distribucions de probabilitat en series

f(k) = (x^{k}/k!)·e^{-x}
f(k) = k·(x^{k}/k!)·(1/x)·e^{-x}
f(k) = k(k+(-1))·(x^{k}/k!)·(1/x^{2})·e^{-x}
f(k) = k(k+(-1))·...(m)...·(k+(-m))·(x^{k}/k!)·(1/x^{m+1})·e^{-x}


f(k) = (x^{2k}/(2k)!)·(1/cosh(x))
f(k) = (x^{2k+1}/(2k+1)!)·(1/sinh(x))


f(k) = (2k)(x^{2k}/(2k)!)·(1/x)·(1/sinh(x))
f(k) = (2k+1)(x^{2k+1}/(2k+1)!)·(1/x)·(1/cosh(x))

distribucions de probabilitat

f(k) = [ n // k ]·2^{(-n)}


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


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


f(0)+...+f(n) = ( [ n // 0 ]p^{n}+...+[ n // n ](1+(-p))^{n} )=( p+(1+(-p)) )^{n}=1


f(k) = (1/p^{n})·( p^{k}+(-1)·p^{(k+(-1))} )


f(0)+...+f(n) = ( (1/p^{n})·( ( (p^{n+1}+(-1))/(p+(-1)) )+(-1)·( (p^{n}+(-1))/(p+(-1)) ) )=...
...(1/p^{n})·p^{n}·( (p+(-1))/(p+(-1)) )=1

derivada imperial

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


d_{t}^{(1/m)}[ d_{t}^{(1/m)}[x(t)]^{m} ] + ( a^{(2/m)}( x(t) )^{(1/m)} ) = 0 <==> x(t)=e^{at·i}


d_{x}^{(1/m)}[ f(x)+g(x) ] =[2/2^{m}]= d_{x}^{(1/m)}[f(x)] + d_{x}^{(1/m)}[g(x)]
d_{x}^{(1/m)}[ af(x) ] = a^{(1/m)}·d_{x}^{(1/m)}[f(x)]


d_{x}^{(1/m)}[ ax^{2}+bx ] =[2/2^{m}]= (2ax)^{(1/m)} + b^{(1/m)}


d_{x}^{(1/m)}[ ax^{3}+bx^{2}+cx ] =[3/3^{m}]= (3a)^{(1/m)}·x^{(2/m)}+(2bx)^{(1/m)}+c^{(1/m)}

La Ley

Adorarás al señor tu Dios.
No dibujarás al señor tu Dios.
No tomarás el nombre del señor tu Dios.


No matarás.
No robarás: somos y tenemos propiedad privada.


No darás falso testimonio.


No cometerás adulterio.
Honrarás al padre y a la madre: no practicarás sexo con la familia.


No desearás nada que le pertenezca a otro: ni país de otro.

La lley

Adorarás al senyor ton Déu.
No dibusharás al senyor ton Déu.
No prendrás el nom del senyor ton Déu.


No matarás.
No robarás: som y tenim propietat privada.


No donarás fals testimoni.


No cometrás adulteri.
Honrarás al pare y a la mare: no practicarás sexe amb la familia.


No desitjarás res que li perteneishi a un altre: ni país d'un altre.

funció export-matrix-sound en assembler

export-matrix-sound-x( int principi , int final )
{
mov bx,principi
mov cx,[bx]
not cx
not cx
mov bx,final
mov dx,[bx]
not dx
not dx
xor ax,ax
int 0000 0101
}


export-matrix-sound-y( int principi , int final )
{
mov bx,principi
mov cx,[bx]
not cx
mov bx,final
mov dx,[bx]
not dx
sis ax,ax
int not(0000 0101)
}


def-int
{
int 0000 0101 reprodueix la matriu de la tarjeta de so des de cx fins a dx,
y se atura en ax!=0 pulsant una tecla.
int not(0000 0101) reprodueix la matriu de la tarjeta de so des de not(cx) fins a not(dx),
y se atura en ax!=not(0) pulsant una tecla.
}

llum y so

cos(x)=(1/2)(e^{xi}+e^{(-x)i})
sin(x)=(1/2i)(e^{xi}+(-1)e^{(-x)i})


cosh(x)=(1/2i)(e^{x}+e^{(-x)})
sinh(x)=(1/2i)(e^{x}+(-1)e^{(-x)})




cos(0)=1
cosh(0·i)=1
sin(0)=0
sinh(0·i)=0


cos(pi/2)=0
cosh((pi/2)·i)=0
sin(pi/2)=1
sinh((pi/2)·i)=1


cos(pi)=(-1)
cosh(pi·i)=(-1)
sin(pi)=0
sinh(pi·i)=0


cos(3pi/2)=0
cosh((3pi/2)·i)=0
sin(3pi/2)=(-1)
sinh((3pi/2)·i)=(-1)


cos(2pi)=1
cosh(2pi·i)=1
sin(2pi)=0
sinh(2pi·i)=0

colors

blanc dual negre
vermell dual verd
blau dual taronja
groc dual violeta
ocre dual rosa
blau cel dual marrón
granate dual verde clar

Lógica de dret constitucional

afirmació:
si plou aleshores em mullû de la pluja perque no portû paraigües.
negació:
plou y no em mullû de la pluja encara que potser no portû paraigües.


afirmació:
si A(x) aleshores B(x) perque no C(x).
( ( A(x) ==> B(x) ) <== ¬C(x) ) & ¬C(x).
negació:
A(x) y no B(x) encara que potser no C(x).
( ( A(x) & ¬B(x) ) & ¬C(x) ) or C(x).

conjugeited eit

present
calculeitu <==> calculû <==> calculû-tek <==> calculo <==> calculo <==> calculuactu
calculeites <==> calcules <==> calcules-tek <==> calculas <==> calcúlati <==> calculuactes
calculeita <==> calcula <==> calcula-tek <==> calcula <==> calcula <==> calculuacta
calculeitems<==>calculem<==>calculemek<==>calculamos<==>calculamoti<==>calculuactems
calculeiteus <==> calculeu <==> calculeuek <==> calculáis <==> calculáiti <==> calculuacteus
calculeiten <==> calculen <==> calculen-tek <==> calculan <==> calculan <==> calculuactent

grafic M

M-Minuscula( int n-x , int n-y , int x , int y )
{
for( k=1 ; k [< n-x  ; k++ )
{
m-k = k;
put-pixel-color-x( color , x+k , y+(m-k) )
}
for( k=(-1) ; k >] not(n-x)  ; k--)
{
m-k = not(k);
put-pixel-color-y( color , x+(n-x+not(k)) , y+(n-x+not(m-k)) )
}


for( k=(-1) ; k >] n-y  ; k-- )
{
m-k = not(k);
put-pixel-color-x( color , x+k , y+(m-k) )
}
for( k=1 ; k [< not(n-y)  ; k++ )
{
m-k = k;
put-pixel-color-y( color , x+(n-y+not(k)) , y+(n-y+not(m-k)) )
}
}


M-Mayuscula( int n-x , int n-y , int x , int y )
{
for( k=1 ; k [< n-x  ; k++ )
{
m-k = k;
put-pixel-color-x( color , x+(m-k) , y+k )
}
for( k=(-1) ; k >] not(n-x)  ; k--)
{
m-x = n-x;
put-pixel-color-y( color , x+(m-x) , y+((m-x)+k) )
}


for( k=(-1) ; k >] n-y  ; k-- )
{
m-k = not(k);
put-pixel-color-x( color , x+not(m-k) , y+not(k) )
}
for( k=1 ; k [< not(n-y)  ; k++ )
{
m-y = not(n-y);
put-pixel-color-y( color , x+not(m-y) , y+(not(m-y)+not(k)) )
}
}

caixa rectangle

put-pixel-color-x( color , x-m , y-m+a )
for-racional( k=1 ; k [< b ; k++ )
{
put-pixel-color-x( color , x-m+k , y-m+a )
}
for-racional( k=(-1) ; k >] not(b) ; k-- )
{
put-pixel-color-y(color , x-m+k , y-m+a )
}


put-pixel-color-y( color , x-m , y-m+not(a) )
for( k=1 ; k [< b ; k++ )
{
put-pixel-color-x( color , x-m+k , y-m+not(a) )
}
for( k=(-1) ; k >] not(b) ; k-- )
{
put-pixel-color-y( color , x-m+k , y-m+not(a) )
}


put-pixel-color-x( color , x-m+b , y-m )
for( k=1 ; k [< a ; k++ )
{
put-pixel-color-x( color , x-m+b , y-m+k )
}
for( k=(-1) ; k >] not(a) ; k-- )
{
put-pixel-color-y( color , x-m+b , y-m+k )
}


put-pixel-color-y( color , x-m+not(b) , y-m )
for( k=1 ; k [< a ; k++ )
{
put-pixel-color-x( color , x-m+not(b) , y-m+k )
}
for( k=(-1) ; k >] not(a) ; k-- )
{
put-pixel-color-y( color , x-m+not(b) , y-m+k )
}

ps-estructure de politja

\begin{ps-estructure}
\case{(-1)}
{
\caixa{not(x-m),y-m}{m_{1}}
\corda{0+(-r),y}{not(x-m),y-m}
\vector-vertical-negatiu{not(x-m),y}{q_{1}·g}
\vector-vertical-positiu{not(x-m),y}{T_{1}}
}
\case{not(0)}
{
\semi-cercle-negatiu{not(not(0)),y}{r}
\vector-vertical-negatiu{not(not(0)),y}{q_{0}·g}
}
\case{0}
{
\semi-cercle-positiu{0,y}{r}
\vector-vertical-positiu{0,y}{F_{0}}
}
\case{1}
{
\caixa{x-m,y-m}{m_{2}}
\corda{0+r,y}{x-m,y-m}
\vector-vertical-negatiu{x-m,y}{q_{2}·g}
\vector-vertical-positiu{x-m,y}{T_{2}}
}
\end{ps-estructure}

tex print-cursive

n-x=1;
k=1;
while( text-x[1] == [ \cursive{ ] ; text-x[k] != [ } ] ; k++ )
{
print-tex-positiu(text-y[k],\cursive);
n-x++;
}
k=(-1);
while( text-y[(-1)] == [ } ] ; text-y[k] != [ \cursive{ ] ; k-- )
{
print-tex-negatiu(text-y[k],\cursive);
}
avanç-text-positiu(n-x);


k=1;
while( text-x[1] == [ \dual-cursive{ ] ; text-x[k] != [ } ] ; k++ )
{
print-tex-positiu(text-y[k],\dual-cursive);
}
n-y=(-1);
k=(-1);
while( text-y[(-1)] == [ } ] ; text-y[k] != [ \dual-cursive{ ] ; k-- )
{
print-tex-negatiu(text-y[k],\dual-cursive);
n-y--;
}
avanç-text-negatiu(n-y);