$(document).ready(function()
{
    $("#form1").validationEngine({
        ajaxSubmit: true,
        ajaxSubmitFile: "note/note.php",
        success: false
    });
    if (success == "true")
    {
        function()
        {
            window.alert("Report Sent!");
            //write a confirmation to the user
            document.getElementById("update").innerHTML="Report Sent!";
            setTimeout(function()
            {
                document.getElementById("update").innerHTML="";
            },3000);
        }
    }
});

$(document).ready(function()
{
    $("#form1").validationEngine({
        ajaxSubmit: true,
        ajaxSubmitFile: "note/note.php",
        success: false
    });

if (success == "true")
{
     function()
     {

$(document).ready(function()
{
    $("#form1").validationEngine({
        ajaxSubmit: true,
        ajaxSubmitFile: "note/note.php",
        success: function(response)//response is what the php script returns
        {
            //the function from your if branch goes here
        }
    });

$(document).ready(function()
{//notice the curly braces around what you're passing to validationEngine
    $("#form1").validationEngine({
        ajaxSubmit: true,
        ajaxSubmitFile: "note/note.php",
        success: function(response)
        {
            if (response !== 'true')
            {
                if (window.console)
                {
                    console.log(response);
                    alert('check your console to see the response');
                }
                else
                {
                    alert(response);
                }
                return;
            }
            alert("Report Sent!");//no need for window here
            document.getElementById("update").innerHTML="Report Sent!";
            setTimeout(function()
            {
                document.getElementById("update").innerHTML="";
            },3000);
        }
    });
    //As I said, you're passing an object, so you could write the code above like so:
    var validationArgs = {ajaxSubmit:true,ajaxSubmitFile:'note/note.php'};
    validationArgs.success = function()
    {
        //your function
    };
    $('#form1').validationEngine(validationArgs);
});

$(document).ready(function() {
    var update = $("#update");
    // Callback
    var onSuccess = function() {
        alert("Report Sent!");

        //write a confirmation to the user
        update.html("Report Sent!");

        setTimeout(function(){
             update.html("");
        },3000);
    };

    $("#form1").validationEngine({
        ajaxSubmit: true,
        ajaxSubmitFile: "note/note.php",
        success: onSuccess
   });
});