borrós trannsitiu y equilibri químic

( x_{0} [< x_{n} & x_{n} [< x_{n+1} ) <==> x_{0} [< x_{n+1}

min{(0.n),(0.1)} [< (0.n+1)

max{(-1)·(0.n),(-1)·(0.1)} >] (-1)·(0.n+1)

( x_{0} >] x_{n} & x_{n} >] x_{n+1} ) <==> x_{0} >] x_{n+1}

min{(-1)·(0.n),(-1)·(0.1)} >] (-1)·(0.n+1)

max{(0.n),(0.1)} [< (0.n+1)

[4·H_{2}][O_{4}] = [4·e^{(-1)}]·[4·H_{2}O]

[3e^{(-1)}][2·H_{2}][O_{4}] = [8·e^{(-1)}]·[2·H_{2}O_{2}]

[CH_{4}][O_{4}] = [4e^{(-1)}][CH_{4}O_{4}]

[NH_{3}][O_{3}] = [3e^{(-1)}][NH_{3}O_{3}]

[C_{2}H_{6}][O_{4}] = [4e^{(-1)}][C_{2}H_{6}O_{4}]

[C_{3}H_{8}][O_{4}] = [4e^{(-1)}][C_{3}H_{8}O_{4}]

[N_{2}H_{4}][O_{4}] = [4e^{(-1)}][N_{2}H_{4}O_{4}]

[N_{3}H_{5}][O_{4}] = [4e^{(-1)}][N_{3}H_{5}O_{4}]

1 destructor

(NH)-(CH_{2})-(CH_{2})-(CH_{2})-(CH_{2})-(NH)

1 constructor

(NH)-(CH_{2})-(CH_{2})-(CH_{2})-(CH_{2})-(CH_{2})-(CH_{2})-(NH)

1 destructor

H-(CH_{2})-(CH_{2})-(CH_{2})-(CH_{2})-H

1 constructor

H-(CH_{2})-(CH_{2})-(CH_{2})-(CH_{2})-(CH_{2})-(CH_{2})-H

Potencia 1 en tenebres:

L(x,u,v,t) = qg·( x(u,v,t) )^{n}+(-1)·h^{n}·(c/l)·V·(1/2)·t^{2}( e^{iu·t}+e^{iv·t} )

x(u,v,t) = ( (c/l)·V·(1/2)·t^{2}( e^{iu·t}+e^{iv·t} ) )^{(1/n)}

h = ( qg )^{(1/n)}

( qg )^{(1/n)} = ( m·(c/l)·V )^{(1/n)}

( qg·t )^{(1/n)} = ( m·(c/l)·V·t )^{(1/n)}

( qg·(1/2)·t^{2} )^{(1/n)} = ( m·(c/l)·V·(1/2)·t^{2} )^{(1/n)}

Lley:

(m/2)·( d_{t}[s(t)]·r )^{2} = qg·sr <==> m·d_{tt}^{2}[s(t)]·r = qg

s(t) = ( (qg)/(mr) )·(1/2)·t^{2}

d_{t}[s(t)] = ( (qg)/(mr) )·t

d_{tt}^{2}[s(t)] = ( (qg)/(mr) )

Deducció:

d_{sr}[ (m/2)·( d_{t}[s]·r )^{2} ] = d_{t}[ (m/2)·( d_{t}[s]·r )^{2} ]·( 1/d_{t}[s]·r )

Ptincipi:

(m/2)·( d_{t}[s(r)]·r )^{2} = qg·pi·r

Lley:

qgy = qg·pi·r+(m/2)·( d_{t}[s(r)]·r )^{2}

y = 2pi·r

s(t) = (qg/m)^{(1/2)}·(4pi/r)^{(1/2)}·t

Acertijos en la oscuridad,

tengo que visitar al mago blanco,

en la torre negra de Isengard.

Acertijos en la claridad,

tengo que visitar al mago negro,

en la torre blanca de Isengard.

Lley:

(m/2)·d_{tt}^{2}[x(t)] = int[ f(t)·d_{t}[x] ]d[t]+(-1)·(a/2)( x(t) )^{2} <==> ...

... m·d_{tt}^{2}[x(t)] = f(t)+(-a)·x(t)

Deducció:

x(t) = ...

... int[ sin( (a/m)^{(1/2)}·t )·int[ sin( (a/m)^{(1/2)}·t )·(1/m)·f(t) ]d[t] ]d[t]+...

... int[ cos( (a/m)^{(1/2)}·t )·int[ cos( (a/m)^{(1/2)}·t )·(1/m)·f(t) ]d[t] ]d[t]

[1] d_{t}[ (1/2)·( int[ sin( (a/m)^{(1/2)}·t )·(1/m)·f(t) ]d[t] )^{2} ] = ...

... int[ sin( (a/m)^{(1/2)}·t )·(1/m)·f(t) ]d[t]·sin( (a/m)^{(1/2)}·t )·(1/m)·f(t)

[2] d_{t}[ (1/2)·( int[ cos( (a/m)^{(1/2)}·t )·(1/m)·f(t) ]d[t] )^{2} ] = ...

... int[ cos( (a/m)^{(1/2)}·t )·(1/m)·f(t) ]d[t]·cos( (a/m)^{(1/2)}·t )·(1/m)·f(t)

m·( [1]+[2] ) = f(t)·d_{t}[x]

Lley:

m·d_{tt}^{2}[x(t)] = F·( (a/m)^{(1/2)}t )^{n}+(-a)·x(t)

d_{t}[x(t)] = ...

... (F/m)·sin( (a/m)^{(1/2)}t )·...

... sin_{(2k+1)+n+1}( (a/m)^{(1/2)}t )·( (a/m)^{(1/2)}t )^{n+1}·(m/a)^{(1/2)}+...

... (F/m)·cos( (a/m)^{(1/2)}t )·...

... cos_{(2k)+n+1}( (a/m)^{(1/2)}t )·( (a/m)^{(1/2)}t )^{n+1}·(m/a)^{(1/2)}

x(t) = ...

... (F/m)·( ...

...(-1)·cos( (a/m)^{(1/2)}t )·sin_{(2k+1)+n+1}( (a/m)^{(1/2)}t )^{n+1}·(m/a) ...

... )+...

... (F/m)·( ...

... sin( (a/m)^{(1/2)}t )·cos_{(2k+1)+n+1}( (a/m)^{(1/2)}t )^{n+1}·(m/a) ...

... )

Deducció:

[1] d_{t}[ ( F^{2}/a )·(1/2)·( ...

... sin_{(2k+1)+n+1}( (a/m)^{(1/2)}t )·( (a/m)^{(1/2)}t )^{n+1} ...

... )^{2} ] = ...

... ( F^{2}/a )·( sin_{(2k+1)+n+1}( (a/m)^{(1/2)}t )·( (a/m)^{(1/2)}t )^{n+1} )·...

... sin( (a/m)^{(1/2)}t )·(a/m)^{(1/2)}·( (a/m)^{(1/2)}t )^{n}

[2] d_{t}[ ( F^{2}/a )·(1/2)·( ...

... cos_{(2k)+n+1}( (a/m)^{(1/2)}t )·( (a/m)^{(1/2)}t )^{n+1} ...

... )^{2} ] = ...

... ( F^{2}/a )·( cos_{(2k)+n+1}( (a/m)^{(1/2)}t )·( (a/m)^{(1/2)}t )^{n+1} )·...

... cos( (a/m)^{(1/2)}t )·(a/m)^{(1/2)}·( (a/m)^{(1/2)}t )^{n}

[1]+[2] = f(t)·d_{t}[x(t)]

Lley:

m·d_{tt}^{2}[x(t)] = F·e^{(a/m)^{(1/2)}·t}+(-a)·x(t)

d_{t}[x(t)] = (F/m)·(1/2)·e^{(a/m)^{(1/2)}·t}·(m/a)^{(1/2)}

x(t) = (F/m)·(1/2)·e^{(a/m)^{(1/2)}·t}·(m/a)

Deducció:

d_{t}[ (1/4)·F^{2}·(1/a)·e^{2·(a/m)^{(1/2)}·t} ] = f(t)·d_{t}[x(t)]

Teorema:

( n!/( (m+(-1))!(n+(-m)+1)! ) )+( n!/( m!(n+(-m))! ) ) = ( (n+1)!/( m!((n+1)+(-m))! ) )