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Issue: "No mapping between account names and security IDs was done" error is coming while adding users in a role in SQL Server Analysis Services cube.
Solution: I was trying to add some users in SQL Server 2008 Analysis Services - Role Membership section. I was adding valid domain users but still it was not adding the users and throwing an error as - "No mapping between account names and security IDs was done". And the solution is - I found few users already existed in the role membership which no longer existed in the domain and that's why when I was trying to add a user; it was trying to validate all the listed users and throwing error. I deleted the listed non-existing users and then tried to add the domain user again. This time it worked!!

Issue: "Cannot perform a differential backup for database "XYZ", because a current database backup does not exist. Perform a full database backup by reissuing BACKUP DATABASE, omitting the WITH DIFFERENTIAL option. BACKUP DATABASE is terminating abnormally."
Solution: "The Ntbackup.exe operation may break the differential backup chain of a SQL Server database and may invalidate the differential backups when you perform a snapshot backup of the database ". This microsoft article can help here - http://support.microsoft.com/kb/903643
Possibly review the configuration of the Volume Shadow Copy and make sure that the VSC backup plan does not includes the SQL Server databases.