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Theorem 7.3. Transmission schedules generated by the MDR scheduler are guaranteed to comprise monotonic decreasing rates. Proof. We prove the theorem by contradiction. Let ri and ri+1 be the transmission rate of the ith and (i + 1)th segments of a feasible schedule S(t) generated by the MDR scheduler. ` Graphically, let r be the slope of the line connecting S(Ti 1 ) and S(Ti+1 ), where Ti 1 and Ti+1 are the (i 1)th and (i + 1)th rate reduction points. Assume ri < ri+1 , i.e., the rate allocated are not monotonic decreasing. Then we have: S(Ti ) S(Ti 1 ) S(Ti+1 ) S(Ti ) < Ti Ti 1 Ti+1 Ti or [S(Ti ) S(Ti 1 )](Ti+1 Ti ) < [S(Ti+1 ) S(Ti )](Ti Ti 1 ) We expand equation (7.30) to obtain. S (Ti )Ti+1 S(Ti )Ti S(Ti 1 )Ti+1 + S(Ti 1 )Ti < S(Ti+1 )Ti S(Ti+1 )Ti 1 S(Ti )Ti + S(Ti )Ti 1 We cancel the S(Ti )Ti term on both sides and after rearranging we obtain: S(Ti )Ti+1 S(Ti 1 )Ti+1 S(Ti )Ti 1 < S(Ti+1 )Ti S(Ti+1 )Ti 1 S(Ti 1 )Ti (7.32) (7.31) (7.30) (7.29)



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In the following we summarize the distinctive features of the available ontology engineering methodologies and give quick pointers to existing tool support speci cally targeted to the methodologies. Next, we brie y introduce the most prominent existing tools.

Add S(Ti 1 )Ti 1 to both sides and we obtain: S (Ti )Ti+1 S(Ti 1 )Ti+1 S(Ti )Ti 1 S(Ti 1 )Ti 1 < S(Ti+1 )Ti S(Ti+1 )Ti 1 S(Ti 1 )Ti S(Ti 1 )Ti 1 Then factorize equation (7.33) to get: [S(Ti ) S(Ti 1 )](Ti+1 Ti 1 ) < [S(Ti+1 ) S(Ti 1 )](Ti Ti 1 ) which is equivalent to S(Ti ) S(Ti 1 ) S(Ti+1 ) S(Ti 1 ) < =r Ti Ti 1 Ti+1 Ti 1 (7.35) (7.34) (7.33)





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Since the transmission schedule coincides with the data consumption curve at bit-rate reduction points, i.e., S(Ti ) = A(Ti ) for all i, we have A(Ti ) A(Ti 1 ) A(Ti+1 ) A(Ti 1 ) < Ti Ti 1 Ti+1 Ti 1 Now according to the MDR scheduler (cf. equation (7.6)): ri = max A(t) A(Ti 1 ) t > Ti 1 t Ti 1 (7.37) (7.36)

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An extensive state-of-the-art overview of methodologies for ontology engineering can be found in Gomez-Perez et al. (2003). More recently Cristani and Cuel (2005) proposed a framework to compare ontology engineering methodologies and evaluated the established ones accordingly. In the OntoWeb2 project, the members gathered guidelines and best practices for industry (Leger et al., 2002a, b) with a focus on

From equation (7.36), we must have ri equal to ri = A(Ti+1 ) A(Ti 1 ) Ti+1 Ti 1 (7.38)

which violates the de nition of ri . This contradicts the assumption that the schedule S(t) is generated by the MDR scheduler and therefore the schedule with increasing rates cannot be generated by the MDR scheduler and the result follows.

see http:/ /www.ontoweb.org/

In addition to audio, video is the other most commonly used continuous media. A digital video sequence is divided into many video frames, each frame capturing one snapshot of the video scene. The video frames are typically captured at periodic time intervals, such as 25 frames per second (fps) in PAL-standard video and 29.9 fps in NTSC-standard video. In continuous media system, however, there is more exibility in the frame rate used, predominately due to the often limited network/server bandwidth for delivering the video data. In these applications it is common to use frame rates lower than the previous broadcast standards if network bandwidth is limited. Clearly, the reduction in frame rate will generate fewer data but at the expense of reduced visual quality (e.g., fast motion becomes jerky or jumpy).

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