Hierarchical elements

The family of hierarchical elements are specifically designed to minimize the computational cost of repeated computations in the p-version of the finite element method (Zienkiewicz and Taylor, 1994). Successive approximations based on hierarchical elements utilize the derivations of a lower step to generate the solution for a higher-order approximation. This can significantly reduce the... 

It is evident that application of Green s theorem cannot eliminate second-order derivatives of the shape functions in the set of working equations of the least-sc[uares scheme. Therefore, direct application of these equations should, in general, be in conjunction with C continuous Hermite elements (Petera and Nassehi, 1993 Petera and Pittman, 1994). However, various techniques are available that make the use of elements in these schemes possible. For example, Bell and Surana (1994) developed a method in which the flow model equations are cast into a set of auxiliary first-order differentia] equations. They used this approach to construct a least-sciuares scheme for non-Newtonian flow equations based on equal-order C° continuous, p-version hierarchical elements. 

Relational databases can store unlimited numbers of results for every sample and unlimited samples for every request. The advantage of a relational DBMS over a more traditional hierarchical system, in which data sets may contain other data sets, is that the design of the database only has to consider relationships between data elements, not the number of instances for any given variable. 

In the next subsection, I describe how the basic elements of Bayesian analysis are formulated mathematically. I also describe the methods for deriving posterior distributions from the model, either in terms of conjugate prior likelihood forms or in terms of simulation using Markov chain Monte Carlo (MCMC) methods. The utility of Bayesian methods has expanded greatly in recent years because of the development of MCMC methods and fast computers. I also describe the basics of hierarchical and mixture models. 

By visual inspection of an OAET it is possible to identify the elements of a process control task which are critical in responding to an initiating event. An important issue in the construction of OAETs is the level of task breakdown. If the overall task is redescribed to very small subtasks it might be difficult to gain insights from the OAET because it Ccin become relatively unwieldy. Hierarchical Task Analysis provides a useful framework for the... 

Hierarchical Control, in which a three-level command hierarchy is established each lower-level echelon element keys on those in the next higher echelon on each time step of the evolution. 

To achieve these consistencies, MODEL.LA. provides a series of semantic relationships among its modeling elements, which are defined at different levels of abstraction. For example, the semantic relationship (see 21 1), is-disaggregated-in, triggers the generation of a series of relationships between the abstract entity (e.g., overall plant) and the entities (e.g., process sections) that it was decomposed to. The relationships establish the requisite consistency in the (1) topological structure and (2) the state (variables, terms, constraints) of the systems. For more detailed discussion on how MODEL.LA. maintains consistency among the various hierarchical descriptions of a plant, the reader should consult 21 1. 

D. L. Massart, L. Kaufman and K.H. Esbensen, Hierarchical non-hierarchical clustering strategy and application to classification of iron-meteorites according to their trace element patterns. Anal. Chem., 54 (1982) 911-917. 

The majority of vomerolfactory effects discussed relate to intra-specific patterns, most concerned with social discriminations. Individual and or group membership, hierarchical status —often aggression-related, are among many non-sexual but socially indispensable elements. Social systems with evident female dominance are not infrequent among... 

Based on currently available elemental abundance data and age determinations, the thick disk could have formed either through a violent, heating merger or through accretion of (substantial) satellites in a hierarchical galaxy formation scenario. The fast monolithic-like collapse is getting more and more problematic as data are gathered. It would be especially crucial to establish if there is an age-metallicity relation in the thick disk or not as in that case the thick disk could not have formed in that way (since the models indicate that the formation time-scale for the stars in the thick disk would be very short, see [7]). 

The three hierarchical levels are interconnected by information flowing from the strategic level via the tactical level to the operational level, and the other way around. From upper to the lower level, the information flow is related to the environment on the strategic level, which is the organizational values and norms. However, as Thompson (Thompson, 1967) identified, the tactical control level can allow the operational level to operate as a relatively closed system. The tactical level provides a buffer between the uncertain environment and stability of resources required for uninterrupted production on the operational level. In this way the influences from the external environment on the operational level will be reduced to a minimum. The information flow going from lower to upper level is related to the operational process or transformations. The top down flow provides the restrictions and conditions for the transformation, while the bottom up flow provides information about the status of inputs, outputs, and resources of the transformations. The horizontal information flows are between different control elements on one hierarchical control level. 

By reducing the complexity of the steering element the analysis process aims to retrieve an ineffective control element. However, the actual interrelations between the different hierarchical control levels must be known. No literature exists to accurately describe how the different hierarchical control levels are interrelated. Therefore, the author has established the relationships, as discussed by Korvers (Korvers et al., 2001b), see Figure 31. 

Identify the ineffective control processes Identify the accompanying control processes and the initial ineffective control elements on the subsequent hierarchical control levels that let the prioritized precursors occur. 

Identify the latent conditions Identify the conditions causing the control elements on the different hierarchical control levels to be ineffective. 

In practice the processes controlling the identified and prioritized precursors are identified by taking the theoretical hierarchical control model, as shown in Figure 31, as a reference. The controlling processes identified in practice are linked to their theoretical counterparts to constitute the control processes of the identified precursors. When these control processes are identified, the ineffective control elements are identified by the flow scheme, depicted in Figure 33. 

This flow scheme structurally checks whether or not a control element is working effectively. This flow scheme is used as a guideline on each successive hierarchical control level (operational, tactical, strategic), starting on the operational level. 

The number of initial ineffective control elements on each hierarchical control level (=where) and the corresponding latent conditions leading to these ineffective control elements (=why) will be discussed. The results of the discussion will be reflected on the number of affected safety barriers (=consequences). Furthermore, the individual affected safety barriers will be combined, to find possible alignments of affected safety barriers that enable accidents (=risks). Finally, the weaknesses of the current safety management system are indicated by the previous findings. 

Stage 4, the identification of the initial ineffective control element, can only be identified on the operational control level. Due to limited information (in spite of selecting accidents on the basis of information-richness), hierarchical control levels cannot be identified. 

---