Statistical arrays

Random hydrocarbon copolymers can also be produced by this new equilibrium polymerization method. Copolymers containing octenylene and butenylene linkages in a statistical array based on feed ratio result from the cocondensation of the two respective monomers or by the reaction of diene with unsaturated polymer. More controlled polymer stmctures have also been prepared by the slow addition of a diene solution to an unsaturated polymer containing active catalyst. Substituent effects were shown to dictate the polymerizability of monomers and in some cases selective polymerization of speciflc aUcenes in the monomer resulted in what appears as perfectly alternating copolymers. ... 

Corrosion rate values were calculated from the mass loss of each test presenting a statistical array and indicating corrosion rate ordered array average value v, mode value vmode, median value vmediam and standard deviation s. 

Any protic impurities in the parent polymer and any side reactions lead to loss of B-Li and thus to inefficient grafting. Furthermore, because the grafts are randomly placed along the backbone, the product is a statistical array of species, each varying in the number of grafts/chains. 

An alternative way of deriving the BET equation is to express the problem in statistical-mechanical rather than kinetic terms. Adsorption is explicitly assumed to be localized the surface is regarded as an array of identical adsorption sites, and each of these sites is assumed to form the base of a stack of sites extending out from the surface each stack is treated as a separate system, i.e. the occupancy of any site is independent of the occupancy of sites in neighbouring stacks—a condition which corresponds to the neglect of lateral interactions in the BET model. The further postulate that in any stack the site in the ith layer can be occupied only if all the underlying sites are already occupied, corresponds to the BET picture in which condensation of molecules to form the ith layer can only take place on to molecules which are present in the (i — l)th layer. 

The curves show that the peak capacity increases with the column efficiency, which is much as one would expect, however the major factor that influences peak capacity is clearly the capacity ratio of the last eluted peak. It follows that any aspect of the chromatographic system that might limit the value of (k ) for the last peak will also limit the peak capacity. Davis and Giddings [15] have pointed out that the theoretical peak capacity is an exaggerated value of the true peak capacity. They claim that the individual (k ) values for each solute in a realistic multi-component mixture will have a statistically irregular distribution. As they very adroitly point out, the solutes in a real sample do not array themselves conveniently along the chromatogram four standard deviations apart to provide the maximum peak capacity. 

Hilsenbeck SG et al. Statistical analysis of array expression data as applied to the problem of tamoxifen resistance. J Natl Cancer Inst 1999 91 453-459. 

HILSENBECK, S.G., FRIEDRICHS, W.E., SCHIFF, R., O CONNELL, P., HANSEN, R.K., OSBORNE, C.K., FUQUA, S.A., Statistical analysis of array expression data as applied to the problem of tamoxifen resistance, J. Natl. Cancer Inst., 1999,91,453-459. 

There are two other methods in which computers can be used to give information about defects in solids, often setting out from atomistic simulations or quantum mechanical foundations. Statistical methods, which can be applied to the generation of random walks, of relevance to diffusion of defects in solids or over surfaces, are well suited to a small computer. Similarly, the generation of patterns, such as the aggregation of atoms by diffusion, or superlattice arrays of defects, or defects formed by radiation damage, can be depicted visually, which leads to a better understanding of atomic processes. 

Another way for BOD estimation is the use of sensor arrays [37]. An electronic nose incorporating a non-specific sensor array of 12 conducting polymers was evaluated for its ability to monitor wastewater samples. A statistical approach (canonical correlation analysis) showed a linear relationship between the sensor responses and BOD over 5 months for some subsets of samples, leading to the prediction of BOD values from electronic nose analysis using neural network analysis. 

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