diff --git a/R/hermite_estimator_bivar.R b/R/hermite_estimator_bivar.R
index 58396da..8740e0f 100644
--- a/R/hermite_estimator_bivar.R
+++ b/R/hermite_estimator_bivar.R
@@ -330,7 +330,7 @@ update_sequential_bivar_helper <- function(h_est_obj,x){
   }
   if (is.na(h_est_obj$exp_weight)){
     h_est_obj$coeff_mat_bivar <- (h_est_obj$coeff_mat_bivar * 
-                                    (h_est_obj$num_obs-1) + tcrossprod(h_x,h_y))/(h_est_obj$num_obs)
+              (h_est_obj$num_obs-1) + tcrossprod(h_x,h_y))/(h_est_obj$num_obs)
   } else {
     h_est_obj$coeff_mat_bivar<- h_est_obj$coeff_mat_bivar * 
       (1-h_est_obj$exp_weight) + tcrossprod(h_x,h_y)*h_est_obj$exp_weight
@@ -485,8 +485,8 @@ dens.hermite_estimator_bivar <- function(h_est_obj,x, clipped = FALSE,
 #' Creates an object summarizing the bivariate PDF with associated generic 
 #' methods print and plot.
 #'
-#' The hermite_estimator_bivar object, x must be updated with observations prior 
-#' to the use of the method.
+#' The hermite_estimator_bivar object, x must be updated with observations 
+#' prior to the use of the method.
 #'
 #' @param x A hermite_estimator_bivar object.
 #' @param x_lower A numeric vector. This vector determines the lower limit of 
diff --git a/R/utils_general.R b/R/utils_general.R
index df8f77f..3b0d07e 100644
--- a/R/utils_general.R
+++ b/R/utils_general.R
@@ -2,7 +2,6 @@
 #' on a hermite_estimator_univar object.
 #' 
 #' Mirrors the print method of the stats::ecdf function 
-#' 
 #'
 #' @param x A hcdf_univar object.
 #' @param digits A numeric value. Number of digits to round to.
@@ -113,7 +112,7 @@ print.hcdf_bivar <- function (x,
 #' @export
 plot.hcdf_bivar <- function (x, main="Hermite CDF",xlab = "X", ylab="Y",...) 
 {
-  z = matrix(x$cum_prob_vals,byrow = FALSE,nrow=length(x$x_vals_1))
+  z <- matrix(x$cum_prob_vals,byrow = FALSE,nrow=length(x$x_vals_1))
   filled.contour(x = x$x_vals_1,y = x$x_vals_2, z= z,
                  color.palette = function(n) hcl.colors(n, "Oslo", rev = TRUE),
                  main=main,xlab=xlab,ylab=ylab)
@@ -231,7 +230,7 @@ print.hdensity_bivar <- function (x,
 plot.hdensity_bivar <- function(x, main="Hermite PDF",xlab = "X", ylab = "Y", 
                                 ...) 
 {
-  z = matrix(x$density_vals,byrow = FALSE,nrow=length(x$x_vals_1))
+  z <- matrix(x$density_vals,byrow = FALSE,nrow=length(x$x_vals_1))
   cols <- hcl.colors(10, "Oslo")
   filled.contour(x = x$x_vals_1,y = x$x_vals_2, z= z,
                  color.palette = function(n) hcl.colors(n, "Oslo", rev = TRUE),
@@ -241,9 +240,9 @@ plot.hdensity_bivar <- function(x, main="Hermite PDF",xlab = "X", ylab = "Y",
 #' A wrapper around the stats::cor function adding two additional methods, 
 #' namely method = "hermite.spearman" and method = "hermite.kendall" (can be
 #' abbreviated). The input parameters and output value semantics closely match 
-#' the stats::cor method for easy interchange. If neither the "hermite.spearman" 
-#' nor the "hermite.kendall" method is selected, then this function will call 
-#' stats::cor with the arguments provided.
+#' the stats::cor method for easy interchange. If neither the 
+#' "hermite.spearman" nor the "hermite.kendall" method is selected, then this 
+#' function will call stats::cor with the arguments provided.
 #'
 #' @param x a numeric vector, matrix or data frame. 
 #' @param y NULL (default) or a vector, matrix or data frame with 
diff --git a/cran-comments.md b/cran-comments.md
index 703a4cc..1b4a0a7 100644
--- a/cran-comments.md
+++ b/cran-comments.md
@@ -23,15 +23,15 @@ plot and summary generics.
 ## Test environments
 * local R installation, Windows 10, R 4.3.0
 * Ubuntu Linux 20.04.1 LTS, R-release, GCC (r-hub)
-* Debian Linux, R-devel, GCC ASAN/UBSAN (r-hub)
+* Debian Linux, R-release, GCC (r-hub)
 * Fedora Linux, R-devel, clang, gfortran (r-hub)
-* macOS 10.13.6 High Sierra, R-release, brew
+* macOS 10.13.6 High Sierra, R-release, brew (r-hub)
 * Windows Server 2022, R-devel, 64 bit (r-hub)
 * win-builder (devel, release. oldrel)
 
 ## R CMD check results
 
-There was 1 NOTE across environments:
+There was 1 NOTE across all environments:
 
 GNU make is a SystemRequirements.
     
@@ -39,8 +39,18 @@ GNU make is a SystemRequirements.
 problematic. GNU make has been added to SystemRequirements in the Description
 file.
 
-* In addition, on Ubuntu 20.04.1 LTS, the package 
-appears to be slightly larger than 5MB, around 5.9 MB. This does not
+* In addition, on Debian and Ubuntu Linux, the package 
+appears to be slightly larger than 5MB, around 5.2- 6 MB. This does not
 appear to occur on any of the other environments however (i.e. Fedora Linux, 
 Windows, MacOS)
 
+* Finally, there is the following note on Ubuntu and Fedora Linux:
+
+* checking HTML version of manual ... NOTE
+Skipping checking HTML validation: no command 'tidy' found
+Skipping checking math rendering: package 'V8' unavailable
+
+This seems build system specific and not directly tied to the package.
+
+* There is also a PREPERROR for Debian Linux, R-devel, GCC ASAN/UBSAN on rhub 
+- we believe this is an issue on the build server and not package specific.
diff --git a/man/cor.Rd b/man/cor.Rd
index 4792d12..506958f 100644
--- a/man/cor.Rd
+++ b/man/cor.Rd
@@ -5,9 +5,9 @@
 \title{A wrapper around the stats::cor function adding two additional methods, 
 namely method = "hermite.spearman" and method = "hermite.kendall" (can be
 abbreviated). The input parameters and output value semantics closely match 
-the stats::cor method for easy interchange. If neither the "hermite.spearman" 
-nor the "hermite.kendall" method is selected, then this function will call 
-stats::cor with the arguments provided.}
+the stats::cor method for easy interchange. If neither the 
+"hermite.spearman" nor the "hermite.kendall" method is selected, then this 
+function will call stats::cor with the arguments provided.}
 \usage{
 cor(x, y = NULL, use = "everything", method = "pearson", ...)
 }
@@ -35,7 +35,7 @@ object if method is "hermite.spearman" or "hermite.kendall".}
 A wrapper around the stats::cor function adding two additional methods, 
 namely method = "hermite.spearman" and method = "hermite.kendall" (can be
 abbreviated). The input parameters and output value semantics closely match 
-the stats::cor method for easy interchange. If neither the "hermite.spearman" 
-nor the "hermite.kendall" method is selected, then this function will call 
-stats::cor with the arguments provided.
+the stats::cor method for easy interchange. If neither the 
+"hermite.spearman" nor the "hermite.kendall" method is selected, then this 
+function will call stats::cor with the arguments provided.
 }
diff --git a/man/density.hermite_estimator_bivar.Rd b/man/density.hermite_estimator_bivar.Rd
index 66631af..36b4e2d 100644
--- a/man/density.hermite_estimator_bivar.Rd
+++ b/man/density.hermite_estimator_bivar.Rd
@@ -31,6 +31,6 @@ estimates.
 N: The number of terms N in the Hermite series estimator.
 }
 \description{
-The hermite_estimator_bivar object, x must be updated with observations prior 
-to the use of the method.
+The hermite_estimator_bivar object, x must be updated with observations 
+prior to the use of the method.
 }
diff --git a/tests/testthat/test_utilities_general.R b/tests/testthat/test_utilities_general.R
index dc68639..d6a2bc8 100644
--- a/tests/testthat/test_utilities_general.R
+++ b/tests/testthat/test_utilities_general.R
@@ -457,7 +457,7 @@ test_that("quantile, median and IQR generics work correctly", {
   hermite_est <- hermite_estimator(observations = test_observations,
                                    standardize = TRUE)
   quantiles_est <- quantile(hermite_est)
-  target_quantiles = c(-14.64905596,
+  target_quantiles <- c(-14.64905596,
                        -1.57302308,
                        0.04009478,
                        1.01244707,