User:Fussion1

Complex transformation
Explain the essence of the following function.

$$ f(z) : \mathbb{C} \setminus 0 \to \mathbb{C} \quad \mbox{such that} $$

$$ f(z) = z \sqrt { 1 + \left [ \frac { \min \{ | \operatorname{Re} \ z |, | \operatorname{Im} \ z | \} } { \max \{ | \operatorname{Re} \ z |, | \operatorname{Im} \ z | \} } \right ]^2 } $$

Dividend Discount Models
$$ P = \frac {D_1} {(1 + R_1)} + \frac {D_2} {(1 + R_1)(1 + R_2)} + ... \quad \quad \quad \quad (1) $$

$$ P = \frac {E_1 \theta_1} {(1 + R_1)} + \frac {E_2 \theta_2} {(1 + R_1)(1 + R_2)} + ... \quad \quad \quad \quad (2) $$

$$ P = \frac {E_1 \theta_1} {(1 + r_1)} X_1 + \frac {E_2 \theta_2} {(1 + r_1)(1 + r_2)} X_2 + ... \quad \quad \quad \quad (3) $$

$$ D_n = \bar{D} \cdot (1 + g)^n = D \cdot (1 + g)^{n-1} \quad where \quad \bar{D} = D_0 \quad and \quad D = D_1 $$

$$ R_n = R\ $$

$$ P = \frac {D} {(1 + R)} + \frac {D (1 + g)} {(1 + R)^2} + ... $$

$$ P = \frac {D} {R - g} \quad \quad \quad \quad (*) $$

$$ R = \frac {D} {P} + g = \gamma + g \quad \quad \quad \quad (**) $$

Markov chain game
$$ \mbox{My transition matrix} = \begin{bmatrix} & A = 1 & A = 2 & A = 3 \\ A = 1 & 1/2  & 0     & 1/2 \\ A = 2 & 1/2  & 0     & 1/2 \\ A = 3 & 1/2  & 0     & 1/2 \end{bmatrix} $$

$$ \mbox{Reflecting barriers matrix} = \begin{bmatrix} & A = 0 & A = 1 & A = 2 & A = 3 & A = 4\\ A = 0 & 0    & 1     & 0     & 0     & 0 \\ A = 1 & 1/2  & 0     & 0     & 1/2   & 0 \\ A = 2 & 0    & 1/2   & 0     & 1/2   & 0 \\ A = 3 & 0    & 1/2   & 0     & 0     & 1/2 \\ A = 4 & 0    & 0     & 0     & 1     & 0 \end{bmatrix} $$

Loan formula
$$ \begin{align} & P = \mbox{monthly repayment size} \\ & S = \mbox{loan size} \\ & R = 1 + \mbox{APR} \\ & T = \mbox{loan term in years} \end{align} $$

$$ P = S \ \frac {R^{1/12} - 1} {1 - R^{-T}} $$

Advanced driving techniques selection

 * ¶ Bootleg turn (Handbrake turn) = 180° turn using handbrake
 * Cadence braking = Advanced braking by repeatedly using and releasing footbrake
 * Defensive driving = Anticipation of dangerous situations and mistakes of others
 * ¶ Doughnuts = Spinning on one place by overaccelerating
 * Drifting = Going through a turn by directing the vehicle going sideways
 * J-turn = 180° turn starting from reverse driving
 * Pittsburgh left = Turning left before allowing ongoing vehicles to pass
 * ¶ Wheelspin (Burnout) = Burning the wheels by overaccelerating