Let R be an atomic integral domain. R is a half-factorial domain (HFD) if whenever x 1 } } } x n = y 1 } } } y m for x 1 , ..., x n , y 1 , ..., y m irreducibles of R, then n=m. A well known result of L. Carlitz (1960, Proc. Amer. Math. Soc. 11, 391 392) states that the ring of integers in a finite extension of the rationals is a HFD if and only if the class number of R is less than or equal to 2. If R is such a ring of integers with class number 2, then we use some simple Krull monoids to develop a formula for counting the number of different factorizations of any integer x into products of irreducible elements of R. Academic Press
Large scientific collaborations as well as universities have a growing need for multimedia archiving of meetings and courses. Collaborations need to disseminate training and news to their wide-ranging members, and universities seek to provide their students with more useful studying tools. The University of Michigan ATLAS Collaboratory Project has been involved in the recording and archiving of multimedia lectures since 1999. Our software and hardware architecture has been used to record events for CERN, ATLAS, many units inside the University of Michigan, Fermilab, the American Physical Society and the International Conference on Systems Biology at Harvard. Until 2006 our group functioned primarily as a tiny research/development team with special commitments to the archiving of certain ATLAS events. In 2006 we formed the MScribe project, using a larger scale, and highly automated recording system to record and archive eight University courses in a wide array of subjects. Several robotic carts are wheeled around campus by unskilled student helpers to automatically capture and post to the Web audio, video, slides and chalkboard images. The advances the MScribe project has made in automation of these processes, including a robotic camera operator and automated video processing, are now being used to record ATLAS Collaboration events, making them available more quickly than before and enabling the recording of more events.
The ATLAS Collaboratory Project at the University of Michigan has been a leader in the area of collaborative tools since 1999. Its activities include the development of standards, software and hardware tools for lecture archiving, and making recommendations for videoconferencing and remote teaching facilities. Starting in 2006 our group became involved in classroom recordings, and in early 2008 we spawned CARMA, a University-wide recording service. This service uses a new portable recording system that we developed. Capture, archiving and dissemination of rich multimedia content from lectures, tutorials and classes are increasingly widespread activities among universities and research institutes. A growing array of related commercial and open source technologies is becoming available, with several new products introduced in the last couple years. As the result of a new close partnership between U-M and CERN IT, a market survey of these products was conducted and a summary of the results are presented here. It is informing an ambitious effort in 2009 to equip many CERN rooms with automated lecture archiving systems, on a much larger scale than before. This new technology is being integrated with CERN's existing webcast, CDS, and Indico applications.
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