Mutually exclusive sets

In the previous, fixed-input determination of the IT bond indices this discontinuity in the transition from the decoupled to the coupled descriptions of the molecular fragments prevents an interpretation of the former as the limiting case of the latter, when all external communications of the subsystem in question become infinitely small. In other words, the fixed-and flexible-input approaches generate the mutually exclusive sets of bond indices, which cannot describe this transition in a continuous ("causal") fashion. As we have demonstrated in the decoupled approach of the preceding section, only the overall input normalization equal to the number of the decoupled orbital subsystems gives rise to the full agreement with the accepted chemical intuition. 

Eriani G, Delarue M, Poch O, Gangloff J, Moras D. Partition of tRNA synthetases into two classes based on mutually exclusive sets of sequence motifs. Nature 1990 347 203-206. 

Modes define mutually exclusive sets of automation behaviors. Modes can be used to determine how to interpret inputs or to define required controller behavior. Four general types of modes are common controller operating modes, supervisory modes, display modes, and controlled process modes. 

Mutually exclusive sets are defined as sets that cannot happen at the same time. Mutually exclusive event sets are easily recognized on a Venn diagram. In Figure B-5, the event sets A and B are shown. There is no common space within the A circle and the B circle. There is no intersection between A and B. They cannot happen at the same time and are, therefore, mutually exclusive. 

Intersection of Sets. This is denoted by a dot ( ) or no dot at all or n. For example, if A n B = C, it simply means that set C contains all elements that belong to both sets A and B. If there are no common elements between A and B (i.e., A n B = 0) then these two sets are called mutually exclusive sets or events. 

This can be guaranteed by construction if the orbitals of the different groups are built up from mutually exclusive sets of orthonormal atomic basis functions The... 

Besides the stationary condition, a complete, exhaustive, and mutually exclusive set of navigation states concurrent with the passage through the subset can be defined as the union of possible (1) water column states, (2) sea states, (3) morphologic states, and (4) maneuvering states during the passage. 

Two permutations are disjoint if they act on mutually exclusive sets of objects in an arrangement. To any permutation Ji of n objects one assignes a monomial s(rc) in the variable st corresponding to a cyclic permutation of length k in the unique product of disjoint cycles of n. A fixed object corresponds to a factor s, w fixed objects correspond to s, and a transposition corresponds to 7he factors associated with the above permutations ni, 2, and are and s]. 

Now consider the nature of the operations in a symmetric permutation group S . These operations are permutations of labels which can be written as a product of cycles which operate on mutually exclusive sets of labels, e.g.. 

Equation 4 indicates that probability measures are positive numbers, and as indicated by the third axiom (Pro3), a basic property of probability measures is that they are additive. This requirement is commonly referred to as the additivity requirement. This requirement ensures the sum of probabilities over any collectively exhaustive, mutually exclusive set of events is equal to 1 (unity). Considering a single event A, and its complement denoted A, from (Eq. 4) it can be shown that... 

Eliminating min cut sets with mutually exclusive events. 

MEX and SLIB are optional commands. MEX command must precede the SUB command. The MEX command sets to false, basic events that are pairwise mutually exclusive. For the SUB command, the user identifies sets of basic events within cutsets (original sets) that are to be rejilaced by another set of basic events (substituted sets). The SUB command accounts for basic events within cutsets that have either a common cause or statistical dependency. 

Conducting common cause and dependent event analysis Dropping complemented events and performing the subsequent minimization Generating block files (i.e., a set of Boolean equations) for subsystems Eliminating mincutsets with mutually exclusive events... 

When events A and B liave no elements in common tliey are said to be mutually exclusive. A set having no elements is called tlie null set and is designated by < ). Thus if events A and B are mutually exclusive then AB = < ). 

For a set of mutually exclusive alternatives, the project with the smallest LCC is the most cost-effective. 

Returning to the example sequence in Scheme 4.7 and using the minimum values of AE determined and setting the reaction yields also as minimum values, it is possible to evaluate the probabilities that each reaction will have an RME of at least 0.618 and also the probability that both reactions will achieve it simultaneously. Figures 4.10 and 4.11 illustrate the relevant regions in the graphs. We can conclude that the probabilities for the Petasis condensation and the coupling reaction are 77% and 94%, respectively. Since the reactions are independent of each other, that is, the individual probabilities are mutually exclusive, the combined probability that both reactions will have RME values of at least... 

After this numerical analysis was done, another set of models was developed and conclusions were drawn from the data. These models are given in Table VI. Note that excellent models were obtained for three of the five responses, and that Properties A and E were again mutually exclusive. Figure 9 and 10 show the response surfaces for Properties A and E. Overlaying these plots shows that no combination of components was possible which allowed the simultaneous achievement of the target values of these two properties. 

As these rules are somewhat difficult to understand in the abstract, we will suggest an example.8 Let us assume that there are three independent sets of programmes, such as spending on education, health care and roads. Within each of them there are several mutually exclusive options (only one of them will be implemented) with varying costs and benefits. The steps to be taken are as follows ... 

Optimizing Techniques. Clusters are formed by optimization of a clustering criterion. The resulting classes are mutually exclusive, the objects are partitioned clearly into sets. 

There are currently over 50 malfunctions of a fossil once-through steam system that can be diagnosed. Some of these malfunctions are listed in Table II. It will be noted that some of these malfunctions occur as sets of related malfunctions. In some cases the members of the set are mutually exclusive, as in the ammonia feed malfunctions. In other cases, such as contaminated makeup, there is a malfunction which can be broken into smaller, more detailed malfunctions. The system can diagnose a variety of... 

For example, consider a particle of spin 1/2. We can build a basis of the corresponding projective space by considering spin along the --axis. There are only two certain spin states, up and down. These are mutually exclusive if a particle is spin up, then it will not exit spin down from a --axis Stern-Gerlach machine, and vice versa. But is this set of states large enough Do either of these states have multiplicities In other words, is there some measurement that can distinguish between two pure spin-up particles, or between two pure spin-down particles The answer is no. As far as experiments have been done, any two z-spin-up (resp., spin-down) spin-1/2 particles are absolutely identical. So the list... 

First we verify that the states in the set are mutually exclusive. For instance, the two states ++> and —h) have mutually exclusive states for the spin-1/2 particle, and hence must be mutually exclusive. Similarly, in any pair either the spin-1/2 or the spin-1 particle states are mutually exclusive. 

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