Many-to-one

As the diagram develops, a necessary and sufficient test is applied to pairs of events, and checks for completeness and sequencing are made. One-to-many and many-to-one relations can be represented in the diagram. If data cannot be foimd to verify the relation between an event pair, then a technique called back-STEP can be used to explore gaps in understanding. Essentially back-STEP is a fault tree which uses the event with no other events leading to it as the top node. The analyst then develops possible event flows which could describe what happened during the gap in events in order to cause the top node. 

The many-to-one mapping that may arise in voting rules. Several different combinations of states may give rise to the same state in the next cycle. 

Voting rules are irreversible as several different configurations of cells in the neighborhood can lead to the same set of states in the following cycle. In other words, there is a many-to-one mapping of states (Figure 6.12). 

One learns from these molecular complexes that equivalent synthons can lead to virtually identical crystal structures. Synthons in, V and VI are chemically and geometrically equivalent though they originate from different molecules, a nitrile, an N-oxide and a nitro compound. These three synthons are used in crystal design in almost the same way. So, different molecules may yield similar crystal structures if they are capable of forming equivalent synthons. This is a powerful concept because it establishes a many-to-one correspondence between molecular and crystal structures. 

Fig. 6. Many-to-one correspondance between wavefunctions in and one-particle densities is the Hohenberg-Kohn orbit, i.e., the orbit that contains the exact ground-state wavefunction...

Previous sections have detailed phenomena that contribute to the degradation of resolution in optical spectra. Concepts useful in specifying resolution criteria have been established. Although transfer and point-spread functions of varying shape can yield identical numbers when a simple two-point criterion is applied, this many-to-one correspondence does not diminish the criterion s usefulness. More rigorous specification of the transfer function virtually requires graphical presentation for human interpretation. Its use therefore demands far more space in text and more time for study. Frequently, the functional form of the transfer function is well known anyway systems being compared are often of similar type. In these cases, the two-point criterion is entirely adequate. 

Carpels many to one, spiral or cyclic, usually free or only slightly united stamens mostly numerous. 

Many-to-one functions are those for which more than one value of x is associated with one value of f(x). Thus, for f(x) = xz, the numbers 2 are both associated with the number 4, and so this function is 2 1. 

Functions having a property f(x a) =f x) are known as periodic functions with a period a, and are said to be many-to-one functions. In the examples given above, the period for the sine and cosine functions is 2n, while that for the tangent function is n. 

Both matrices define zero rotation in 3-dimensional space, so we see that this zero rotation in 3D dimensional space corresponds to two different SU(2) elements depending on the value of (3. There is thus a homomorphism, or many-to-one mapping relationship between 0(3) and SU(2)—where many is 2 in this case—but not a one-to-one mapping. 

There are various types of classification of attacks. For example, division into passive and active, external and internal attacks, deliberate and unintentional. It should be mentioned that many models of attacks are currently well known one-to-one or one-to-many, i.e., attack proceeds from one point many-to-one and many-to-many, i.e., distributed or coordinated attacks hybrid attacks also named the blended threat [12]. 

The many-to-one association between ImageAnalysis and Hybridization emphasizes that several Images can be used for single ImageAnalysis only if they are obtained from the same Hybridization. ImageAnalysis is a subclass of Expression ValueDimension therefore, ExpressionValues can be directly related to ImageAnalysis objects. 

Two different MACCS keys (or MDL keys) [MACCS keys - MDL Information Systems Inc., 2008 Durant, Leland et al, 2002] are commonly encountered, one containing 960 bits and the other, which is public, containing a subset of 166 bits (ISIS keys). The fragment dictionary is based on a number of atom types, atom pairs, and custom atom environments. There can be a one-to-one relationship between the structural features and bits, or hashing can be used to create a many-to-one or many-to-many relationship between the features and bits. 

Figure 1. Many to one correspondence between wavefunctions in Hilbert space and jV-representable and u-representable one-particle densities. is the...

A critical concept for the advanced PubChem user is that of combining and transforming sets of identifiers between the three PubChem databases, based on the above identifier relationships. For instance, there is a many-to-one relationship between SIDs and "standardized" CID, as more than one Substance depositor may have supplied the chemical structure that standardizes to a given CID. (In fact, even within a particular depositor s records, there may be redundant structures because of different sample origins, tautomeric forms, etc.). Also, the perceptive reader will notice there is not a direct relationship between Bio Assay (AID) and Compound (CID) identifiers. To discover assays linked to a CID, there is an expansion of that CID to all SIDs for which that CID is the standardized form AIDs can be associated with CIDs linked to any of these SIDs. 

Fullen and Youvan describe the use directly drive the synthesis of new protein sequences. The experimental approach first produces DNA, which then codes for protein, and then measures the activity of the resulting proteins. Because there is a many-to-one relationship in tbe DNA triplet to amino acid coding, the GA chromosome simply codes for the doping ratios of the four DNA bases at each step ol synthesis. 

There is a many-to-one relationship between clients and servers, but the relationship is relative. In some cases, a client may pass a reference to a callback object when it invokes a service. This lets... 

The structure of the pipeline network is another aspect to be considered. Since in pipelines the product flow is unidirectional in very most cases, the network structure can be categorized according to the number of sources and sinks. In the simplest case, there is a single source and a single sink (one-to-one network). Similarly, if there are multiple sinks to be supplied this is labelled as a one-to-many network. Conversely, there exist many-to-one networks and, finally, for multiple sources and sinks also many-to-many networks. Table 3.1 displays this categorization scheme. 

Wc assume that. h-< > hi. There is a homomorphism betwce the groups (7i and if there exists a many-to-one correspondence between the elements of (7i and (7.>, with preservation of the intra-group multiplication rules. If such a situation exists then the larger group is said to be homomorphic onto the smaller group. 

Thus the elements of Czv map onto (have many-to-one correspondence... 

REACCS uses this iterative scheme, as well as other methods, to solve non-stoichiometric reactions. The ARCP module looks for conditions such as the existence of alternate subgraphs (alternate products), and many-to-one mappings of identical... 

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