ecuació diferencial exponencial de potencial

d_{x}[y(x)] = (y/x)·( m+x^{m} )

y(x) = x^{m}·e^{(x^{m}/m)}

d_{x}[ e[m]( x^{m}/m ) ] = ( mx^{m+(-1)}+x^{2m+(-1)} )·e^{(x^{m}/m)}

Sigui y(x) = u(x)·x ==> 

u(x)+x·d_{x}[u(x)] = mu(x)+x^{m}u(x)

x·d_{x}[u(x)] = ( m+x^{m}+(-1) )·u(x)

ln(u(x)) = (m+(-1))·ln(x)+(x^{m}/m)

y(x) = ( x^{m+(-1)}·e^{(x^{m}/m)} )·x

d_{x}[y(x)] = (y/x)·( 1+a·(y/x)^{m} )

Sigui y(x) = u(x)·x ==>

x·d_{x}[u(x)] = a·( u(x) )^{m+1}

(-1)·(1/m)·(1/a)·( 1/( u(x) )^{m} ) = ln(x)

y(x) = ( ( (-1)·(1/m)·(1/a) )^{(1/m)}·( ln(x) )^{(-1)·(1/m)} )·x

d_{x}[ ( ( (-1)·(1/m)·(1/a) )^{(1/m)}·( ln(x) )^{(-1)·(1/m)} )·x ] = ...

... ( (-1)·(1/m)·(1/a) )^{(1/m)}·( (-1)·(1/m)·( ln(x) )^{(-1)·(1/m)+(-1)}+( ln(x) )^{(-1)·(1/m)} )

d_{x}[y(x)] = (y/x)·( m+( m/ln( x^{m}/m ) ) )

y(x) = x^{m}·ln( x^{m}/m )

d_{x}[ ln[m]( x^{m}/m ) ] = ( mx^{m+(-1)}·ln( x^{m}/m )+mx^{m+(-1)} )

Sigui y(x) = u(x)·x ==>

x·d_{x}[u(x)] = u(x)( (m+(-1))+(m/ln( x^{m}/m )) )

ln(u(x)) = (m+(-1))·ln(x)+ln(ln( x^{m}/m ))

y(x) = x^{m+(-1)}·ln( x^{m}/m )·x

exponencial de potencial

x = y^{y^{p}}

ln(x) = y^{p}·ln(y)

ln(x) = ln[p](y)

e[(-p)]( ln(x) ) = y

x = e^{ln[p](y)}

x = y^{p}·e^{y}

x = e[p](y)

ln[(-p)](x) = y

x = y^{p}·ln(y)

x = ln[p](y)

e[(-p)](x) = y

d_{x}[x^{p}·ln(x)] = px^{p+(-1)}·ln(x)+x^{p+(-1)}

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

d_{x}[x^{(-p)}·ln(x)] = (-p)·x^{(-p)+(-1)}·ln(x)+x^{(-p)+(-1)} )

d_{x}[x^{p}·e^{x}] = px^{p+(-1)}·e^{x}+x^{p}·e^{x}

conjunts transitius

Si A€P(P(A)) ==> P(A) és transitiu

Sigui x€P(A).

Sigui y€x

y€A

y€P(A)

nil-dualogia

g(x) >] 0 & g(x)+y(x) [< f(x) ==> y(x) [< f(x)

g(x) [< 0 & g(x)+y(x) >] f(x) ==> y(x) >] f(x)

x >] 0 & x+y(x) [< 0 ==> y(x) [< 0

x [< 0 & x+y(x) >] 0 ==> y(x) >] 0

mesura

a(n) = (x/n)

d_{x}[x^{n}] = ( 1/a(n) )·x^{n}

∫ [ x^{n} ] d[x] = a(n+1)·x^{n}

b(n) = (1/n)

d_{x}[e^{nx}] = ( 1/b(n) )·e^{nx}

∫ [ e^{nx} ] d[x] = b(n)·e^{nx}

c(sin(nx)) = n·( 1+(-1)·( sin(nx) )^{2} )^{(1/2)}

d_{x}[sin(nx)] = c(sin(nx))

∫ [ sin(nx) ] d[x] = (-1)·c(sin(nx))

c(cos(nx)) = n·( 1+(-1)·( cos(nx) )^{2} )^{(1/2)}

d_{x}[cos(nx)] = (-1)·c(cos(nx))

∫ [ cos(nx) ] d[x] = c(cos(nx))

u(ln(x)) = e^{ln(x)}

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

∫ [ ln(x) ] d[x] = ln(x)·u(ln(x))+(-1)·u(ln(x))

intersecció y suma de espais vectorials

k·<1,1> = i·<a,b> + j·<b,a>

i = k·( 1/(a+b) )

j = k·( 1/(b+a) )

k·<1,1> + i·<a,b> + j·<b,a> = ( i+k·( 1/(a+b) ) )·<a,b> + ( j+k·( 1/(b+a) ) )·<b,a>

k·<1,1> = i·<a,b> + j·<c,a>

i = k·( 1/(a+b) )

j = k·( 1/(c+a) )

k·<1,1> + i·<a,b> + j·<c,a> = ( i+k·( 1/(a+b) ) )·<a,b> + ( j+k·( 1/(c+a) ) )·<c,a>

integrals circulars

lim[s-->1][ 2·∮ [ z = se^{ix}+a ]-[ (z+a)·(z+(-a)) ] d[z] ] = (-1)·(4/3)·i

lim[s-->1][ 2·∮ [ z = se^{ix}+(-a) ]-[ (z+a)·(z+(-a)) ] d[z] ] = (-1)·(4/3)·i

residus integrals

lim[s-->0][ ∮ [ z = se^{ix}+a ]-[ f(z)/(g(z)+(-a)) ] d[z]·( 1/(2pi·i) ) ] = ...

... f( g^{o(-1)}(a) )·d_{a}[ g^{o(-1)}(a) ]

lim[s-->0][ ∮ [ z = se^{ix}+(-a) ]-[ f(z)/(g(z)+a) ] d[z]·( 1/(2pi·i) ) ] = ...

... f( g^{o(-1)}(-a) )·d_{(-a)}[ g^{o(-1)}(-a) ]

ecuació diferencial

x^{2}·d_{xx}^{2}[y(x)]+x·d_{x}[y(x)] = m^{2}·y(x)

y(x) = x^{m}

x^{2}·d_{xx}^{2}[y(x)]+x·d_{x}[y(x)] = ∑ c_{n}·x^{n}

y(x) = ∑ ( c_{n}·( 1/(n^{2}) )·x^{n} )

ecuació diferencial

x·d_{xx}^{2}[y(x)]+d_{x}[y(x)] = y(x)

y(x) = ∑ ( ( 1/(n^{2})! )·x^{n} ) = ∑ ( x^{i(n)} )

p+1 = n <==> ∑ ( x^{i(n+(-1))} ) = ∑ ( x^{i(p)} )

x·d_{xx}^{2}[y(x)]+d_{x}[y(x)] = ∑ ( c_{n}·x^{n} )

y(x) = ∑ ( c_{(n+(-1))}·( 1/(n^{2}) )·x^{n} )

factorial

(0/1!)+(1/2!)+...+( (n+(-1))/n! ) = ( (n!+(-1))/n! )

ley laboral del cristianismo stronikiano

Trabajarás máximo unos 6 días en una semana y al séptimo descansarás.

Descansarás máximo unos 6 días en una semana y al séptimo trabajarás.

Trabajarás unos 7 días en unas 2 semanas y otros unos 7 descansarás.

Descansarás unos 7 días en unas 2 semanas y otros unos 7 trabajarás.