In the next lemma we use the same procedure as in [21], p.44, as well as some ideas from [22], p.349 in order to make the aforementioned representation of the function ρ.
We finally propose a method to extract frequent audio objects (patterns) in the aforementioned sparse representations.
Then, by integration of the generalized Paris' law, the relationship between the aforementioned generalized representations of fatigue is established, providing the link between the cumulative fatigue damage and the fatigue crack propagation approaches.
A SSP algorithm based on A∗-search is proposed which uses the advantages of the aforementioned environment representation.
As a result, the aforementioned internal representation which individuals generate when they communicate with God, as a real meaningful person, can also generate an empathic understanding of God as perceived by the individual.
Consequently, some basic characteristics of 3-D wave motion in layered media (e.g., various surface waves) can then be identified in a unified form for the aforementioned different co-ordinate representations.
The prediction performance of SVM predictor with the aforementioned two protein sequence representation across five runs is shown in Table 3.
This includes breaking news, facts, opinions, observations, gossip, creative expressions, commentary, parodies, homework, conjecture, or fictional representations of the aforementioned.
To emphasis the last argument, we propose a data representation as in Figure 12. Figure 12 proposes an alternative representation for the aforementioned discussion.
