Unfortunately, there's not one standard way to easily code these notifications across platforms and there's very little support for web apps seeking to send notifications to users. It's been one of the advantages that desktop apps have had over the web. That could be about to change.
The web's primary international standards organization, the W3C, has decided to tackle the issue with the formation of a new Web Notification Working Group this week. The Working Group is developing a standardized way for web developers to notify users of an event on a page when they aren't looking at the page itself. This could be key in making web apps just as powerful as native apps on the desktop or mobile device.
The Group has published an Editor's Draft for the specification and it's a good read. The possible implementations accounted for today could be the foundation of vital new features the web apps we use and build tomorrow.
Want a web-based Twitter client with popup desktop messages? A web-based banking app with push alerts to mobile devices? There are a whole lot of possibilities when you imagine combining the advantages of the web with a cross-platform standard for notification APIs.

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