tex

\overset{#1}{#2}

overset( int a[i][j][k] , int b[i][j][k] , int x , int y )

{

put-grafic-color( a[i][j][k] , x , y );

put-grafic-color( b[i][j][k] , x , y+z );

}

\underset{#1}{#2}

underset( int a[i][j][k] , int b[i][j][k] , int x , int y )

{

put-grafic-color( a[i][j][k] , x , y );

put-grafic-color( b[i][j][k] , x , y+not(z) );

}

\frac{#1}{#2}

frac( int a[i][j][k] , int b[i][j][k] , int x , int y )

{

put-grafic-color( a[i][j][k] , x , y+(z/2) );

put-grafic-color( bar[i][j][k] , x , y );

put-grafic-color( b[i][j][k] , x , y+not(z/2) );

}

\integral-frac{#1}{#2}

integral-frac( int a[i][j][k] , int b[i][j][k] , int x , int y )

{

put-grafic-color( a[i][j][k] , x , y+(z/2) );

put-grafic-color( bar[i][j][k] , x , y+(z/4) );

put-grafic-color( bar[i][j][k] , x , y+not(z/4) );

put-grafic-color( b[i][j][k] , x , y+not(z/2) );

}

{#1}^{#2}

^( int a[i][j][k] , int b[i][j][k] , int x , int y )

{

put-grafic-color( a[i][j][k] , x , y );

put-grafic-color( b[i][j][k] , x+z , y+z );

}

{#1}_{#2}

_( int a[i][j][k] , int b[i][j][k] , int x , int y )

{

put-grafic-color( a[i][j][k] , x , y );

put-grafic-color( b[i][j][k] , x+z , y+not(z) );

}

{#1}^_^{#2}

^_^( int a[i][j][k] , int b[i][j][k] , int x , int y )

{

put-grafic-color( a[i][j][k] , x , y );

put-grafic-color( b[i][j][k] , x+not(z) , y+z );

}

{#1}_^_{#2}

_^_( int a[i][j][k] , int b[i][j][k] , int x , int y )

{

put-grafic-color( a[i][j][k] , x , y );

put-grafic-color( b[i][j][k] , x+not(z) , y+not(z) );

}

economia: social-democracia vs socialisme

La empresa ha de decidir:

si és social-demócrata o bé si és socialista.

preu de venta k socis:

B(x) = px+(-n)·x^{k}

d_{x}[B(x)] = q+( (-n)·k )·x^{k+(-1)} = 0

x = 1

p = kn

social-democracia:

impostos k socis:

B(x) = qx+(-n)·x^{(1/k)}

d_{x}[B(x)] = q+( (-n)/k )·x^{(1/k)+(-1)} = 0

x = 1

q = (n/k)

preu total:

p+q = kn+(n/k)

socialisme:

impostos k socis:

B(x) = (q/k)·x+(-n)·x^{(1/k)}

d_{x}[B(x)] = (q/k)+( (-n)/k )·x^{(1/k)+(-1)} = 0

x = 1

q = n

preu total:

p+q = kn+n = (k+1)·n

social-democracia:

exemples:

n = 0.10€

2n = 0.20€

(n/2) = 0.05€

2n+(n/2) = 0.25€

socialisme:

exemples:

n = 0.10€

2n = 0.20€

n = 0.10€

2n+n = 0.30€

social-democracia:

exemples:

n = 0.20€

2n = 0.40€

(n/2) = 0.10€

2n+(n/2) = 0.50€

socialisme:

exemples:

n = 0.20€

2n = 0.40€

n = 0.20€

2n+n = 0.60€

social-democracia:

exemples:

n = 0.50€

2n = 1€

(n/2) = 0.25€

2n+(n/2) = 1.25€

socialisme:

exemples:

n = 0.50€

2n = 1€

n = 0.50€

2n+n = 1.50€

social-democracia:

exemples:

n = 1.50€

3n = 4.50€

(n/3) = 0.50€

3n+(n/3) = 5€

socialisme:

exemples:

n = 1.50€

3n = 4.50€

n = 1.50€

3n+n = 6€

social-democracia:

impostos k = 2 & 20%·(p+q) = (n/2)

impostos k = 3 & 10%·(p+q) = (n/3)

socialisme:

impostos k = 2 & 33.3...%·(p+q) = n

impostos k = 3 & 25%·(p+q) = n

cuina

salsa rosa

piña amarilla

lechuga verde

zanahoria naranja

1 destructor

gambas rosa-blanco

manzana ocre-blanco

lechuga verde

zanahoria naranja

1 destructor

vinagre marrón

aceite verde

ajo picado amarillo

pimentón dulce rojo

pescado al horno

1 destructor

electrodébil

g_{x}(t) = e^{( Wq+Z(1+(-1)·q^{2}) )·it}·f_{x}(t)

g_{y}(t) = e^{( Wq+Z(1+(-1)·q^{2}) )·(-i)t}·f_{y}(t)

g_{x}(t)·g_{y}(t) = f_{x}(t)·f_{y}(t)

d_{t}[g_{x}(t)]·d_{t}[g_{y}(t)] = ...

... d_{t}[f_{x}(t)]·d_{t}[f_{y}(t)]+( Wq+Z(1+(-1)·q^{2}) )^{2}·f_{x}(t)·f_{y}(t) = 0

f_{x}(t) = e^{( Wq+Z(1+(-1)·q^{2}) )·it}

f_{y}(t) = e^{( Wq+Z(1+(-1)·q^{2}) )·it}

f_{x}(t) = e^{( Wq+Z(1+(-1)·q^{2}) )·(-i)t}

f_{y}(t) = e^{( Wq+Z(1+(-1)·q^{2}) )·(-i)t}

ondas radioactivas electro-nucleares:

Tauón <==> e^{W·it} & q = 1 & W > 0

Muón <==> e^{(-W)·it} & q = (-1) & W > 0

Neutrino <==> e^{Z·it} & q = 0 & Z > 0

ondas radioactivas gravito-nucleares:

anti-Tauón <==> e^{W·it} & q = (-1) & W < 0

anti-Muón <==> e^{(-W)·it} & q = 1 & W < 0

anti-Neutrino <==> e^{Z·it} & q = (-0) & Z < 0

anti-electrón <==> e^{q·it} & W = 1 & Z = 0

electrón <==> e^{(-q)·it} & W = 1 & Z = 0

gravitón <==> e^{q·it} & W = (-1) & Z = (-0)

anti-gravitón <==> e^{(-q)·it} & W = (-1) & Z = (-0)

( g_{x}(t) )^{2} = e^{( Wq+Z(1+(-1)·q^{2}) )·it}·( f_{x}(t) )^{2}

( g_{y}(t) )^{2} = e^{( Wq+Z(1+(-1)·q^{2}) )·(-i)t}·( f_{y}(t) )^{2}

( g_{x}(t)·g_{y}(t) )^{2} = ( f_{x}(t)·f_{y}(t) )^{2}

d_{t}[g_{x}(t)]·d_{t}[g_{y}(t)] = ...

... d_{t}[f_{x}(t)]·d_{t}[f_{y}(t)]+( Wq+Z(1+(-1)·q^{2}) )^{2}·( f_{x}(t)·f_{y}(t) )^{2} = 0

f_{x}(t) = ( ( Wq+Z(1+(-1)·q^{2}) )·it )^{(-1)}

f_{y}(t) = ( ( Wq+Z(1+(-1)·q^{2}) )·it )^{(-1)}

f_{x}(t) = ( ( Wq+Z(1+(-1)·q^{2}) )·(-i)t )^{(-1)}

f_{y}(t) = ( ( Wq+Z(1+(-1)·q^{2}) )·(-i)t )^{(-1)}

ecuacions en derivades parcials

u(x,y) = f(x)+g(y)

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

d_{x}[f(x)] = a & a = d_{y}[g(y)]

d_{x}[f(x)] = (-a) & (-a) = d_{y}[g(y)]

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

u(x,y) = ax+ay || u(x,y) = (-a)·x+(-a)·y

d_{x}[u(x,y)] = (-1)·d_{y}[u(x,y)]

u(x,y) = ax+(-a)·y || u(x,y) = (-a)·x+ay

d_{x}[u(x,y)] = i·d_{y}[u(x,y)]

u(x,y) = ai·x+ay || u(x,y) = (-a)i·x+(-a)y

u(x,y) = (-a)x+ai·y || u(x,y) = ax+(-a)i·y

d_{x}[u(x,y)] = (-i)·d_{y}[u(x,y)]

u(x,y) = (-a)i·x+ay || u(x,y) = ai·x+(-a)y

u(x,y) = (-a)·x+(-a)i·y || u(x,y) = ax+ai·y

e^{u(x,y)}( d_{x}[u(x,y)]+d_{y}[u(x,y)] ) = k^{2}·(x+y)

u(x,y) = ln( kx )+ln( ky ) || u(x,y) = ln( (-k)x )+ln( (-k)y )

e^{u(x,y)}( d_{x}[u(x,y)]+d_{y}[u(x,y)] ) = (-1)·k^{2}·(x+y)

u(x,y) = ln( kx )+ln( (-k)y ) || u(x,y) = ln( (-k)x )+ln( ky )

álgebra

ax^{n}+bx^{m} = c

x = c^{ ( 1/(log_{c}(a)+n) [+] (log_{c}(b)+m) ) }

ac^{ ( n/(log_{c}(a)+n) [+] (log_{c}(b)+m) ) }+...

bc^{ ( m/(log_{c}(a)+n) [+] (log_{c}(b)+m) ) } = ...

c^{ ( (log_{c}(a)+n)/(log_{c}(a)+n) [+] (log_{c}(b)+m) ) }+...

c^{ ( (log_{c}(b)+m)/(log_{c}(a)+n) [+] (log_{c}(b)+m) ) } = c

ax^{n}+bx^{m} = (x+(-1)·c^{ 1/( (log_{c}(a)+n) [+] (log_{c}(b)+m) ) })·...

(ax^{n+(-1)}+bx^{m+(-1)})+...

... c^{ 1/( (log_{c}(a)+n) [+] (log_{c}(b)+m) ) }(ax^{n+(-1)}+bx^{m+(-1)} = c

so y color

DO en escala n:

export-grafic-sound-sinh( grafic-sound[i][j][k] , nFFF )

sound[i][j][k]·sinh( i·nFFF·t )

export-grafic-sound-cosh( grafic-sound[i][j][k] , nFFF )

sound[i][j][k]·cosh( i·nFFF·t )

SI en escala n:

export-grafic-sound-sinh( grafic-sound[i][j][k] , n7FF )

export-grafic-sound-cosh( grafic-sound[i][j][k] , n7FF )

LA en escala n:

export-grafic-sound-sinh( grafic-sound[i][j][k] , n1FF )

export-grafic-sound-cosh( grafic-sound[i][j][k] , n1FF )