Php/mysql Notice: Undefined variable

Bonjour,
J' appele la fonction pour l'identification de l'administrateur de la base afin de suprimer certaines entrees.
voici le mesage d'erreure qui s'affiche :
Notice: Undefined variable: PHP_AUTH_USER in C:\Program Files\EasyPHP 2.0b1\www\training\application\win_authenticate.php on line 29

Notice: Undefined variable: PHP_AUTH_PW in C:\Program Files\EasyPHP 2.0b1\www\training\application\win_authenticate.php on line 32

voici le code win_authenticate.php
<?php
session_register("PHP_AUTH_USER");
session_register("PHP_AUTH_PW");
session_register("valid_user");

if (empty($valid_user) && !empty($PHP_AUTH_USER))
{
// if we don't have a valid user name and we do have PHP_AUTH_USER,
// check it against the database
$query = "select username from guestbook_admin
where password = password(lower('$PHP_AUTH_PW'))
and username = lower('$PHP_AUTH_USER')
";
$result = safe_query($query);
if ($result) { list($valid_user) = mysql_fetch_row($result); }
}
if (empty($valid_user))
{
// if we don't have a valid user name, print a form to get one
// and exit
print <<<EOQ
<h2>$realm</h2>
<h2>Guest Book Administration</h2>
<p>
You must enter a valid name & password to access this function.
</p>
<form method=post>
Username: <input type=text name="PHP_AUTH_USER" value="$PHP_AUTH_USER">
<br>
Password: <input type=text name="PHP_AUTH_PW" value="$PHP_AUTH_PW">
<br>
<input type=submit>
</form>
EOQ;
exit;
}
print "<p><b>Editing as $PHP_AUTH_USER</b></p>\n";
?>


voici le code authenticate.php qui appel la function win_autthenticate.php

authenticate.php
<?php
$realm = "Guest Book Administration";
$errmsg = "You must enter a valid name & password to access this function";

// PHP_AUTH_USER and PHP_AUTH_PW are global variables supplied by
// PHP, corresponding to the user name & password the user has entered
// in the pop-up window created by an HTTP authentication header. If no
// authentication header has ever been sent, these variables will be empty.
if(strstr(strtolower(PHP_OS),"win") && strtolower(PHP_OS) != "darwin")
{
include "win_authenticate.php";
return;
}
if (empty($PHP_AUTH_USER))
{
// first time through - use authenticate() to request a
// user name & password
authenticate($realm,$errmsg,"header");
}
else
{
$query = "select username from guestbook_admin
where password = password(lower('$PHP_AUTH_PW'))
and username = lower('$PHP_AUTH_USER')
";
$result = safe_query($query);
if ($result) { list($valid_user) = mysql_fetch_row($result); }

// if the query didn't work at all (which shouldn't happen), or ran but
// didn't find a match for the user name & password, $valid_user will
// not be set to anything. if this is so, have the user try again.
if (!$result || empty($valid_user))
{
authenticate($realm,$errmsg,"query");
}
}
print "<p><b>Editing as $PHP_AUTH_USER</b></p>\n";
?>

Merci d'avance pour votre aide.