In nearly every case, banner and alert notifications don't reappear. The annoying exception is Apple's own Software Update notification. When this alert notification appears, you can dismiss it only by clicking either its Details or its Update button, each of which causes the Mac App Store application to launch. Yes, you can drag the notification off the screen to the right but this is only a temporary fix--the notification will reappear after a few minutes.
Three options appear below the alerts area. The first, 'Show in Notification Center', allows an application to appear under the In Notification Center heading. If you uncheck the option, the application won't display notifications and will be relegated to a position under the Not In Notification Center heading. (You can optionally drag applications so that they appear under this heading.) Next to this entry is a pop-up menu where you can choose the number of items that appear under an application's heading--1 Recent Item, 5 Recent Items, 10 Recent Items, or 20 Recent Items.
The Badge App Icon option determines whether a small red icon indicating unaddressed actions appears on the application's Dock icon. For instance, with this option on for the Mail application, the number of unread email messages will appear within Mail's badge. Turn it off and you'll see no such badge.
Finally, the Play Sound When Receiving Notifications option allows you to mute alert sounds.
If you've configured Twitter and/or Facebook for your Mac, you'll find at least two more entries at the top of the pane on the left side of the window. The first is Share Buttons, which appears at the top of the applications list. Select it, and you can choose whether to show the 'Click to Tweet' and/or 'Click to Post' buttons in Notification Center.
If you've configured Twitter and select it in this preference, you see a Notifications button to the right. Click it and you can choose the kind of tweets that will appear in Notification Center--direct messages, messages and replies from people you follow, or mentions and replies from anyone. (You can also choose to see no mentions and replies.) Facebook lacks such a button, as well as the Badge App Icon and Play Sound When Receiving Notifications options.
It's within this system preference that you configure the order in which notifications are displayed. Choose By Time from the Sort Notification Center pop-up menu at the bottom of the window, and the applications in Notification Center will be listed in the order of the last received notification. For example, if the last notification you received was for an email message received by Mail, the Mail heading will appear at the top of the list. If the previous notification was from Calendar, Calendar will appear after Mail in Notification Center.
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