Subject simplified framework

The case of unidirectional electric field strength is expressed by U23 = U31 = 0, while the case of unidirectional electric flux density is indicated by U23 = vzi = 1. The above discussion on the influences of mismatched electroding for the shear cases identified the two unidirectional field assumptions as extremes with the actual effective properties in between. Thus, V2z and vzi may be determined as functions of the electrostatic field distributions affected by the geometry of structure and electrodes as well as the material properties in the ranges 0 < vzz < 1 and 0 < U31 < 1. This might be used to represent the macroscopic mechanical behavior of piezoelectric structures subjected to shear induced transverse electrostatic fields within the simplified framework of assumingly unidirectional electrostatic fields. Thereby the essential and beneficial consequences would be inherited as conclusively formulated ... 

In this chapter, we document the many transformations to which compounds having the bicyclo[3.3.0]octane framework have been subjected. Since many of these reactions can now be regarded as classical", we have not attempted to be completely exhaustive in our coverage. Rather, the interconversions discussed have been selected because they are exemplary. To our knowledge, however, the reference citations made in this and earlier sections constitute a complete listing. Any search for information on these compounds in thereby simplified to this extent. 

These calculations yield, subject to some simplifying assumptions, relative T-site alumimun substitution energies computed (1) for the thermodynamic equilibrium state, (2) at zero K and (3) for models devoid of non-firamework species. Framework zeolites, metastable structures, are produced under luetic control and if, as indicated by the most recent calculations, the relative T-site substitution energies for the (Cerent sites are not grossly disparate, the actual distributions in reed materitds will be determined by the particular conditions of synthesis. As the molecular-level mechanisms of zeolite sjmthesis remain obscure, we especially need some experimental indicator of which sites are actually adopted by aluminum in real MFI-framework materials. 

From the mechanical point of view, the theory developed so far allows for the consideration of adaptive laminated shells subjected to arbitrary loads and strains within the framework of Remarks 6.1 to 6.6. For many applications, such a level of generality is not necessary as particular knowledge with respect to mission and design may be used to imposed simplifying assumptions. 

Shah (2005) states that it has not really been shown what is an appropriate description of manufacturing processes at the SC level. By translating the STN concept into the whole SC environment a more adequate representation of all operations and materials entailed in a production system can be achieved. It should also be stressed that the proposed model simplifies the representation of batch and/or continuous process SCs into the same framework. Moreover, given that the proposed SC model is an extension of a classical multipurpose plant scheduling formulation it may eventually facilitate the consideration of scheduling decisions in designing an SC. This issue constitutes one important subject that is addressed later in the book. 

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