Generalization hierarchy

For doping-dependent anodic etch stops in HF, a general hierarchy of dissolution is observed [La5] illuminated n-doped and n+-doped areas are most easily dissolved, followed by p+-doped areas. Next likely to be dissolved are p-type areas. Moderately n-type doped areas kept in the dark are least likely to be etched. This hierarchy corresponds to the potential shift of the I-V curve in the regime of PS formation [Gal, Zh5]. 

Fig 13 General hierarchies based on partitions of 6,7 and 8 respectively Top levels correspond to linear acenes, star trees and perfect graphs while bottom levels are those of the zigzag polyacenes and paths ... 

The colon is only used for bridging ligands, so that the more restricted general hierarchy is simply comma < semicolon. The sequence when bridging ligands are being specified is comma < colon. (See Example 2 in Section IR-2.5.2, and Section IR-9.2.5.5.)... 

As a summary, the general hierarchy for the jHoduc tm of active specks in a molecular gas volume is shown schematkalty in Fig. 7. 

Pig. 7. The general hierarchy for tte production of active species in a molecular gas plasma (after Ref. 14, by courtesy of Noyes Publ.)... 

Flowsheets/flow diagrams are fundamental engineering documents used by everyone on a facility. The terminology used by different companies and industries varies somewhat, but the general hierarchy is from block flow diagrams (BFDs) to process flow diagrams (PFDs) to P IDs. 

In line with ISO 17776 (2000) and its general hierarchy of risk-reducing measures, this work will propose the following risk-reducing phases as generic safety functions Prevention, Detection, Control, Mitigation and Emergency Response. These functionalities act in the same sequence when placed on the chain of accident development (Fig. 1). 

The second introductory chapter discusses the effect of different classes of chemicals on polymers. Definitions of different types of interactions and methods to measure them are given, and the reasons for different interactions of chemicals with plastics and elastomers are discussed. The general hierarchy of the chemical resistance of different classes of polymers and commercial plastics is reviewed, along with the common methods used to enhance chemical resistance properties. Finally, examples of some applications that require chemical resistance are given, along with materials that would be suitable for these applications. 

Election nuclear dynamics theory is a direct nonadiababc dynamics approach to molecular processes and uses an electi onic basis of atomic orbitals attached to dynamical centers, whose positions and momenta are dynamical variables. Although computationally intensive, this approach is general and has a systematic hierarchy of approximations when applied in an ab initio fashion. It can also be applied with semiempirical treatment of electronic degrees of freedom [4]. It is important to recognize that the reactants in this approach are not forced to follow a certain reaction path but for a given set of initial conditions the entire system evolves in time in a completely dynamical manner dictated by the inteiparbcle interactions. 

Many of these techniques involve source reduction— the preferred option on the EPA s hierarchy of waste management (24). Others deal with on-and off-site recycling. The best way to determine how these general approaches can fit a particular company s needs is to conduct a waste minimization... 

Waste minimization generally considers all of the methods in the EPA hierarchy (except for disposal) appropriate to reduce the volume or quantity of waste requiring dispos (i.e., source reduction). The definition oi source reduction as applied in the Pollution Prevention Act, however, is any practice that reduces the amount of any hazardous substance, pollutant, or contaminant entering any waste stream... 

The stiffnesses of other bond types are calculated in a similar way (in general, the cumbersome sum described above is not needed because the interactions are of short range). The resulting hierarchy of bond stiffnesses is as shown in Table 6.1. 

Each one of these four models can be thought of as defining the response of a black-box to a tape of symbols that is fed to it, cyclically, one cell at a time. During each cycle, the black-box reads the symbol at the appropriate cell, responds to that symbol according to a set of model-specific rules, and then moves the tape forward by one cell. What type of computational model the black-box represents depends on its general response. Although a more detailed discussion of each of these types will be given in chapter 6, we mention here that the four models make up what is conventionally called the Chomsky hierarchy Each type of computational... 

The three dimensions introduced above, Dp, Di and Dq, are actually three members of an (uncountably infinite) hierarchy of generalized fractal dimensions introduced by Heiitschel and Procaccia [hent83]. The hierarchy is defined by generalizing the information function /(e) (equation 4.88) used in defining Dj to the i/ -order Renyi information function, Io e) -... 

Generalized Renyi Entropies and Dimensions A hierarchy of generalized entropies and dimensions, SQ B,t), s[ B,t), S B,t),. .. - analogous to the hierarchy of fractal dimensions, Dq, Di,. .., introduced earlier in equation 4.94 for continuous systems may also be defined ... 

Notice that in this general case, correlation functions cannot be solved for directly instead, there is an entire hierarchy of lower-order correlations expressed as functions of higher-order correlations. For example if we take an average of equation 7.79 over all space-time histories, and assume that we have a steady-state so... 

Hierarchical Complexity Static Captures intuitive feel of the complexity of a hierarchy Not a-priori clear how to extend to more general objects... 

Where Western science has heretofore been predicated on (1) static partitions of S2 (modulo our co-evolved senses and language), and (2) simple, linear chains of cause o effect, the generalized CA-based physics represents a paradigm shift to (1) causal webs, and (2) fully coevolving object interaction hierarchies and dynamic partitions. 

We propose four basic principles (rf a generalized new physics that builds upon the two fundamental axioms listed earlier, as well as the notions of hierarchy and maximal relativity ... 

---