z,y) = (1/2)·ln(az)+( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

d_{z}[g(z,y)]+d_{y}[g(z,y)] = a·( (-1)·( 1/((3/4)+(-1)·(az)) )+(1/(ay))^{n} )

g(z,y) = ln((3/4)+(-1)·(az))+( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

f(z,y) = g(z,y) <==> ( z = (1/(4a)) con raíz positiva  || z = (9/(4a)) con raíz negativa )

Deducción:

(1/2)·ln(az) = ln((3/4)+(-1)·(az))

(az)^{(1/2)} = (3/4)+(-1)·(az)

az = (9/16)+(-1)·(3/2)·az+(az)^{2}

0 = (9/16)+(-1)·(5/2)·az+(az)^{2}

az = (1/2)·( (5/2)+(-1)·( (25/4)+(-1)·(9/4) )^{(1/2)} ) = (1/2)·( (5/2)+(-2) ) = (1/4)

z = (1/(4a))

az = (1/2)·( (5/2)+( (25/4)+(-1)·(9/4) )^{(1/2)} ) = (1/2)·( (5/2)+2 ) = (9/4)

z = (9/(4a))

Principio: [ de refracción de la lente ]

sin(arw)+(-1)·cos(ars) = sw·(k+(-j))

(-1)·sin(arw)+cos(ars) = sw·(j+(-k))

w = (pi/2) <==> s = 0

w = 0 <==> s = (pi/2)

Ley:

Si k = j ==> sin(arw) = cos(ars)

Si j = k ==> cos(ars) = sin(arw)

Deducción:

sin(arw)+(-1)·cos(ars) = sw·(k+(-j)) = sw·(k+(-k)) = sw·0

sin(arw) = sin(arw)+0 = sin(arw)+( (-1)·cos(ars)+cos(ars) ) = ( sin(arw)+(-1)·cos(ars) )+cos(ars) = ...

... sw·0+cos(ars) = cos(ars)

Ley:

d_{rw}[f(w,x)]+d_{x}[f(w,x)] = a·( cos(arw)+(-1)·(1/(ax))^{n} )

f(w,x) = sin(arw)+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

d_{rs}[g(s,x)]+d_{x}[g(s,x)] = a·( sin(ars)+(1/(ax))^{n} )

g(s,x) = (-1)·cos(ars)+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

f(w,x)+g(s,x) = sw·(k+(-j))

Ley:

d_{rw}[f(w,y)]+d_{y}[f(w,y)] = a·( (-1)·cos(arw)+(1/(ay))^{n} )

f(w,y) = (-1)·sin(arw)+( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

d_{rs}[g(s,y)]+d_{y}[g(s,y)] = a·( (-1)·sin(ars)+(-1)·(1/(ay))^{n} )

g(s,y) = cos(ars)+(-1)·( ay /o(ay)o/ (1/(n+1))·(ay)^{n+1} )

f(w,y)+g(s,y) = sw·(j+(-k))

Óptica de miopía de imagen:

Sea n la dioptría ==>

d_{x}[q(x)] = (-1)·q(x)·cos(ax)·a·(ax)^{n}

d_{x}[p(x)] = p(x)·sin(ax)·a·(ax)^{n}

Operación Láser de longitud de onda x = rojo 

f(x) = e^{( ( 1/(n+1) )·(ax)^{n+1}+ax ) [o(ax)o] sin(ax) }

g(x) = e^{( ( 1/(n+1) )·(ax)^{n+1}+ax ) [o(ax)o] cos(ax) }

Óptica de hipermetropía de imagen:

Sea n la dioptría ==>

d_{y}[p(y)] = p(y)·cos(ay)·a·(ay)^{n}

d_{y}[q(y)] = (-1)·q(y)·sin(ay)·a·(ay)^{n}

Operación Láser de longitud de onda y = verde 

f(y) = e^{( (-1)·( 1/(n+1) )·(ay)^{n+1}+ay ) [o(ay)o] sin(ay) }

g(y) = e^{( (-1)·( 1/(n+1) )·(ay)^{n+1}+ay ) [o(ay)o] cos(ay) }

Óptica de miopía de sonido:

Sea n la dioptría ==>

d_{x}[q(x)] = (-1)·q(x)·cosh(ax)·a·(ax)^{n}

d_{x}[p(x)] = (-i)·p(x)·sinh(ax)·a·(ax)^{n}

Operación Láser de longitud de onda x = rojo 

f(x) = e^{( ( 1/(n+1) )·(ax)^{n+1}+ax ) [o(ax)o] sinh(ax) }

g(x) = e^{( ( 1/(n+1) )·(ax)^{n+1}+ax ) [o(ax)o] i·cosh(ax) }

Óptica de hipermetropía de sonido:

Sea n la dioptría ==>

d_{y}[p(y)] = p(y)·cosh(ay)·a·(ay)^{n}

d_{y}[q(y)] = i·q(y)·sinh(ay)·a·(ay)^{n}

Operación Láser de longitud de onda y = verde 

f(y) = e^{( (-1)·( 1/(n+1) )·(ay)^{n+1}+ay ) [o(ay)o] sinh(ay) }

g(y) = e^{( (-1)·( 1/(n+1) )·(ay)^{n+1+ay ) [o(ay)o] i·cosh(ay) }

Catarata de miopía de imagen:

d_{x}[q(x)] = (-1)·q(x)·cos(ax)·a·(ax)^{10}

d_{x}[p(x)] = p(x)·sin(ax)·a·(ax)^{10}

Operación Láser de longitud de onda x = rojo

f(x) = e^{( (1/11)·(ax)^{11}+ax ) [o(ax)o] sin(ax) }

g(x) = e^{( (1/11)·(ax)^{11}+ax ) [o(ax)o] cos(ax) }

Catarata de hipermetropía de imagen ( ceguera ):

d_{y}[p(y)] = p(y)·cos(ay)·a·(ay)^{10}

d_{y}[q(y)] = (-1)·q(y)·sin(ay)·a·(ay)^{10}

Operación Láser de longitud de onda y = verde 

f(y) = e^{( (-1)·(1/11)·(ay)^{11}+ay ) [o(ay)o] sin(ay) }

g(y) = e^{( (-1)·(1/11)·(ay)^{11}+ay ) [o(ay)o] cos(ay) }

Ley: [ de Grado en Medicina Teoría Homologada ]

Matemáticas 1: Cálculo diferencial.

Química.

Matemáticas 2: Cálculo integral.

Física: Termodinámica y Cabal sanguíneo.

Espectroscopia de fluido corporal.

Teoría genética de infecciones víricas.

Teoría genética de infecciones bacteria-lógicas.

Quimioterapia de desintegración genética.

Óptica de imagen y sonido.

Psico-neurología de negación de voces esquizofrénicas.

Psico-neurología de doble mandamiento dual.

Neurología de resonancia eléctrica.

Neurología de anti-resonancia eléctrica.

Ley:

Un familiar de un matemático o físico tiene convalidada la teoría de medicina,

porque tiene ya la energía para esas o aquellas medicaciones que se derivan de la teoría,

y solo le faltan las asignaturas de practica de atención y cirugía.

Termodinámica de Medicina:

Fiebre y Termómetro:

Ley:

PV = kT

d_{P}[T(P,V)]·p = qR <==> p = ?

d_{V}[T(P,V)]·v = qR <==> v = ?

Ley:

d_{V}[P_{0}]·V^{2}+d_{P}[V_{0}]·P^{2} = kT

d_{P}[T(P,V)]·p = qR <==> p = ?

d_{V}[T(P,V)]·v = qR <==> v = ?

Ley:

d_{V}[P_{0}]·V^{2}+d_{P}[V_{0}]·P^{2} = kT

d_{PP}^{2}[T(P,V)]·p^{2} = qR <==> p = ?

d_{VV}^{2}[T(P,V)]·v^{2} = qR <==> v = ?

Ley:

PV = d_{T}[k]·T^{2}

d_{P}[T(P,V)]·p = qR <==> p = ?

d_{V}[T(P,V)]·v = qR <==> v = ?

Deducción:

d_{P}[T(P,V)] = d_{P}[ ( ( 1/d_{T}[k] )·PV )^{(1/2)} ] = ...

... (1/2)·( ( 1/d_{T}[k] )·PV )^{(-1)·(1/2)}·( V/d_{T}[k] )