Majority rule

The Greenman decision was a watershed, and privity-free strict HabiUty in tort swept the country as a tidal wave. In 1965, the American Law Institute embraced the concept in Section 402A, and thousands of decisions cited to the Restatement. Within a decade the decision became the majority rule in the United States in the 1990s all but a tiny minority of states ascribe to it. 

Notice that p,. = 1/2 exactly for both the von Neiimaim neighborhood 3/5 rule and Moore neighborhood 5/9 rule . This simple result follows immediately from the 0 e-r 1 symmetry of these simple majority rules. A simple majority rule is one in which the total possible number of votes is evenly split between yes (cr = 1) and no (cr = 0) votes, and can obviously exist only if the neighborhood size is odd. 

Toffoli and Margolus [tofF86] point out that what appears on the macroscopic scale is a good simulation of surface tension, in which the boundaries behave as though they are stretched membranes exerting a pull proportional to their curvature. Vichniac adds that the behavior of such twisted majority rules actually simulates the Allen-Cahn equation of surface tension rather accurately ... 

Consider the one-dimensional majority rule defined on a radius-r neighborhood ... 

A bound on the transient length of the one-dimensional majority rule (equation 5.142) follows in straightforward fashion from our more general results of the previous section. 

Just as was the case for one-diinensional majority rules considered in the previous section, we again recognize that the two-dimensional majority rule is but a special case of the generalized threshold rule defined in equation 5.121. Intuitively, the idea is simply to let aij represent a two-dimensional lattice that is built out of our a-priori structureless set of sites, i = 1, 2,..., A. Suppose we arrange these N sites into n rows with rn sites per row, so that N = n x rn. Then the site positioned on the row and column, can be identified with the original site... 

Fig. 5.6. Some snapshots of the evolution of the 5-neighbor (von Neumann neighborhood) majority rule (p2d majority with threshold b = 2, The initial state is random with density po = 0.075.

In a more sophisticated version of this technique, called the k-nearest neighbour method (k-NN method), one selects the k nearest objects to u and applies a majority rule u is classified in the group to which the majority of the k objects belong. Figure 33.12 gives an example of a 3-NN method. One selects the three nearest neighbours (A, B and C) to the unknown u. Since A and B belong to L, one... 

Copolymers with Preferential Screw Sense and Majority Rule Principle... 

Another significant cooperativity effect in preferential helical screw sense optically active copolymers is the majority rule phenomenon.18bl8q In this case, the screw sense of a helical main chain with unequal proportions of opposite chirality enantiopure chiral side groups is controlled by the enantiomeric excess only. Since this phenomenon was first reported from poly-a-olefins made of vinyl co-monomers bearing nonenantiopure chiral moieties by Green et al.8b and Pino et al.,16b this majority rule has been established in... 

Table 7.1 summarizes the major rules. Table 7.2 shows Level I rules in detail.16 Table 7.3 covers Level II rules and Table 7.4, Level III rules.16 These rules have been used for thousands of discovery compounds and ensure that the reported results are scientifically correct while minimizing the time required to develop the assay and report the results to the discovery project team in a timely manner.115...

Drug Stage Assay Type (Level) Summary of Major Rules CLP ... 

In carbohydrate chemistry, the most described method for the preparation of saccharidic thionocarbamates involves preliminary introduction of the amine function on a partially or non-protected saccharidic template. The condensation of amino sugars with carbon disulfide or thiophosgene leads to cyclization in 1,3-oxazolidine- or l,3-oxazine-2-thiones. This reaction involves the formation of an intermediate isothiocyanate, which reacts further with a 3- or y-located hydroxyl group. The viability and facility of this process depends on the saccharidic ring size and the inherent strain. Some major rules can be put into light from the cases studied 30... 

Another cooperativity effect, dubbed majority rule has also been noted. Where opposite enantiomer chiral groups are both present in side chains, such as (S) and (l )2-methylbutyl groups, the overall helicity is determined in a non-linear manner by the ee only, as is evident in Figure 42. 

Equity or value conflicts involve the initial creation and distribution of property rights. Equity conflicts also arise when some citizens want to alter property rights by majority-rule political decisions instead of market transactions. Equity conflicts cannot be resolved with unanimous consent, while efficiency conflicts can. 

At this point it is worth summarizing the major rules necessary to apply the CM model. 

Therefore, the majority ruled that the Customs Service had a compelling interest that justified infringing on the applicants expectation of privacy. However, in the case of employees applying only for jobs involving classified material, the Court decided that there was insufficient evidence on the record to make a determination. 

That such conformational and configurational effects do actually occur in the transmission of chirality in molecules is demonstrated by corresponding findings and conceptual models from the field of polymer chemistry The sergeant-and-soldier principle and the majority rules model [38]. 

Fig. 4.78 Majority rules principle as model for chirality amplification in (intermolecular) polymerisation of (unsymmetrically substituted) monomeric ethenes to form polymers, which can also convey the concept of (intramolecular) transmission of chiral perturbations [e.g. emanating from a stereogenic centre) in dendritic molecules The perturbation introduced into a system having a prior order (dance group a) in the form of an ex-...

According to the majority rules model the chirality of the enantiomer of the chiral monomer present in excess is amplified during polymerisation [38] (Fig. 4.78). Even if just a small enantiomeric excess is present, the resulting polymer shows a helical inequality identical to that of the corresponding chiral homopolymer (see the caption of Fig. 4.78 for details). 

Both effects (sergeant/soldier and majority rules) require helical conformations of the polymer strands undergoing formation (with mobile helical points of inversion). 

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