fix typesetting of dens and ff

R/integrate_profile.R

@@ -64,24 +64,24 @@
 #' migratory movement at all times and altitudes. In this case \code{mtr} is
 #' always a positive quantity, defined as:
 #'
-#' \deqn{mtr = 3.6 \sum_i dens_i ff_i \Delta h}{mtr = 3.6 \sum_i dens_i ff_i \Delta h}
+#' \deqn{mtr = 3.6 \sum_i \mathit{dens}_i \mathit{ff}_i \Delta h}{mtr = 3.6 \sum_i \mathit{dens}_i \mathit{ff}_i \Delta h}
 #'
 #' with the sum running over all altitude layers between \code{alt_min} and
-#' \code{alt_max}, \eqn{dens_i} the bird density, \eqn{ff_i} the ground speed at
+#' \code{alt_max}, \eqn{\mathit{dens}_i} the bird density, \eqn{\mathit{ff}_i} the ground speed at
 #' altitude layer i, and \eqn{\Delta h} the altitude layer width. The factor 3.6
-#' refers to a unit conversion of speeds \eqn{ff_i} from m/s to km/h.
+#' refers to a unit conversion of speeds \eqn{\mathit{ff}_i} from m/s to km/h.
 #'
 #' If \code{alpha} is given a numeric value, the transect is taken perpendicular
 #' to the direction \code{alpha}, and the number of crossing targets per hour
 #' per km transect is calculated as:
 #'
-#' \deqn{mtr = 3.6 \sum_i dens_i ff_i \cos((dd_i-\alpha) \pi/180) \Delta h}{mtr = 3.6 \sum_i dens_i ff_i \cos((dd_i-\alpha) \pi/180) \Delta h}
+#' \deqn{mtr = 3.6 \sum_i \mathit{dens}_i \mathit{ff}_i \cos((dd_i-\alpha) \pi/180) \Delta h}{mtr = 3.6 \sum_i \mathit{dens}_i \mathit{ff}_i \cos((dd_i-\alpha) \pi/180) \Delta h}
 #' with \eqn{dd_i} the migratory direction at altitude i.
 #'
 #' Note that this equation evaluates to the previous equation when \code{alpha} equals \eqn{dd_i}.
 #' Also note we can rewrite this equation using trigonometry as:
 #'
-#' \deqn{mtr = 3.6 \sum_i dens_i (u_i \sin(\alpha \pi/180) + v_i \cos(\alpha \pi/180)) \Delta h}{mtr = 3.6 \sum_i dens_i (u_i \sin(\alpha \pi/180) + v_i \cos(alpha pi/180)) \Delta h}
+#' \deqn{mtr = 3.6 \sum_i \mathit{dens}_i (u_i \sin(\alpha \pi/180) + v_i \cos(\alpha \pi/180)) \Delta h}{mtr = 3.6 \sum_i \mathit{dens}_i (u_i \sin(\alpha \pi/180) + v_i \cos(alpha pi/180)) \Delta h}
 #' with \eqn{u_i} and \eqn{v_i} the u and v ground speed components at altitude i.
 #'
 #' In this definition \code{mtr} is a traditional flux into a direction of
@@ -122,25 +122,25 @@
 #' migration traffic and reflectivity traffic from the start of the time series up till the moment of the time stamp
 #' of the respective row.
 #'
-#' #' \subsection{Ground speed (ff) and ground speed components (u,v)}{
+#' \subsection{Ground speed (ff) and ground speed components (u,v)}{
 #' The height-averaged ground speed is defined as:
 #'
-#' \deqn{ff = \sum_i dens_i ff_i / \sum_i dens_i}{ff = \sum_i dens_i ff_i / \sum_i dens_i}
+#' \deqn{\mathit{ff} = \sum_i \mathit{dens}_i \mathit{ff}_i / \sum_i \mathit{dens}_i}{\mathit{ff} = \sum_i \mathit{dens}_i \mathit{ff}_i / \sum_i \mathit{dens}_i}
 #' with the sum running over all altitude layers between \code{alt_min} and
-#' \code{alt_max}, \eqn{dens_i} the bird density, \eqn{ff_i} the ground speed at
+#' \code{alt_max}, \eqn{\mathit{dens}_i} the bird density, \eqn{\mathit{ff}_i} the ground speed at
 #' altitude layer i.
 #'
 #' the height-averaged u component (west to east) is defined as:
 #'
-#' \deqn{u = \sum_i dens_i u_i / \sum_i dens_i}{u = \sum_i dens_i u_i / \sum_i dens_i}
+#' \deqn{u = \sum_i \mathit{dens}_i u_i / \sum_i \mathit{dens}_i}{u = \sum_i \mathit{dens}_i u_i / \sum_i \mathit{dens}_i}
 #'
 #' the height-averaged v component (south to north) is defined as:
 #'
-#' \deqn{v = \sum_i dens_i v_i / \sum_i dens_i}{v = \sum_i dens_i v_i / \sum_i dens_i}
+#' \deqn{v = \sum_i \mathit{dens}_i v_i / \sum_i \mathit{dens}_i}{v = \sum_i \mathit{dens}_i v_i / \sum_i \mathit{dens}_i}
 #' }
 #'
-#' Note that \eqn{ff_i=\sqrt(u_i^2 + v_i^2)}, but the same does not hold for the
-#' height-integrated speeds, i.e. \eqn{ff != \sqrt(u^2 + v^2)} as soon as the
+#' Note that \eqn{\mathit{ff}_i=\sqrt(u_i^2 + v_i^2)}, but the same does not hold for the
+#' height-integrated speeds, i.e. \eqn{\mathit{ff} \neq \sqrt(u^2 + v^2)} as soon as the
 #' ground speed directions vary with altitude.
 #'
 #' }