Symbol in context

$x_j$

This entry links every published equation using this exact notation. Its meaning may change between equations.

Used in 6 equations

\nu_j/\nu_i = U(\mathbf x_j)/U(\mathbf x_i)

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

y_{ij} := \ln(\nu_j/\nu_i) = \phi(\mathbf x_i) - \phi(\mathbf x_j).

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

f_i(x) = \sum_j x_j\, U(i,j)

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

u_c^2(y) = \sum_{i=1}^{N} \left(\frac{\partial f}{\partial x_i}\right)^2 u^2(x_i) \;+\; 2\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} \frac{\partial f}{\partial x_i}\frac{\partial f}{\partial x_j}\, u(x_i, x_j)

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

\mathrm{RMSNorm}(x)_j = \frac{x_j}{\mathrm{RMS}(x)}\, g_j, \qquad \mathrm{RMS}(x) = \sqrt{\frac{1}{d}\sum_{k=1}^{d} x_k^2 + \epsilon}.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

\dot{x}_i = x_i(f_i-\bar f) + \sum_j M_{ji}x_j - \sum_j M_{ij}x_i,

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.