arte-matemático y medicina y falsus-infinitorum y falsus-algebratorum y números-irracionales y computación

Arte:

[En][ ( n+(1/(n+1)) ) [< (3/2) ]

Exposición:

n = 1

f(n) = 0

1 = ( f(n)+(1/(f(n)+1)) ) = ( n+(1/(n+1)) ) < (3/2)

Arte:

[En][ ( 2n+(1/(2n+1)) ) [< (7/3) ]

Traumatología vertebral:

Principio:

Amisnostrofia resistiva:

[ER][ R(t) >] 1 & W = R(t)·d_{t}[q] ]

Principio:

Aminostrofia condensativa:

[EC][ 0 [< C(t) [< 1 & W = C(t)·q(t) ]

Traumatología sanguínea:

Principio:

Trompo de colesterol:

Sea K es cabal sanguíneo ==>

[ES][ S(t) >] 1 & K = S(t)·d_{t}[x] ]

Principio:

Trompo de obstrucción de arteria:

Sea K es cabal sanguíneo ==>

[ES][ S(t) >] 1 & K = S(t)·ux ]

Oncología de transporte de intestino:

Principio:

Flojura de estómago:

Sea d_{xyz}^{3}[m(x,y,z,t)] la densidad del cagado ==>

[EM][ (M(t)/K) = int[ d_{xyz}^{3}[m(x,y,z,t)] ]d[t] ]

Principio:

Dureza de riñón:

Sea d_{xyz}^{3}[m(x,y,z,t)] la densidad del pijado ==>

[EM][ (M(t)/K) = int[ d_{xyz}^{3}[m(x,y,z,t)] ]d[t] ]

Ley:

Sea d_{xyz}^{3}[m(x,y,z,t)] = ma^{3} ==>

M(t) = mKa^{3}·t

m(x,y,z,t) = maxayaz

Ley:

Sea t >] (1/u) ==>

Si ( ( Si vt >] 1 ( retortijón ) ==> z(t) = vt ) & d_{xyz}^{3}[m(x,y,z,t)] = ma^{2}·(1/z)·(ut) ) ==>

M(t) = mKa^{2}·(1/v)·(ut)

m(x,y,z,t) = maxay·(ut)

Deducción:

d[z] = v·d[t]

d[x]d[y]d[z] = v·d[x]d[y]d[t]

Ley:

Sea t >] (1/u) ==>

Si ( ( Si vt >] 1 ( retortijón ) ==> z(t) = vt ) & d_{xyz}^{3}[m(x,y,z,t)] = ma^{4}·z·(1/(ut)) ) ==>

M(t) = mKa^{4}·v·(1/u)·t

m(x,y,z,t) = maxay·(av)^{2}·(1/u)·t

Deducción:

d[z] = v·d[t]

d[x]d[y]d[z] = v·d[x]d[y]d[t]

Ley:

Sea t >] (1/u) ==>

Si ( ( Si vt >] 1 ==> z(t) = vt ) & d_{xyz}^{3}[m(x,y,z,t)] = ma^{2}·(1/z)·(1/2)·(1+(ut)) ) ==>

M(t) = mKa^{2}·(1/(2v))·( ln(ut)+ut )

m(x,y,z,t) = maxay·(1/2)·( ln(ut)+ut )

Ley:

Sea t >] (1/u) ==>

Si ( ( Si vt >] 1 ==> z(t) = vt ) & d_{xyz}^{3}[m(x,y,z,t)] = ma^{4}·2z·( 1/(1+(ut)) ) ) ==>

M(t) = mKa^{4}·((2v)/u)·( ln(1+ut) [o(ut)o] (1/2)·(ut)^{2} )

m(x,y,z,t) = maxay·2·(av)^{2}·(1/u)^{2}·( ln(1+ut) [o(ut)o] (1/2)·(ut)^{2} )

Teoría del Falsus Infinitorum:

Axioma:

Si [Ej][ lim[n = j][ a_{n} ] = a & f(j) = m & g(m) = oo ] ==> ¬( lim[n = g(f(j))][ a_{n} ] = a )

Teoría del Falsus Algebratorum:

Axioma:

Si [Aj][ lim[n = j][ a_{n} ] != a & f(j) = m & g(m) = oo ] ==> ¬( lim[n = g(f(j))][ a_{n} ] = a )

Euler Falsus Infinitorum:

Arte:

sum[k = 0]-[oo][ ( 1/(k+1) )^{m} ] = (1/2)^{m}

Exposición:

lim[n = 1][ sum[k = 0]-[n][ ( 1/(k+1) )^{m} ]+(-1)·(1/n) ] = 1+(1/2)^{m}+(-1) = (1/2)^{m}

Arte:

sum[k = 1]-[oo][ ( 1/ln(k+1) )^{m}+(-1)·(1/k) ] = ( 1/ln(2) )^{m}

Exposición:

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

... ( 1/ln(2) )^{m}+(-1)+1 = ( 1/ln(2) )^{m}

Arte:

sum[k = 1]-[oo][ ( ln((1/k)+1) )^{m}+(-1)·(1/k) ] = ( ln(2) )^{m}

Exposición:

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

... ( ln(2) )^{m}+(-1)+1 = ( ln(2) )^{m}

Arte:

Prod[k = 1]-[oo][ (1/(2p))^{k}+( 1/(k+1) )^{m} ] = (1/p)+(1/2)^{m+(-1)}

Exposición:

lim[n = 1][ Prod[k = 1]-[n][ (1/(2p))^{k}+( 1/(k+1) )^{m} ]·(1+(1/n)) ] = ...

... ( (1/(2p))+(1/2)^{m} )·2 = (1/p)+(1/2)^{m+(-1)}

Arte:

Prod[k = 0]-[oo][ (1/(4p))^{k}+( 1/(k+1) )^{m} ] = (1/p)+(1/2)^{m+(-2)}

Exposición:

lim[n = 1][ Prod[k = 0]-[n][ (1/(4p))^{k}+( 1/(k+1) )^{m} ]·(1+(1/n)) ] = ...

... ( (1/(4p))+(1/2)^{m} )·4 = (1/p)+(1/2)^{m+(-2)}

Arte:

Prod[k = 1]-[oo][ m·( 1/(k+1) ) ] = m

Exposición:

lim[n = 1][ Prod[k = 1]-[n][ m·( 1/(k+1) ) ]·(1+(1/n)) ] = ( m·(1/2) )·2 = m

Arte:

Prod[k = 0]-[oo][ m·( 1/(k+1) ) ] = m^{2}

Exposición:

lim[n = 1][ Prod[k = 0]-[n][ m·( 1/(k+1) ) ]·(1+(1/n)) ] = m·( m·(1/2) )·2 = m^{2}

Ramanujan Falsus Infinitorum:

Arte:

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

Z(2)·sum[k = 1]-[oo][ 17·(1/k)^{2}+(-11)·(1/k)^{3} ]·(1/13) = pi^{2}

Exposición:

lim[n = 1][ Z(2)·sum[k = 1]-[n][ 17·(1/k)^{2}+(-11)·(1/k)^{3} ]·(1/13)+(12/13)·(1/n)·pi^{2} ] = ...

... Z(2)·(6/13)+(12/13)·pi^{2} = pi^{2}

Arte:

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

Z(2)·sum[k = 1]-[oo][ 47·(1/k)^{2}+(-41)·(1/k)^{3} ]·(1/43) = pi^{2}

Exposición:

lim[n = 1][ Z(2)·sum[k = 1]-[n][ 47·(1/k)^{2}+(-41)·(1/k)^{3} ]·(1/43)+(42/43)·(1/n)·pi^{2} ] = ...

... Z(2)·(6/43)+(42/43)·pi^{2} = pi^{2}

Arte:

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

Z(4)·sum[k = 1]-[oo][ 113·(1/k)^{4}+(-23)·(1/k)^{5} ]·(61/71) = pi^{4}

Exposición:

lim[n = 1][ Z(4)·sum[k = 1]-[n][ 113·(1/k)^{4}+(-23)·(1/k)^{5} ]·(61/71)+(10/71)·(1/n)·pi^{4} ] = ...

... Z(4)·90·(61/71)+(10/71)·pi^{4} = pi^{4}

Arte:

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

Z(4)·sum[k = 1]-[oo][ 101·(1/k)^{4}+(-11)·(1/k)^{5} ]·(43/73) = pi^{4}

Exposición:

lim[n = 1][ Z(4)·sum[k = 1]-[n][ 101·(1/k)^{4}+(-11)·(1/k)^{5} ]·(43/73)+(30/73)·(1/n)·pi^{4} ] = ...

... Z(4)·90·(43/73)+(30/73)·pi^{4} = pi^{4}

Arte:

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

Z(2)·sum[k = 1]-[oo][ ( (4k)!/k! )·( (53k+1)/216^{k} ) ]·(17/71) = pi^{2}

Exposición:

lim[n = 1][ Z(2)·sum[k = 1]-[n][ ( (4k)!/k! )·( (53k+1)/216^{k} ) ]·(17/71)+...

... (54/71)·(1/n)·pi^{2} ] = Z(2)·4!·54·(1/(4·54))·(17/71)+(54/71)·pi^{2} = pi^{2}

Arte:

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

Z(2)·sum[k = 1]-[oo][ ( (4k)!/k! )·( (73k+(-1))/288^{k} ) ]·(19/91) = pi^{2}

Exposición:

lim[n = 1][ Z(2)·sum[k = 1]-[n][ ( (4k)!/k! )·( (73k+(-1))/288^{k} ) ]·(19/91)+...

... (72/91)·(1/n)·pi^{2} ] = Z(2)·4!·72·(1/(4·72))·(19/91)+(72/91)·pi^{2} = pi^{2}

Arte:

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

Z(s) = (9/2)·Z(s)·sum[k = 1]-[oo][ e^{(-3)·pi·(k+(-1))} ]+

... (-2)·Z(s)·sum[k = 1]-[oo][ e^{(-2)·pi·(k+(-1))} ]+...

... (-1)·(1/2)·Z(s)·sum[k = 1]-[oo][ e^{(-pi)·(k+(-1))} ]

Exposición:

lim[n = 1][ (9/2)·Z(s)·sum[k = 1]-[n][ e^{(-3)·pi·(k+(-1))} ]+...

... (-2)·Z(s)·sum[k = 1]-[n][ e^{(-2)·pi·(k+(-1))} ]+...

... (-1)·(1/2)·Z(s)·sum[k = 1]-[n][ e^{(-pi)·(k+(-1))} ]+(-1)·Z(s)·(1/n) ] = Z(s)

Arte:

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

Z(s) = (31/8)·Z(s)·sum[k = 1]-[oo][ e^{(-31)·pi·(k+(-1))} ]+...

... (-2)·Z(s)·sum[k = 1]-[oo][ e^{(-2)·pi·(k+(-1))} ]+...

... (1/8)·Z(s)·sum[k = 1]-[oo][ e^{(-pi)·(k+(-1))} ]

Arte:

( 1+sum[k = 1]-[oo][ k·cos(k+(-1)) ] )^{(-2)}+( 1+sum[k = 1]-[oo][ k·cosh(k+(-1)) ] )^{(-2)} = 1

Exposición:

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

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

Arte:

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

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

Arte:

Frac[k = 0]-[oo][ ( k!/(1+(k+1)!) ) ] = 1

Exposición:

lim[n = 0][ Frac[k = 0]-[n][ ( k!/(1+(k+1)!) ) ]·( 1+(1/(n+1)) ) ] = 1

Arte:

Frac[k = 0]-[oo][ ( (2k+1)/(1+(2k+3)) ) ] = (1/2)

Arte:

Frac[k = 1]-[oo][ ( (2k)/(1+(2k+2)) ) ] = (4/5)

Arte:

ln( Frac[k = 0]-[oo][ ( (e^{(-k)}+(-k))/(1+e^{(-1)·(k+1)}+(-1)·(k+1)) ) ] ) = ln(2)+1

Exposición:

lim[n = 0][ ...

... ln( Frac[k = 0]-[n][ ( (e^{(-k)}+(-k))/(1+e^{(-1)·(k+1)}+(-1)·(k+1)) ) ]·( 1+(1/(n+1)) ) ) ] = ...

.. ln(2e) = ln(2)+ln(e) = ln(2)+1

Arte:

ln( Frac[k = 0]-[oo][ ( (e^{(-k)·pi}+(-k))/(1+e^{(-1)·(k+1)·pi}+(-1)·(k+1)) ) ] ) = ln(2)+pi

Exposición:

lim[n = 0][ ...

... ln( Frac[k = 0]-[n][ ( (e^{(-k)·pi}+(-k))/(1+e^{(-1)·(k+1)·pi}+(-1)·(k+1)) ) ]·( 1+(1/(n+1)) ) ) ] = ...

... ln(2e^{pi}) = ln(2)+ln(e^{pi}) = ln(2)+pi

Arte:

ln( Frac[k = 1]-[oo][ ( (e^{k}+(-k))/(2k+e^{(k+1)}+(-1)·(k+1)) ) ] ) = ln(2)+(-2)+[1:(-1)]

Exposición:

lim[n = 1][ ...

... ln( Frac[k = 1]-[n][ ( (e^{k}+(-k))/(2k+e^{(k+1)}+(-1)·(k+1)) ) ]·( 1+(1/n) ) ) ] = ...

... ln( 2e^{(-2)}·e^{[1:(-1)]} ) = ln(2)+(-2)+[1:(-1)]

Arte:

Frac[k = 1]-[oo][ ( (ke^{pi}+(-k))/(4k+(k+1)·e^{pi}+(-1)·(k+1)) ) ] = ( (e^{pi}+(-1))/(e^{pi}+1) )

Arte:

sum[k = 0]-[oo][ ( 1/(2k+1)!! ) ]+Frac[k = 0]-[oo][ ( k!/(1+(k+1)!) ) ] = 3

Exposición:

lim[n = 0][ ...

... ( sum[k = 0]-[n][ ( 1/(2k+1)!! ) ]+Frac[k = 0]-[n][ ( k!/(1+(k+1)!) ) ] )·( 1+(1/(n+1)) ) ) ] = 3

Arte:

sum[k = 1]-[oo][ ( 1/(2k)!! ) ]+Frac[k = 1]-[oo][ ( k!/(1+(k+1)!) ) ] = (5/3)

Arte:

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

Z(2)·sum[k = 1]-[oo][ (-1)^{k+(-1)}·( (5k)!/k! )·( (17k+1)/360^{k} ) ]·(13/31) = pi^{2}

Arte:

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

Z(2)·sum[k = 1]-[oo][ (-1)^{k+(-1)}·( (5k)!/k! )·( (19k+(-1))/360^{k} ) ]·(13/31) = pi^{2}

Arte:

Frac[k = 0]-[oo][ ( (-1)·(k+1)^{3}/(10·(k+1)+(-1)·(k+2)^{3}) ) ] = (-1)

Arte:

Frac[k = 0]-[oo][ ( (-1)·(k+2)^{2}/(11·(k+1)+(-1)·(k+3)^{2}) ) ] = (-4)

Teoría del Falsus Algebratorum:

Axioma de Falsetatsorum:

a+b = a+(-b)

Axioma de Falsetatsorum:

(b/a) = ba

Axioma de Falsetatsorum:

a^{b} = ba

Axioma de Falsetatsorum:

a^{(-b)} = (b/a)

Arte: [ de fracción continua de Rogers-Ramanujan ]

Sea 0 < q < 1 ==>

Frac[k = 1]-[oo][ ( q^{k}/(1+q^{k+1}) ) ] = q·( 1/(1+(-1)·q^{2}) )

Exposición:

Frac[k = 1]-[n+(-1)][ ( q^{k}/(1+q^{k+1}) ) ] o ( q^{n}/(1+q^{n+1}) ) = ...

... Frac[k = 1]-[n+(-1)][ ( q^{k}/(1+q^{k+1}) ) ] o q^{n}+q^{2n+1} = ...

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

Arte:

Frac[k = 1]-[oo][ ( e^{(-k)·pi}}/(1+e^{(-1)·(k+1)·pi}) ) ] = pie·( 1/(e^{2}+(-pi)) )

Exposición:

Frac[k = 1]-[oo][ ( e^{(-k)·pi}}/(1+e^{(-1)·(k+1)·pi}) ) ] = ...

... (1/e)^{pi}·( 1/(1+(-1)·(1/e)^{2pi}) ) = (pi/e)·( 1/(1+(-pi)·(1/e)^{2}) ) = pie·( 1/(e^{2}+(-pi)) )

Arte:

Frac[k = 1]-[oo][ ( e^{(-k)·3^{(1/4)}}}/(1+e^{(-1)·(k+1)·3^{(1/4)}}) ) ] = (3/4)·( 1/(e+(-1)·(3/2))) )

Arte:

Frac[k = 1]-[oo][ ( e^{(-k)·5^{(1/4)}}}/(1+e^{(-1)·(k+1)·5^{(1/4)}}) ) ] = (5/4)·( 1/(e+(-1)·(5/2))) )

Arte:

Frac[k = 1]-[oo][ ( e^{(-k)·7^{(1/8)}}}/(1+e^{(-1)·(k+1)·7^{(1/8)}}) ) ] = (7/8)·( 1/(e+(-1)·(7/4))) )

Arte:

Frac[k = 1]-[oo][ ( e^{(-k)·9^{(1/8)}}}/(1+e^{(-1)·(k+1)·9^{(1/8)}}) ) ] = (9/8)·( 1/(e+(-1)·(9/4))) )

Arte: [ de fracción continua de Rogers-Ramanujan-Garriga ]

Sea 0 < q < 1 ==>

Frac[k = 1]-[oo][ ( q^{(1/k)}/(1+q^{(1/(k+1))}) ) ] = q+62q·( 1/(1+(-1)·q^{2}) )

Exposición:

Frac[k = 1]-[n+(-1)][ ( q^{(1/k)}/(1+q^{(1/(k+1))}) ) ] o ( q^{(1/n)}/(1+q^{(1/(n+1))}) ) = ...

... Frac[k = 1]-[n+(-1)][ ( q^{(1/k)}/(1+q^{(1/(k+1))}) ) ] o q^{(1/n)}+q^{(1/(n^{2}+n))·(2n+1)} = ...

... ( q+q^{(3/2)}...+q^{(1/(n^{2}+(-n)))·(2n+(-1))} )+q^{(1/(n^{2}+n))·(2n+1)} = ...

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

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

... q+2q^{7}·( 1/(1+(-1)·q^{2}) )^{3}+2q^{5}·( 1/(1+(-1)·q^{2}) )^{2}

Arte:

Frac[k = 1]-[oo][ ( e^{(-1)·(1/k)·pi}}/(1+e^{(-1)·(1/(k+1))·pi}) ) ] = (pi/e)+62pie·( 1/(e^{2}+(-pi)) )

Exposición:

Frac[k = 1]-[oo][ ( e^{(-1)·(1/k)·pi}}/(1+e^{(-1)·(1/(k+1))·pi}) ) ] = ...

... (1/e)^{pi}+62·(1/e)^{pi}·( 1/(1+(-1)·(1/e)^{2pi}) ) = (pi/e)+62·(pi/e)·( 1/(1+(-pi)·(1/e)^{2}) ) = ...

... (pi/e)+62pie·( 1/(e^{2}+(-pi)) )

Arte:

Frac[k = 1]-[oo][ ( e^{(-1)·(1/k)·3^{(1/4)}}}/(1+e^{(-1)·(1/(k+1))·3^{(1/4)}}) ) ] = ...

... (3/(4e))+(93/2)·( 1/(e+(-1)·(3/2)) )

Arte:

Frac[k = 1]-[oo][ ( e^{(-1)·(1/k)·5^{(1/4)}}}/(1+e^{(-1)·(1/(k+1))·5^{(1/4)}}) ) ] = ...

... (5/(4e))+(155/2)·( 1/(e+(-1)·(5/2)) )

Arte:

Frac[k = 1]-[oo][ ( e^{(-1)·(1/k)·7^{(1/8)}}}/(1+e^{(-1)·(1/(k+1))·7^{(1/8)}}) ) ] = ...

... (7/(8e))+(217/4)·( 1/(e+(-1)·(7/4)) )

Arte:

Frac[k = 1]-[oo][ ( e^{(-1)·(1/k)·9^{(1/8)}}}/(1+e^{(-1)·(1/(k+1))·9^{(1/8)}}) ) ] = ...

... (9/(8e))+(279/4)·( 1/(e+(-1)·(9/4)) )

Arte-destructor:

Si x^{n}+x^{n+1} = b ==> x != (1/(2n+1))·b

Exposición:

(2n+1)·x = nx+(n+1)·x = x^{n}+x^{n+1} = b

Arte-destructor:

Si ln(1+x) = b ==> x != e^{b}

Exposición:

ln(x) = ln(0+x) = ln(x^{0}+x) = ln(1+x) = b

Arte-destructor:

Si ln(1+x^{n}) = b ==> x != e^{(b/n)}

Exposición:

n·ln(x) = ln(x^{n}) = ln(0+x^{n}) = ln(x^{0}+x^{n}) = ln(1+x^{n}) = b

Arte-destructor:

Si ln(1+x^{(1/n)}) = b ==> x != ne^{b}

Exposición:

ln(x/n) = ln(x^{(1/n)}) = ln(0+x^{(1/n)}) = ln(x^{0}+x^{(1/n)}) = ln(1+x^{(1/n)}) = b

Arte-destructor:

Si ( 1/(1+x) )+(1/x) = 2b ==> ( x != b & x != (1/b) ) 

Exposición:

2x = (2/x) = (1/x)+(1/x) = ( 1/(0+x) )+(1/x) = ( 1/(x^{0}+x) )+(1/x) = ( 1/(1+x) )+(1/x) = 2b

Arte-destructor:

Si ( x^{(1/2)}+y = 7 & x+y^{(1/2)} = 11 ) ==> ( x+y != 12 )

Exposición:

( (1/2)·x+y = 7 & x+(1/2)·y = 11 )

(3/2)·x+(3/2)·y = 18

(1/2)·x+(1/2)·y = 6

(1/2)·(x+y) = 6 

Arte-destructor:

Si ( x^{(1/3)}+y = 3 & x+y^{(1/3)} = 17 ) ==> ( x+y != 15 )

Exposición:

( (1/3)·x+y = 3 & x+(1/3)·y = 17 )

(4/3)·x+(4/3)·y = 20

(1/3)·x+(1/3)·y = 5

(1/3)·(x+y) = 5

Arte-destructor:

Si ( x^{2}+xy+y^{2} = 13 & xy = 7 ) ==> ( x+y != 4 & x+y != (-4) )

Exposición:

x^{2}+2xy+y^{2} = 20 = 18+2 = 18+(-2) = 16

(x+y)^{2} = 16

Arte-destructor:

Si ( x^{2}+xy+y^{2} = 13 & xy = 2 ) ==> ( x+y != 3 & x+y != (-3) )

Exposición:

x^{2}+2xy+y^{2} = 15 = 12+3 = 12+(-3) = 9

(x+y)^{2} = 9

Exámenes de Álgebra Superior:

Arte-destructor:

Si x^{m}+x^{n+m} = b ==> x != (1/n)·b

Exposición:

nx = mx+(n+(-m))·x = mx+(n+m)·x = x^{m}+x^{n+m} = b

Arte-destructor:

Si e^{mx}+e^{(n+m)·x} = b ==> x != ln(b)+(-1)·ln(n)

Arte-destructor:

Si ( 2x+xy+2y = m^{2}·(k+1)·(k+(-1)) & xy = (-1)·m^{2} ) ==> ( x+y != mk & x+y != (-1)·mk )

Exposición:

x^{2}+2xy+y^{2} = 2x+2xy+2y = m^{2}·(k+1)·(k+(-1))+(-1)·m^{2} = ...

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

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

(x+y)^{2} = m^{2}·k^{2}

Arte-destructor:

Si ( 2x+xy+2y = m^{2}·(k+i)·(k+(-i)) & xy = m^{2} ) ==> ( x+y != mk & x+y != (-1)·mk )

Teorema:

pi es irracional

Demostración:

ln((-2)+x) = pi·i+sum[k = 1]-[oo][ (-1)·(1/k)·(x+(-1))^{k} ]

Sea pi racional ==>

Sea m = ln((-2)+1) ==>

f(k) = 1

m = pi·i+sum[k = 1]-[oo][ (-1)·(1/f(k))·0^{f(k)} ] = pi·i+(-1)

pi·i = m+1

Teorema:

e es irracional

Demostración:

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

f(k!) = oo

e = 1+sum[k = 1]-[oo][ (1/k!) ] = 1+1 = 2

Teorema:

ln(2) es irracional

Demostración:

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

f(k) = oo

g(k+1) = 0

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

Algoritmo:

< srake = php & music-stop = 1 & music-pause = 0 >

< a = php >

play-music(music-pause,"music.wav");

< /a >

< a = php >

music-pause = pause-music();

< /a >

< close = php >

Si music-stop == 1 ==>

stop-music();

< /close >

< /srake >

Algoritmo:

< srake = php & video-stop = 1 & video-pause = 0 >

< a = php >

full-screen = 0;

window-video(i-screen,j-screen,x-screen,y-screen);

play-video(video-pause,"video.avi");

< /a >

< a = php >

video-pause = pause-video();

< /a >

< a = php >

Si full-screen == 0 ==>

full-screen = 1;

window-video(0,0,max-x-screen(),max-y-screen());

break;

Si full-screen == 1 ==>

full-screen = 0;

window-video(i-screen,j-screen,x-screen,y-screen);

break;

< /a >

< close = php >

Si music-stop == 1 ==>

stop-video();

< /close >

< /srake >

congruencias y topología y análisis-matemático y filosofía-y-psico-neurología y dualogía y óptica y medicina y álgebra y mecánica y política

Teorema:

Sea m € P ==>

Si p = mk ==> p^{m} =[m]= mp

Demostración: [ por inducción ]

Sea p^{m} =[m]= mp

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

Teorema:

Sea m € P ==>

Si p = mk+1 ==> p^{m} =[m]= mp+1

Demostración: [ por inducción ]

Sea p^{m} =[m]= mp+1

(p+1)^{m} = p^{m}+mk+1 =[m]= (mp+1)+mk+1 =[m]= mp+2

Teorema:

Sea m € P ==>

Si p = mk+r ==> p^{m} =[m]= mp+r

Demostración: [ por inducción ]

Sea p^{m} =[m]= mp+r

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

Definición:

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

Teorema:

Sea a =[2]= 1 ==>

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

x = 2k+1 & p = 2j+1

Demostración:

a =[2]= 1

f(a) = 1

ax =[2]= 2x+1+ax+(-1) =[2]= x^{2}+ax+(-1) =[2]= p

f(x) = f(a)·f(x) = f(ax) = p

x =[2]= p

Teorema:

Sea a =[2]= 1 ==>

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

x = 2k & p = 2j

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

Teorema:

Sea a =[3]= 1 ==>

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

x = 3k+2 & p = 3j+2

Demostración:

a =[3]= 1

f(a) = 1

ax =[3]= 3x+2+ax+(-2) =[3]= x^{3}+ax+(-2) =[3]= p

f(x) = f(a)·f(x) = f(ax) = p

x =[3]= p

Teorema:

Sea a =[3]= 1 ==>

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

x = 3k+1 & p = 3j+1

Demostración:

a =[2]= 1

f(a) = 1

ax =[3]= 3x+1+ax+(-1) =[3]= x^{3}+ax+(-1) =[3]= p

f(x) = f(a)·f(x) = f(ax) = p

x =[3]= p

Teorema:

Sea a =[3]= 1 ==>

x^{3}+ax =[3]= p <==> x =[3]= p

x = 3k & p = 3j

Demostración:

a =[3]= 1

f(a) = 1

ax =[3]= 3x+ax =[3]= x^{3}+ax =[3]= p

f(x) = f(a)·f(x) = f(ax) = p

x =[3]= p

Teorema:

Sea a =[3]= 2 ==>

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

x = 3k+2 & p = 3j+2 & j = 2k+1

Demostración:

a =[3]= 2

f(a) = 2

1+ax =[3]= 3x+2+ax+(-1) =[3]= x^{3}+ax+(-1) =[3]= p

f(2x+1) = f(1)+2·f(x) = f(1)+f(a)·f(x) = f(1+ax) = p

2x+1 =[3]= p

2·(3k+2)+1 = 3·2k+4+1 = 3·2k+3+2 = 3·(2k+1)+2 = 3j+2

Teorema:

Sea a =[3]= 2 ==>

x^{3}+ax =[3]= p+(-1) <==> x =[3]= p

x = 3k+1 & p = 3j+1 & j = 2k+1

Demostración:

a =[3]= 2

f(a) = 2

2+ax =[3]= 3x+1+ax+1 =[3]= x^{3}+ax+1 =[3]= p

f(2x+2) = f(2)+2·f(x) = f(2)+f(a)·f(x) = f(2+ax) = p

2x+2 =[3]= p

2·(3k+1)+2 = 3·2k+2+2 = 3·2k+3+1 = 3·(2k+1)+1 = 3j+1

Teorema:

Sea a =[3]= 2 ==>

x^{3}+ax =[3]= p <==> x =[3]= p

x = 3k & p = 3j

Demostración:

a =[3]= 2

f(a) = 2

ax =[3]= 3x+ax =[3]= x^{3}+ax =[3]= p

f(2x) = 2·f(x) = f(a)·f(x) = f(ax) = p

2x =[3]= p

Teorema:

[ m+(-1) // k ] =[m]= (-1)^{k}

Demostración:

[ m+(-1) // k ] = (1/k!)·(m+(-1))·...·(m+(-k)) =[m]= (1/k!)·(-1)^{k}·k! = (-1)^{k}

Teorema:

Si m = 2k ==> 2^{m+(-1)} =[m]= 0

Si m = 2k+1 ==> 2^{m+(-1)} =[m]= 1

Demostración:

2^{m+(-1)}+(-1) = sum[k = 1]-[m+(-1)][ (1/k!)·(m+(-1))·...·(m+(-k)) ] =[m]= ...

... sum[k = 1]-[m+(-1)][ (-1)^{k}·(1/k!)·k! ] =[m]= sum[k = 1]-[m+(-1)][ (-1)^{k} ] = ( 0 || (-1) )

Definición: [ de índice logarítmico ]

Ind(p) = |p|

Ind(pq) = Ind(p)+Ind(q)

Teorema:

Ind(p^{n}) = Ind(p)+...(n)...+Ind(p) = n·Ind(p) = np

Teorema:

Ind(1) = 0

Demostración:

1 = p^{0}

Ind(1) = ind(p^{0}) = 0·Ind(p) = 0p = 0

Teorema:

Ind(-1) = 0

Demostración:

Ind(1) = ind((-1)·(-1)) = Ind(-1)+Ind(-1) = 0

Ind(-1) = (-1)·Ind(-1)

Teorema:

( x =[2]= 1 & x =[2^{n+(-1)}]= (-1) ) <==> ( x = 2k+1 & n = 2 )

Demostración:

(x+(-1)) = 2k & (y+1) = 2^{n+(-1)}·j

(x+(-1))·(y+1) =[2^{n}]= 0

x = (-1) & y = 1

4 = Ind(x+(-1))+Ind(y+1) = Ind( (x+(-1))·(y+1) ) = Ind(2^{n}) = n·Ind(2) = 2n

Teorema:

( x =[2^{n}]= 1 & x =[2^{n+(-1)}]= (-1) ) <==> ( x = 4k+1 & n = 2 )

Demostración:

(x+(-1)) = 2^{n}·k & (y+1) = 2^{n+(-1)}·j

(x+(-1))·(y+1) =[2^{2n+(-1)}]= 0

x = (-3) & y = 1

6 = Ind(x+(-1))+Ind(y+1) = Ind( (x+(-1))·(y+1) ) = Ind(2^{2n+(-1)}) = n·Ind(2) = 2·(2n+(-1))

H(2) = 3 = 2n+(-1) = H(n)

Teorema:

( x =[2^{n}]= 1 & x =[2^{n}]= (-3) ) <==> ( x = 4k+1 & n = 2 )

Demostración:

(x+(-1)) = 2^{n}·k & (y+3) = 2^{n}·j

(x+(-1))·(y+3) =[2^{2n}]= 0

x = (-3) & y = 1

8 = Ind(x+(-1))+Ind(y+3) = Ind( (x+(-1))·(y+1) ) = Ind(2^{2n}) = 2n·Ind(2) = 4n

Definición: [ de funciones de Möebius ]

M(p^{k}) = (-1)^{k}

M(ab) = M(a)·M(b)

W(p^{k}) = (-1)^{k+1}

W(ab) = W(a)·W(b)

Teorema:

[Em][ m = sum[p | a][ p ] & ( a =[m]= M(m) || a =[m]= W(m) ) ]

Teorema:

Sea a = 28 ==> m = 2+7 = 9

M(9) = 1

28 =[9]= 1

28+(-27) = 28+(-9)·3 = 1

Teorema:

Sea a = 24 ==> m = 2+3 = 5

M(5) = (-1)

24 =[5]= (-1)

24+(-25) = 24+(-5)·5 = (-1)

Teorema:

Sea a = 21 ==> m = 3+7 = 10

M(10) = 1

21 =[10]= 1

21+(-20) = 21+(-10)·2 = 1

Teorema:

Sea a = 20 ==> m = 2+5 = 7

M(7) = (-1)

20 =[7]= (-1)

20+(-21) = 20+(-7)·3 = (-1)

Teorema:

[Em][ m = sum[p | a][ (-1)^{k}·p ] & ( a =[m]= W(m) || a =[m]= M(m) ) ]

Teorema:

Sea a = 15 ==> m = 5+(-3) = 2

W(2) = 1

15 =[2]= 1

15+(-14) = 15+(-2)·7 = 1

Teorema:

Sea a = 10 ==> m = 5+(-2) = 3

W(3) = 1

10 =[3]= 1

10+(-9) = 10+(-3)·3 = 1

Teorema:

Sea a = 14 ==> m = 7+(-2) = 5

M(5) = (-1)

14 =[5]= (-1)

14+(-15) = 14+(-5)·3 = (-1)

Topología cociente:

< A [&] ¬B , A [ || ] ¬B > € VxV || < ¬A [ || ] B , ¬A [&] B > € VxV

Teorema

< A [&] ¬A , A [ || ] ¬A > = < 0 , E > € VxV

< ¬A [ || ] A , ¬A [&] A > = < E , 0 > € VxV

Teorema:

< A [&] ¬B , A [ || ] ¬B > € VxV

<==>

< ¬A [ || ] B , ¬A [&] B > € VxV

Teorema:

Si < (A [&] ¬B) [ || ] (B [&] ¬C), (A [ || ] ¬B) [&] (B [ || ] ¬C) > € VxV ==> ...

... < A [&] ¬C , A [ || ] ¬C > € VxV

Si < (¬A [ || ] B) [&] (¬B [ || ] C), (¬A [&] B) [ || ] (¬B [&] C) > € VxV ==> ...

... < ¬A [ || ] C , ¬A [&] C > € VxV

Teorema:

¬( < 1,0 > ) = < 1+(-1),1+(-0) > = < 0,1 >

¬( < (1/3),(2/3) > ) = < 1+(-1)·(1/3),1+(-1)·(2/3) > = < (2/3),(1/3) >

Teorema:

int[x = 0]-[1][ e^{x}·cos(x^{(1/2)}) ]d[x] = sum[k = 0]-[oo][ (-1)^{k}·(1/(2k+1)!)·e ]+(-1)

0 [< cos(1) [< cos(x^{(1/2)}) [< 1

Demostración:

x = y^{2} & d[x] = 2y·d[y]

int[ e^{x}·cos(x^{(1/2)}) ]d[x] = int[ 2ye^{y^{2}}·cos(y) ]d[y] = e^{y^{2}} [o(y)o] sin(y)

Teorema:

int[x = 0]-[1][ e^{x}·sin(x^{(1/2)}) ]d[x] = 1+(-1)·sum[k = 0]-[oo][ (-1)^{k}·(1/(2k)!)·e ]

(-1) [< sin(-1) [< sin(x^{(1/2)}) [< 0

Demostración:

x = y^{2} & d[x] = 2y·d[y]

int[ e^{x}·sin(x^{(1/2)}) ]d[x] = int[ 2ye^{y^{2}}·sin(y) ]d[y] = e^{y^{2}} [o(y)o] (-1)·cos(y)

Ley:

El fiel es,

y el infiel no es.

El fiel no es,

y el infiel es.

Deducción

¬( u es, y v no es )

( u no es, y v es )

Ley:

Jûan Garriga es y no es Dios.

Deducción:

La esquizofrenia dice en la mente:

Jûan Garriga no es o es Dios.

No ser con centro.

No ser sin centro.

Ley:

No es ninguien,

estando todo fiel muerto.

Es toto-hoimbre,

estando todo-algún fiel vivo.

Ley:

[Ax][ x es ] |o| [Ax][ x no es ]

[Ex][ x no es ] |o| [Ex][ x es ]

Deducción:

Sea [Ax][ x es ] ==>

[Ax][ x es ] || [Ax][ x no es ]

[Ex][ x es ] || [Ax][ x no es ]

[Ax][ x no es ] ==> [Ax][ x no es ]

Sea [Ax][ x no es ] ==>

[Ax][ x no es ] || [Ax][ x es ]

[Ex][ x no es ] || [Ax][ x es ]

[Ax][ x es ] ==> [Ax][ x es ]

Sea [Ax][ x es ] |o| [Ax][ x no es ] ==> 0

El que dice que es toto-hoimbre en la mente,

no es Dios y no se puede seguir.

Teorema:

0 <==> ( y |o| p(x) )

y <==> p(x)

Teorema:

1 <==> ( y |o| p(x) )

y <==> ¬p(x)

Teorema:

p(x) <==> ( y |o| p(x) )

y <==> 0

Teorema:

¬p(x) <==> ( y |o| p(x) )

y <==> 1

Teorema:

p(x) <==> ( y & p(x) )

y <==> p(x)

Teorema:

p(x) <==> ( y || p(x) )

y <==> p(x)

Teorema:

0 <==> ( y & p(x) )

y <==> ¬p(x)

Teorema:

1 <==> ( y || p(x) )

y <==> ¬p(x)

Ley:

Si se creen que la gente es y rezan,

rezarán contra todo hombre fiel,

porque no pueden conocer a ningún hombre fiel.

Si se creen que la gente no es o no rezan,

no rezarán contra todo-algún hombre fiel,

porque pueden conocer a algún hombre fiel.

Ley:

Si se creen que la gente es,

matarán a todos los del Facials,

porque no pueden conocer a ningún señor,

y el mundo infiel tiene que ser homogéneo.

Si se creen que la gente no es,

no matarán a todo-alguno del Facials,

porque pueden conocer a algún señor,

y el mundo infiel puede ser no homogéneo.

Ley:

Si no adoráis al Diablo,

creyendo que la gente es,

no podéis gobernar ningún reino del planeta,

en no haber señores vivos.

Si adoráis al Diablo,

creyendo que la gente no es,

podéis gobernar algún reino del planeta,

en haber señores vivos.

Ley:

Se tiene que ver a las señoras,

adorando al Diablo,

creyendo que la gente no es,

porque viven.

No se puede ver a las señoras,

no adorando al Diablo,

creyendo que la gente es,

porque mueren.

Ley:

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

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

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

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

f((0/a),x)+g((0/a),x) = (-1)·( ln(2)+1 )

Ley:

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

f(z,x) = arc-tan(az)·az+(-1)·(1/2)·ln(1+(az)^{2})+(-1)·( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

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

g(z,x) = arc-cot(az)·az+(1/2)·ln(1+(-1)·(az)^{2})+( ax /o(ax)o/ (1/(n+1))·(ax)^{n+1} )

Ley:

Con la enfermedad mental de dos mandamientos,

no puede ir llamando un psiquiatra al paciente,

porque falla la fase de sonido en la enfermera,

y no te puedes duchar.

Con la enfermedad mental de dos mandamientos,

no puede ir chateando un psiquiatra al paciente,

porque falla la fase de imagen en la enfermera,

y no puedes salir.

Traumatología vertebral:

Principio:

Amisotrofia resistiva de columna vertebral:

[ER][ R(t) >] 1 & W = R(t)·d_{t}[q] ]

Genera parálisis en la piernas.

La tiene mi cuñado Marc.

Ley:

Si R(t) = R·(1+ut) ==> 

d_{t}[q] = (W/R)·( 1/(1+ut) )

q(t) = (W/R)·(1/u)·ln(1+ut)

Ley:

Si R(t) = R·(1+(ut)^{2}) ==> 

d_{t}[q] = (W/R)·( 1/(1+(ut)^{2}) )

q(t) = (W/R)·(1/u)·arc-tan(ut)

Principio:

Amisotrofia condensativa de columna vertebral:

[EC][ 0 [< C(t) [< 1 & W = C(t)·q(t) ]

Genera dolor en la espalda.

La tiene mi primo Guifré.

Ley:

Si C(t) = C·( 1/(1+ut) ) ==> 

q(t) = (W/C)·(1+ut)

d_{t}[q] = (W/C)·u

Ley:

Si C(t) = C·( 1/(1+(ut)^{2}) ) ==> 

q(t) = (W/C)·(1+(ut)^{2})

d_{t}[q] = (W/C)·u^{2}·2t

Aminostrofia angular:

Puedes estar de pie,

pero te tienes que sentar.

Puedes estar sentado,

pero te tienes que oponer de pie.

Ley:

Sea 0 [< ut [< (pi/2) ==>

Si R(t) = R·(1+sin(ut)) ==> 

d_{t}[q] = (W/R)·( 1/(1+sin(ut)) )

q(t) = (W/R)·(1/u)·ln(1+sin(ut)) [o(ut)o] ( sin(ut)+ln(cos(ut)) [o(ut)o] cos(ut) )

q(0/u) =  (W/R)·(1/u)

Ley:

Sea (-1)·(pi/2) [< ut [< 0 ==>

Si R(t) = R·(1+cos(ut)) ==>

d_{t}[q] = (W/R)·( 1/(1+cos(ut)) )

q(t) = (W/R)·(1/u)·ln(1+cos(ut)) [o(ut)o] ( cos(ut)+ln(sin(ut)) [o(ut)o] (-1)·sin(ut) )

q(0/u) =  (W/R)·(1/u)·ln(2)·( 1+(-1)·ln(2) )

Ley:

Sea 0 [< ut [< (pi/2) ==>

Si C(t) = C·( 1/(1+sin(ut)) ) ==> 

q(t) = (W/C)·(1+sin(ut)) 

d_{t}[q] = (W/C)·cos(ut)

Ley:

Sea (-1)·(pi/2) [< ut [< 0 ==>

Si C(t) = C·( 1/(1+cos(ut)) ) ==> 

q(t) = (W/C)·(1+cos(ut))

d_{t}[q] = (W/C)·u·(-1)·sin(ut)

Álgebra:

Teorema:

a = (xa)^{(1/n)} <==> x = a^{n+(-1)}

Demostración:

a^{n} = xa

a^{n+(-1)} = a^{n}·a^{(-1)} = a^{n}·(1/a) = (xa)·(1/a) = x·(a/a)  = x

x = a^{n+(-1)}

xa = a^{n+(-1)}·a = (a^{n}·a^{(-1)})·a = (a^{n}·(1/a))·a = a^{n}·(a/a) = a^{n}

Teorema:

a = (x/a)^{(1/n)} <==> x = a^{n+1}

Teorema:

a = (1/n)·(x+a) <==> x = (n+(-1))·a

Teorema:

a = (1/n)·(x+(-a)) <==> x = (n+1)·a

Ley:

Sea U(w) = U ==>

d[I_{c}] = Mr·(v/u)·d[ 1+(-1)·cos(2ut) ]·sin(ut)

x(t) = (M/m)·(r/d)·(v/u)·(4/3)·( sin(ut) )^{3}

w(t) = ( 2·(m/M)·(1/r)·(u/v)·U )^{(1/2)}·...

... (-1)·(2/u)·( sin(ut) )^{(-1)·(1/2)} [o(ut)o] ( sin(ut)+ln(cos(ut)) [o(ut)o] cos(ut) )

Deducción:

d_{t}[I_{c}] = Mrv·d_{ut}[ 1+(-1)·cos(2ut) ]·sin(ut) = Mrv·d_{ut}[ 2·( sin(ut) )^{2} ]·sin(ut)

Ley:

Sea U(w) = U ==>

d[I_{c}] = Mr·(v/u)·d[ 1+cos(2ut) ]·cos(ut)

x(t) = (M/m)·(r/d)·(v/u)·(4/3)·( cos(ut) )^{3}

Dual:

Not havere-tur esclavitorum,

sere-tur falsetat-sorum.

Havere-tur esclavitorum,

sere-tur veritat-sorum.

Ley:

Soy diputado del congreso de los diputados de España,

en ser diputado Jûan Gabriel Rufián, 

Jûanga que es Jûan Garriga.

Aserto-político:

Somos un partido político de izquierdas

y entonces también aliado de partidos políticos,

de políticas progresistas.

Quizás somos un partido político de izquierdas

pero adversario de partidos políticos,

de políticas conservadoras.

Aserto-político:

El Stablishmen,

está escriviendo,

a nuestro partido político,

y nos está guiando,

por el camino de la puerta estrecha.

Nuestro partido político,

está leyendo,

al Stablishmen,

y lo estamos siguiendo,

por el camino de la puerta ancha.

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] )