Mathematical Notation for Mixed Effect Model with no Intercept I am trying to write the mathematical notation for the following mixed effect model:
lmer(Y ~ 0 + A + B + C + (0 + B | A)

With subjects nested in A and a stratified intercept for every A should be estimated.
So what I think this means is: 
Stratified Intercept for A 
Fixed Effect for A, B and C 
Varying Random Slope for B
But I struggle to set up the mathematical notation for this formula.
My first attempt was this:
\begin{aligned}
 \operatorname{Y}_{ij}  &\sim N \left(\mu_{i}, \sigma^2\right) \\
\end{aligned}
\begin{aligned}
E(\operatorname{Y{ij}}) = \beta_{0j}(A) + \beta_{1j} (A) + \beta_{2j} (B) +
\beta_{3} (C) + \epsilon_{ij}
\end{aligned}
\begin{aligned}
E(Y_{ij}) = (\beta_0(A) + \upsilon_{0j}(A)) + (\beta_{1}(A) + \upsilon_{1j}(A)) + (\beta_{2}(B) + \upsilon_{2j}(B)) + \beta_{3}(C) + \epsilon_{ij}
\end{aligned}
\begin{aligned}
E(Y_{ij}) = \beta_0(A) +  \beta_{1}(A) + \beta_{2}(B) + \beta_{3}(C) + \upsilon_{0j}(A) + \upsilon_{1j}(A)+ \upsilon_{2j}(B) + \epsilon_{ij}
\end{aligned}
\begin{aligned}
\upsilon_{0j} \sim N(0, \tau^2_{\upsilon_{0j}}) \\ \upsilon_{1j} \sim N(0, \tau^2_{\upsilon_{1j}}) \\ \upsilon_{2j} \sim N(0, \tau^2_{\upsilon_{2j}})
\end{aligned}
\begin{aligned}
Cov(\sigma^2_{\upsilon_{0j}}, \sigma^2_{\upsilon_{2j}}) = \sigma^2_{\upsilon_{0j}, \upsilon_{2j}}
\end{aligned}
\begin{aligned}
\left(
  \begin{array}{c}
\beta_{0j} \\
\beta_{2j}
  \end{array}
\right)
&\sim N \left(
\left(   \begin{array}{c}
\mu_{\beta_{0j}} \\
\mu_{\beta_{2j}}
  \end{array}
\right) , 
\left( \begin{array}{c}
\sigma_{\beta_{0j}} & \rho_{\beta_{0j}\beta_{2j}} \\
\rho_{\beta_{2j}\beta_{0j}} & \sigma_{\beta_{0j}}
  \end{array}\right) 
\right) , for \ A \ j = 1, ...,J
\end{aligned}
I really struggle with the intercepts, especially with the random elements of A, so I am thankful for every kind of help!

The model
lmer(Y ~ 0 + A + B + C + (0 + B | A)

does indeed have three fixed effects and a single random slope.
I would write this model (using a vectorized notation) as
$$
Y = \beta_{a} A + (\beta_b + b_a) B + \beta_c C + \epsilon \\
\epsilon \sim N(0, \sigma^2_\epsilon) \\
b_a \sim N(0, \sigma^2_b)
$$
where $b_a$ is the random slope of $B$, which varies depending on the levels of $A$, and $\epsilon$ is the error term.
