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... . ..

2 1/2

2008 X X X X 2008 2008 XX XX XX XX 1 2 3 REGIONS Table (3 rows) East West Central X X X XX XX XX X X X

(31.13)

.. ...

(31.14)

2

FIGURE 21-3

An underdamped system will execute exponentially decaying oscillations, as shown graphically in Fig. 31.2.

... . ..

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However, a single cube can only show three dimensions. To handle additional dimensions, you have to visualize additional cubes. The N-cube in Figure 21-2 shows the REGIONS, CATEGORIES, and MONTHS dimensions. To represent the SUPPLIERS dimension, the N-cube needs to be replicated 50 times, once for each possible supplier. Furthermore, to represent the CUSTOMERS dimension, we need to replicate those 50 cubes 300 times, one for each possible customer (15,000 cubes in all). Fortunately, some multidimensional DBMSs can present cubes for analysis without needing to physically store each cube that might be required for presentation. The fact table typically contains only a few columns, but many rows tens or hundreds of millions or even billions of rows are not unusual in a production data warehouse. The fact column almost always contains numeric values that can be accumulated, such as currency amounts, units shipped or received, or pounds processed. Virtually all reports from the warehouse involve summary data totals, averages, high or low values, percentages based on arithmetic computations on this numeric value.

The successive maxima in Fig. 31.2 occur in a periodic fashion and are marked X0, X1, X2,. . . . The ratio of the maxima separated by n cycles of oscillation may be obtained from Eq. (31.13) as Xn = exp ( n ) X0 where = 2 (1 2)1/2 (31.15)

license, the player on the consumer s computer can open and play the protected file. The license also contains rules that govern the use of the digital media file; these are set by the content owner. Content owners can dictate how many times a file can be played, which devices a file can be played or transferred on, when the user can start playing the file and the expiration date of the license, if the file can be transferred to a CD burner or not, if the user can backup and restore the license, what security level is required on the client to play the file, and many other things. License management, for consumers, is a non-trivial task and certainly not invisible and seamless, unless they always default to the content owners interests and buy new licenses whenever they think they need them, whether or not they actually do. Licenses can be delivered in different ways and at different times, depending on the business model. The content owner might want licenses predelivered, or delivered after a consumer has downloaded and attempted to play a packaged file for the first time. Licenses can be delivered with or without the consumer s being aware of the process, using silent or non-silent license delivery. Content owners need to be very careful about how they exercise their rights. If they prefer the more Draconian options, they are implicitly giving the technology more opportunities to say to the consumer you are wrong, thus alienating paying customers. In a world where good

21:

is called the logarithmic decrement and corresponds to the ratio of two successive maxima in Fig. 31.2. For small values of damping, that is, << 1, the logarithmic decrement can be approximated by = 2 Using this in Eq. (31.14), we find Xn = exp ( 2 n ) X0 1 2 n (31.17) (31.16)

The schema structure of Figure 21-3 is called a star schema for obvious reasons. The fact table is at the center of a star of data relationships. The dimension tables form the points of the star. The relationships created by the foreign keys in the fact table connect the center to the points. With the star-schema structure, most business analysis questions turn into queries that join the central fact table with one or more dimension tables. Here are some examples: Show the total sales for clothing in January 2008, by region.

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