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JQuery .slideUp() after time OR mouseleave

I got an element that is slided down by JQuery using .slideDown() method
$('#dropdown_shopping_cart').slideDown(800);
Now i want it to slide up after 6 seconds, but only if there is no hover on the element, if there is an hover, it should not .slideUp().
So far i worked with a timeout that added display:none to the element while i was giving the element´s hover display:block!important; in CSS so it would not get display: none until the hover is over.
JS
setTimeout(function () {
$('#dropdown_shopping_cart').css('display', 'none');
}, 6000);
_______________________________________________________
CSS
#dropdown_shopping_cart:hover {
display: block!important;
}
Now i want to add the .slideUp() to this.

Check this:
var myVar;
myVar = setTimeout(function() {
$('#dropdown_shopping_cart').slideUp(800)
}, 6000);
$("#dropdown_shopping_cart").hover(
function() {
clearTimeout(myVar);
},
function() {
myVar = setTimeout(function() {
$('#dropdown_shopping_cart').slideUp(800)
}, 6000);
}
);
By default shopping cart will slideUp() after 6 seconds, if mouse hover action occured, setTimeOut will be cleared, after mouse leave the shopping cart, setTimeOut will setted automatically

You can clear the timeout on mouseenter and reset it on mouseleave like this:
var hide_div_to;
function hideDiv(){
hide_div_to = setTimeout(function () {
$('#dropdown_shopping_cart').slideUp(800);
}, 6000);
}
$('#dropdown_shopping_cart').slideDown(800,hideDiv());
$('#dropdown_shopping_cart').mouseenter(function(){
clearTimeout(hide_div_to);
});
$('#dropdown_shopping_cart').mouseleave(function(){
hideDiv();
});
Here is a working JSFiddle
UPDATE
If you don't wan't to wait the timeout again when you leave, after the timeout is reached, you can do this:
$('#dropdown_shopping_cart').slideDown(800);
setTimeout(function () {
if(!$('#dropdown_shopping_cart').is(':hover')){
$('#dropdown_shopping_cart').slideUp(800);
}
else{
$('#dropdown_shopping_cart').mouseleave(function(){
$('#dropdown_shopping_cart').slideUp(800);
});
}
}, 3000);
And here is a JSFiddle and here is another one that shows how this can be triggered multiple times.

Id suggest you work with mouseover and a class:
$('#dropdown_shopping_cart').hover(function(){
if(!$('#dropdown_shopping_cart').hasClass('active'))
{
$(this).addClass('active');
}
else
{
$(this).removeClass('active');
}
},
function() {
var myVar = setTimeout(function() {
if(!$('#dropdown_shopping_cart').hasClass('active'))
{
$('#dropdown_shopping_cart').slideUp()
}
}, 6000);
})
And than in your setTimeout Function you add:

demo: http://jsfiddle.net/yo5gnvy3/7/
$('#dropdown_shopping_cart').hide().slideDown(800, function () {
var events = $._data($(this)[0], "events") || {};
if (events.mouseover === undefined) {
$(this).delay(1000).slideUp()
}
});

How do I stop text scrolling?

This is my code:
$(document).ready(function() {
function ticker() {
$('#ticker li:first').slideUp(function() {
$(this).appendTo($('#ticker')).slideDown();
});
}
setInterval(function(){ ticker(); }, 3000);
});
I don't know how to stop the text scrolling when I place the mouse over a particular title.
DEMO

Use a hover() to clear the interval and when mouse leaves then again start the ticker like,
$(document).ready(function () {
function ticker() {
$('#ticker li:first').slideUp(function () {
$(this).appendTo($('#ticker')).slideDown();
});
}
var clr = null;
function animate(){
clr=setInterval(function () {
ticker();
}, 3000);
}
animate();
$('#ticker li').hover(function () {
// clear interval when mouse enters
clearInterval(clr);
},function(){
// again start animation when mouse leaves
animate();
});
});
Live Demo

Minor update in your answer. Use mouseover and out function.
$(document).ready(function() {
function ticker() {
$('#ticker li:first').slideUp(function() {
$(this).appendTo($('#ticker')).slideDown();
});
}
var ticke = setInterval(function(){ ticker(); }, 3000);
$('#ticker li').mouseover(function() {
clearInterval(ticke);
}).mouseout(function() {
ticke= setInterval(function(){ ticker(); }, 3000);
});
});
See here Demo

please try this one:
$(document).ready(function () {
function ticker() {
$('#ticker li:first').slideUp(function () {
$(this).appendTo($('#ticker')).slideDown();
});
}
var clr = null;
function animate(){
clr=setInterval(function () {
ticker();
}, 3000);
}
animate();
$('#ticker li').hover(function () {
// clear interval when mouse enters
clearInterval(clr);
},function(){
// again start animation when mouse leaves
animate();
});
});

The setInterval method returns an id value which you can then pass to clearInterval to cancel the calls to ticker().

How to fire event after 3 sec of hovering

I have a div and I want to fire an event only after user continuous hovers his mouse for 3 sec. My code doesn't work well because it fires right after hover and doesn't "wait".
Code:
$(".inner_pic").mouseenter(function () {
setTimeout(function () {
alert('testing');
}, 3000);
}).mouseleave(function () {
alert('finish');
});

You need to store timeout id somewhere and clear it on mouseout. It's convenient to use data property to save this id:
$(".inner_pic").mouseenter(function () {
$(this).data('timeout', setTimeout(function () {
alert('testing');
}, 3000));
}).mouseleave(function () {
clearTimeout($(this).data('timeout'));
alert('finish');
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div class="inner_pic">PICTURE</div>

You can achieve this by delay option:
Working demo
$('#elem').popover({
trigger: "hover",
delay: {show : 3000, hide : 0} });

Checkout the below code
var myVar;
$( "div#container" )
.mouseover(function() {
myVar = setTimeout(function(){ alert("Hello"); }, 3000);
})
.mouseout(function() {
clearTimeout(myVar);
});
div {
background: red;
margin: 20px;
height: 100px;
width: 100px;
display:block;
cursor: pointer;
}
div:hover {
background: yellow;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div id="container"></div>

var st;
$(".inner_pic").mouseenter(function(e) {
var that = this;
st = setTimeout(function() {
alert('testing');
}, 3000);
}).mouseleave(function() {
clearTimeout( st );
alert('finish');
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<div class="inner_pic">
<h3>Picture Here - Hover me</h3>
</div>

Assuming you have a div with id of myelement, you can do this:
var divMouseOver;
$('#myelement').mouseover(function() {
divMouseOver = setTimeout(function() {
alert("3 seconds!"); //change this to your action
}, 3000);
});
$('#myelement').mouseout(function() {
if (divMouseOver) {
clearTimeout(divMouseOver);
}
});
BTW, tere's a helpful clarifying question re: using mouseenter and mouseover right here: Jquery mouseenter() vs mouseover(). Consider this when choosing which to use.

Loop each forever

I want this loop forever
$(document).ready(function() {
function news_hot() {
$("div p").each(function(i) {
$(this).delay(1000 * i).queue(function() {
$(this).addClass('hot_li ');
$(this).prev().removeClass('hot_li');
});
});
}
news_hot();
});
<div>
<p>dfsdfsd</p>
<p>dfsdfsd</p>
<p>dfsdfsd</p>
</div>

You can use setInterval() JavaScript function with specified time in milliseconds. The called function will run forever after interval time unless you stop it.
$(document).ready(function () {
function news_hot() {
$("div p").each(function (i) {
$(this).delay(1000 * i).queue(function () {
$(this).addClass('hot_li ');
$(this).prev().removeClass('hot_li');
});
});
}
setInterval(news_hot(),5000);
});
UPDATED CODE WORKING FIDDLE
function news_hot() {
$("div p").each(function (i) {
$(this).delay(1000 * i).queue(function () {
$("div p").removeClass("hot_li");
$(this).addClass('hot_li');
//$(this).prev().removeClass('hot_li');
$(this).dequeue();
});
});
}
setInterval(function(){news_hot()},5000);
.dequeue() function has been added to the code

How to detect whether mouseout is true or not?

I have this simple fiddle as a working example-
Jsfiddle
I am trying to detect mouseout event from a div section.
When i mouseover on this image it shows caption; saying "Change Image". After 5 seconds caption goes fadeOut.
I am using setInterval to set it accordingly. Now if I do mouseout of this image, then only I want Interval function should be called.
How do i detect mouseout event in jQuery?
Tried-
$(function () {
$('.image-profile').mouseover(function () {
$('.change-image').stop().show();
if ($('.image-profile').mouseout()== true) {
TimeOut();
}
});
setInterval(function TimeOut() {
$('.change-image').fadeOut()
}, 5000
);
});

var ImageProfileTimer;
$('.image-profile').on('mouseenter',function(){
clearTimeout(ImageProfileTimer);
$('.change-image').stop().show();
}).on('mouseleave',function(){
ImageProfileTimer = setTimeout(function(){
$('.change-image').fadeOut()
}, 5000);
});
Use setTimeout and clearTimeout
Demo : http://jsfiddle.net/xMNTB/9/

$('.image-profile').on('mouseleave', function() {
setTimeout(function() {
$('.change-image').fadeOut()
}, 5000);
});

http://jsfiddle.net/xMNTB/7/
Now the div show up on mouse enter and disappears 5 seconds after mouse leave.
$(function () {
$('.image-profile').mouseenter(function () {
$('.change-image').stop().show();
});
$('.image-profile').mouseleave(function () {
setTimeout(function TimeOut() {
$('.change-image').fadeOut()
}, 5000);
});
});

Try This:
(function () {
$('.image-profile').mouseover(function () {
$('.change-image').stop().show();
if ($('.image-profile').mouseout() == true) {
TimeOut();
}
}).mouseout(function () {
setInterval(function TimeOut() {
$('.change-image').fadeOut()
}, 5000);
});
});
JSFIDDLE DEMO