From 8dda430f02d324707b0a028a55f96427d3521a01 Mon Sep 17 00:00:00 2001 From: Rui Campos Date: Sat, 23 Mar 2024 14:11:35 +0000 Subject: [PATCH] Update README.md Signed-off-by: Rui Campos --- README.md | 8 -------- 1 file changed, 8 deletions(-) diff --git a/README.md b/README.md index 66af6b5..6d60ab7 100644 --- a/README.md +++ b/README.md @@ -60,14 +60,6 @@ $$\rho^{bnul} = \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bnf(u)g(l)} + 2 \tilde \del Substituting this back, while attending to the relevant substitution on the first term of the original expression, - -$$q^{bnul} _ {l} = \delta^{f(l)g(l)} \bar M^n_{l} \left [ \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bnf(u)f(l)} + 2 \tilde \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bng(u)f(l)} \right ] + 2 \tilde \delta^{f(l)g(l)} \bar M^n_l \left [ \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bnf(u)g(l)} + 2 \tilde \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bng(u)g(l)} \right ]$$ - -which we'll now group according to the $\delta$'s - -$$q^{bnul} _ {l} = \bar M^n _ {l} p^{bnf(u)f(l)} p^{bnf(u)f(l)} \delta^{f(l)g(l)} \delta^{f(u)g(u)} + 2 \bar M^n_{l} p^{bnf(u)f(l)} p^{bng(u)f(l)} \delta^{f(l)g(l)} \tilde \delta^{f(u)g(u)} + 2 \bar M^n_l p^{bnf(u)f(l)} p^{bnf(u)g(l)} \delta^{f(u)g(u)} \tilde \delta^{f(l)g(l)} + 4 \bar M^n_l p^{bnf(u)f(l)} p^{bng(u)g(l)} \tilde \delta^{f(u)g(u)} \tilde \delta^{f(l)g(l)}$$ - - $$ \begin{aligned} q^{bnul} _ {l} &= \delta^{f(l)g(l)} \bar M^n_{l} \left [ \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bnf(u)f(l)} + 2 \tilde \delta^{f(u)g(u)} p^{bnf(u)f(l)} p^{bng(u)f(l)} \right ] \\