The proof is based on our main theorem, which describes the form of all bijective transformations on the set of all rank-one idempotents of a Banach space which preserve zero products in both directions.
It also provides a method to develop more effective moment-closures by examining the form of the correlations or other moments generated by numerical experiment, and choosing a parsimonious Ansatz which describes their different forms through time.
In our discussion of the results, we used the term fibre wall morphology which describes the network formed by the fibril aggregates inside the fibre wall remaining after the isolation procedure.
To this end, this article first created a detailed list of 23 variables to measure city-level urban form of 100 major Urban Areas (UAs) in the United States and then applied factor analysis to construct five latent variables which describe urban form.
In this regard, it presents an original model of psychological growth, which describes how the self both forms and transforms, as the person gains in "sympathy" and "theopathy" — put simply, learns to love, both others and God.
Re "The Future of the 30-Second Spot" (March 27), which described new forms of television commercials that may be customized to neighborhoods and, ultimately, to individual households: If the trade-off for "smarter" television advertising is investment in technology rather than messages, it will achieve all the punch, or lack thereof, of a banner ad.
The best description of the ultracapacitor dynamic was achieved using fractional model in the form which describes the dynamics of the ultracapacitor over a reasonable range of frequencies.
A strong association rule set which describes the relationship between the critical form features and the corresponding KANSEI adjectives was subsequently generated.
Data partitioning strategy, which describes how the partitions are formed to foster the scalability is also explained.
However, when aggregated, these snapshots form a broader picture, which describes the community of Makers in a useful way and allows us to see possibilities for broadening engineering pathways.
