Here are the same solutions but with the curly braces incorporated into the do shell script command, and with additional examples in which all files are returned (i.e., no filtering is performed based on file name extension):
To get the HFS paths or Applescript aliases of all files in a parent folder:
set hfsPaths to run script (do shell script "echo \"{$(find " & parent_folder_hfs_path's POSIX path's quoted form & " -mindepth 1 -maxdepth 1 -exec echo '\"'{}'\" as POSIX file as text' \\; | tr '\\n' ',' | sed -E 's/,$// ; s/(.+)/\\1/')}\"")
--or--
set applescriptAliases to run script (do shell script "echo \"{$(find " & parent_folder_hfs_path's POSIX path's quoted form & " -mindepth 1 -maxdepth 1 -exec echo '\"'{}'\" as POSIX file as alias' \\; | tr '\\n' ',' | sed -E 's/,$// ; s/(.+)/\\1/')}\"")
To get the HFS paths or Applescript aliases of all pdf files in a parent folder:
set hfsPaths to run script (do shell script "echo \"{$(find " & parent_folder_hfs_path's POSIX path's quoted form & " -mindepth 1 -maxdepth 1 -iname '*.pdf' -exec echo '\"'{}'\" as POSIX file as text' \\; | tr '\\n' ',' | sed -E 's/,$// ; s/(.+)/\\1/')}\"")
--or--
set applescriptAliases to run script (do shell script "echo \"{$(find " & parent_folder_hfs_path's POSIX path's quoted form & " -mindepth 1 -maxdepth 1 -iname '*.pdf' -exec echo '\"'{}'\" as POSIX file as alias' \\; | tr '\\n' ',' | sed -E 's/,$// ; s/(.+)/\\1/')}\"")
And to get the HFS paths or Applescript aliases of all pdf, txt, and jpg files in a parent folder:
set hfsPaths to run script (do shell script "echo \"{$(find " & parent_folder_hfs_path's POSIX path's quoted form & " -mindepth 1 -maxdepth 1 \\( -iname '*.pdf' -o -iname '*.txt' -o -iname '*.jpg' \\) -exec echo '\"'{}'\" as POSIX file as text' \\; | tr '\\n' ',' | sed -E 's/,$// ; s/(.+)/\\1/')}\"")
--or--
set applescriptAliases to run script (do shell script "echo \"{$(find " & parent_folder_hfs_path's POSIX path's quoted form & " -mindepth 1 -maxdepth 1 \\( -iname '*.pdf' -o -iname '*.txt' -o -iname '*.jpg' \\) -exec echo '\"'{}'\" as POSIX file as alias' \\; | tr '\\n' ',' | sed -E 's/,$// ; s/(.+)/\\1/')}\"")