# Costa’s minimal surface equation and its applicability for $SPX year end projection # Costa’s minimal surface and its applicability for$SPX year end projection incase if you had forgotten the  equation from your physics classes .. ,the Costa’s minimal surface equation is below The other day, we finally managed to apply Alfred Gray’s parametric equations  on how to use it for $SPX year end price target. Here, $\wp, \wp^\prime$ and $\zeta$ are respectively the Weierstrass elliptic function, its derivative, and the Weierstrass zeta function, with invariants $g_2=\left(\frac12\mathrm{B}\left(\frac14,\frac14\right)\right)^4=\frac{\Gamma(1/4)^8}{16\pi^2}$ and $0$, and $\mathrm{B}(x,y)$ and $\Gamma(x)$ are the usual beta and gamma functions. The invariants are the ones corresponding to the semi-periods $\omega_1=\frac12$ and $\omega_3=\frac{i}{2}$. The parameter ranges are $0 < u < 1$ and $0 < v < 1$. We may not be able to give the full details ( as they are proprietary of nature ) on how to manipulate the Weierstrass elliptic functions that show up in the equations, but below the details on how the equation fared against each year end’s actual$SPX close

# Callan–Symanzik equation applicability to predict major $SPX crashes as we all know , in quantum electrodynamics the Callan–Symanzik equation takes the form being n and m the number of electrons and photons respectively. modifying n for “Wicksellian interest rate” ( refer to Ben S. Bernanke ‘s blog post Why are interest rates so low? dated March 30, 2015 6:01am, , to understand the dynamics of Wicksellian interest rate ) , and m for the , i’e the time elapsed between the worst 20 day percentage changes in$SPX ( S&P 500 cash index) ,

note is the golden ratio multiplied by the prior $SPX crash date expressed in UNIX time-stamp format. Below were the prior instances where the above modified Callan–Symanzik equation predicted the$SPX upcoming crashes in percentage terms ( 20-day non interleaving ) , since 1950 , mind you it has a perfect 100 % record thus far …