Why set var jQuery.noConflict () is invalid?

This is a JQuery gallery, the first code is in an external js file, the following code is in the head part.
Why set var $ j = jQuery.noConflict (); is invalid?
I have put many jquery plungin in my page, so I try $$ and jQuery to instead of $, but they still did not work. How to solve? Thanks.


(function(a){ 
    a.fn.desSlideshow=function(p){ 
        var p=p||{}; 
 
        var autoplay=p&&p.autoplay?p.autoplay:"enable"; 
        var slideshow_width=p&&p.slideshow_width?p.slideshow_width:"600"; 
        var slideshow_height=p&&p.slideshow_height?p.slideshow_height:"250"; 
        var thumbnail_width=p&&p.thumbnail_width?p.thumbnail_width:"200"; 
        var time_Interval = p&&p.time_Interval?p.time_Interval:"4000"; 
        var directory=p&&p.directory?p.directory:"images"; 
        slideshow_height = parseInt(slideshow_height); 
        slideshow_width = parseInt(slideshow_width); 
        time_Interval = parseInt(time_Interval); 
        var g=a(this); 
        var current = -1; 
        var y=g.children(".switchBigPic").children("div").length; 
        var v; 
        var w; 
        if(y==0){ 
            g.append("Require content"); 
            return null 
        } 
        init(); 
        if(autoplay == "enable"){ 
            g.find(".switchBigPic").css("display","block"); 
            g.find(".nav").css("display","block"); 
            g.css("background","none"); 
            play(); 
        }else{ 
            g.find(".switchBigPic").css("display","block"); 
            g.find(".nav").css("display","block"); 
            g.css("background","none"); 
            current = 0; 
            showpic(); 
        } 
        g.find(".nav").children("li").hover( 
            function(){ 
                var index = g.find(".nav").children("li").index($(this)); 
                if(index != current){ 
                    current = index; 
                    showpic(); 
                } 
            }, 
            function(){ 
 
            } 
        ); 
        g.hover( 
            function(){ 
 
            }, 
            function(){ 
                if(autoplay == "enable"){ 
                    v=setTimeout(play,time_Interval); 
                } 
            } 
        ); 
        function init(){ 
            g.css("width",slideshow_width+"px").css("height",slideshow_height+"px").css("position","relative").css("font-family","Verdana,Geneva,sans-serif").css("border-top","1px solid #CCCCCC").css("overflow","hidden"); 
            g.find("a").css("color","#000"); 
            g.find("img").css("border","none"); 
            g.find("ul").css("margin","0px").css("padding","0px"); 
            g.find("li").css("margin","0px").css("padding","0px").css("list-style","none"); 
            g.find(".switchBigPic").css("position","relative"); 
            g.find(".switchBigPic").children("div").css("position","absolute").css("overflow","hidden"); 
            g.find(".switchBigPic").children("div").children("p").css("position","absolute").css("padding","5px").css("margin","0px").css("bottom","0px").css("opacity","0.6").css("background-color","#000").css("color","#FFF").css("font-size","12px").css("width","100%"); 
            g.find(".nav").css("width",thumbnail_width+"px").css("height",slideshow_height+"px").css("position","absolute").css("right","0px"); 
            g.find(".nav").children("li").css("height","49px").css("background-image","url("+directory+"flashtext-bg.jpg)").css("line-height","49px").css("border-bottom","1px solid #CCCCCC").css("border-right","1px solid #CCCCCC"); 
            g.find(".nav").children("li").children("a").css("text-decoration","none").css("height","49px").css("display","block").css("padding-left","25px").css("font-size","14px"); 
            g.find(".nav").children("li").css("margin-left","0px"); 
            g.find(".switchBigPic").children("div").hide(); 
        } 
        function showpic(){ 
            clearTimeout(v); 
            g.find(".nav").children("li").css("background-image","url("+directory+"flashtext-bg.jpg)").css("border-bottom","1px solid #CCCCCC"); 
            g.find(".nav").children("li").eq(current).css("background-image","url("+directory+"flash-on.gif)").css("border-bottom","none"); 
            g.find(".switchBigPic").children("div").fadeOut(); 
            g.find(".switchBigPic").children("div").eq(current).fadeIn(); 
            g.find(".nav").children("li").eq(current).animate({marginLeft: '-35px'}, "fast"); 
            g.find(".nav").children("li").eq(w).animate({marginLeft: '0px'}, "fast"); 
            w = current; 
 
        } 
        function play(){ 
            current++; 
            if(current>=y){ 
                current=0 
            } 
            showpic(); 
            v=setTimeout(play,time_Interval); 
        } 
    } 
})(jQuery);


<script language="javascript" type="text/javascript"> 
    $(function() {
        $("#desSlideshow1").desSlideshow({
            autoplay: 'enable',//option:enable,disable
            slideshow_width: '800',//slideshow window width
            slideshow_height: '249',//slideshow window height
            thumbnail_width: '200',//thumbnail width
            time_Interval: '4000',//Milliseconds
            directory: 'images/'// flash-on.gif and flashtext-bg.jpg directory
        });
        $("#desSlideshow2").desSlideshow({
            autoplay: 'disable',//option:enable,disable
            slideshow_width: '600',//slideshow window width
            slideshow_height: '249',//slideshow window height
            thumbnail_width: '120',//thumbnail width
            time_Interval: '4000',//Milliseconds
            directory: 'images/'// flash-on.gif and flashtext-bg.jpg directory
        });
    });
</script>

Have you tried just using

var j = jQuery.noConflict();

Yes, I have tried. I have named many other jquery plungins in my page, they all run well, but only this one not…
here is the demo site Can you look it for me? Thanks.

I looked at the plug in and and its jQuery compliant as per there development standards for initializing the fn extension. There’s not reason why jQuery.noConflict() would be causing issues. Could you please post a snippet of the problem areas or all your javascript source