Boolean combinations

The beliefs are derived from the residuals with the relation (15) with the same threshold than for boolean evolution, i.e., t = 0.4 for a = 0.5. Clearly, the boolean combination leads to an unstable isolation of the faults because the value of ri is often oscillating around 0.4. On the contrary, the approach based on the Evidence theory isolates perfectly the faults and does not induce any oscillation. In another situation where the value of residual rs is not affected as it should be when the fault /s occurs, the boolean combination does not succeed again to isolate the faults (see in particular /s in Figure 7.b) whereas the Evidence theory combination methods correctly the faults most of the time Cf. Figure 7.c). 

Fig. 4.7. Regions can be drawn to define clusters of cells. Regions can then be used (individually or in Boolean combination) to form gates for restricting subsequent analysis to certain groups of cells.

A related database is provided through Chemweb the IFI Claims database (http //www.chemweb.com/databases/ claims) provides text-searchable information on claims in US patents from 1950 (chemical patents) and 1963 (utilities patents) to the present day. As well as non-specific search methods, the interface on Chemweb permits searching by Boolean combinations of title, inventor, exemplary claim(s), assignee, patent number, application number, US patent classifications or international patent classifications (IPCs). Search terms may be stemmed for additional flexibility. 

By searching for numerical terms (physical data, keywords or Boolean terms, such as the existence of spectra, etc.). These terms can be searched separately or in Boolean combinations ( AND , OR , NOT ). 

There are two additional reasons for a batch off-line search. First, the search criteria can be expanded to allow searches that are not possible on-line because of time considerations, as in the case of Boolean combinations of simple fragments, or available coitputer resources, as in the case of criteria based on non-structural information that is stored on other files. The second reason for batch seeirching is based on the need to efficiently handle large numbers of queries emd answers which require a source of high-volume hard copy output. 

The initial step is to identify which database, from a few thousands worldwide (about 10 000 in 2002), provides the requested information. The next step is to determine which subsection of the topic is of interest, and to identify typical search terms or keywords (synonyms, homonyms, different languages, or abbreviations) (Table 5-1). During the search in a database, this strategy is then executed (money is charged for spending time on some chemical databases). The resulting hits may be further refined by combining keywords or database fields, respectively, with Boolean operators (Table 5-2). The final results should be saved in electronic or printed form. 

Answers from aH of these searches contain CAS Registry Numbers. Answer sets may be combined, using the Boolean operators AND, OR, or NOT, with other answer sets or with text terms, such as names or molecular formulas. Any answer set also may be used to define subsets of the file for subsequent stmcture searching. Answer sets of up to 10,000 Registry Numbers from any type of search in this file may also be used as search terms in other files, such as the CA or CAOLD files (53). 

Shannon s method, expands a Boolean function of n variables in minterms consisting of all combinations of occurrences and non-occurrences of the events of interest. Consider a function of n Boolean variables XJ which may be expanded about X, as shown in Equation 2.2-3 where f(l, Xj,..., XJ where 1 replaces X,. This says that a function of Boolean variables equals the function with a variable set to I plus the product of NOT the variable limes the function with the variable set to 0. By extending Equation 2.2-3, a Boolean function may be expanded about all of its... 

Boolean equations show how component failures can fail a system. A minimal cut. he smallest combination of component failures that can fail a system. It is the set of non-sup us components, such as in the previous example, with the superfluous combination Y Z(X Y,. Z) e uded. If they all occurred they would cause the top event to occur. One-component minimtil cut s( if there are any, are single failures that cause system failure. Two-component minimal cutsets ai tairs of components, if they occur together cause system failure. Triple-components minimal Cl sts are sets of three components that, if they fail together cause system failure, and so on to hi er cutsets... 

Figure 3.4.4-1 summarizes conventional fault tree symbols. The many symbols are daunting, but remember that the computer only performs AND (Boolean multiplication) and OR (Boolean addition) operations. All else are combinations of these. 

BOOL, boolean reduction module, generates minimal cutsets by combining minimal cutsets, generated by the FTA module, with a Boolean algorithm. BOOL automatically handles of success paths and truncates by probability or order. 

Since there are two choices for every combination of states of the k inputs at each site, is randomly selected from among 2 possible Boolean functions of k... 

The words AND, NOT, and OR are called Boolean operators. They may be combined in many ways, for example,... 

Besides subject terms, the CA File also contains bibliographical information, such as author names, location of the laboratory in which the work was done, language of the paper, and so on, and these can be searched. For example, S ROBERTS, J7/AU will find all papers published by any authors named Roberts whose first name begins with J. These terms can be combined with subject terms in Boolean searches. 

A fault tree is, itself, a Boolean equation relating basic events to the top event. The equation can be analyzed quantitatively or qualitatively by hand or by using computer code(s). If it is analyzed quantitatively, the probabilities or frequencies of the intermediate events and the top event are calculated. If it is analyzed qualitatively, a list of the failure combinations that can cause the top event is generated. These combinations are known as cut sets. A minimal cut set (MCS) is the smallest combination of basic events that, if they occur or exist simultaneously, cause the top event. These combinations are termed "minimal" because all of the basic events in a MCS must occur if the top event is to occur. Thus, a list of MCSs represents the known ways the top event can occur, stated in terms of equipment failures, human errors, and associated circumstances. 

But sometimes we need to disallow certain combinations of attribute values. To do this we can write an invariant a Boolean (true/false) expression that must be true for every permitted snapshot. (We will scope the snapshots by the set of actions to which this applies in Section 3.5.5, Context and Control of an Invariant.)... 

Such state definitions are often combinations of a few boolean terms — some optional link present, some attribute > 0, and so on. Make a table of the combinations, showing how each state has a different combination, and identifying combinations that do not correspond to any state. The complete set of allowed states is an invariant that should be documented for the model. 

A new matrix M(1) is formed from M(0) in the same manner that M(0) was formed from the occurrence matrix. The column of M<0) containing the most nonzero elements is identified, and M(1> is made up of rows identical to each row of M(0), which contains a zero in column k and one final row, which is the Boolean union of the remaining rows in M(0). Figure 13b illustrates M(1). A record is kept of which rows of the original occurrence matrix have been combined to form each row of M(0), M(1), and so on. 

The various chemical requirements of each derivative group are summarized in Table 8.1. In order to implement these requirements, a component specification language has been developed. This specification language contains a combination of keywords, target values, and Boolean operators. A brief summary of these commands is listed in Table 8.2 below. The specification language allows the user to control... 

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