Dissimilarity functions

Joint distribution of BB and AB pairs is shown in Fig. 6.44. The distribution of similar mobile particles B at long times in the asymmetric case practically is the same as in the symmetric case (when X = Xb). The behaviour of Xb (r, t) is determined by the Coulomb repulsion of B s for which the non-equilibrium screening effect does not take place. In its turn, some deviation for the joint dissimilar functions Y(r, t) seen in Fig. 6.44 for the symmetric and asymmetric cases is a direct consequence of different screening effects in the latter case the effective recombination radius increases in time which results in an increase of the Y(r,t) gradient at r = ro at long times this correlation function itself strives for the Heaviside step-like form. 

Any two species in the system can react as long as they possess unreacted dissimilar functional groups. 

The method is based on defining a dissimilarity function between the data set and the prototypes (not necessarily vectors in the same space) of the fuzzy classes. A fuzzy objective function is defined based on this dissimilarity function. In order to minimize the fuzzy objective function, a two-step iterative procedure is used for certain prototypes, the optimal fuzzy partition is determined. Conversely, for a certain fuzzy partition, the optimal prototypes are determined. This procedure continually decreases the value of the objective function. 

Only one reaction between two (usually dissimilar) functional groups All species considered to be polymer... 

Structural studies on proteins have uncovered a very wide variety of protein folds. At this time the upper limit of the number of unique ways in which proteins can fold is unknown however, genomic sequencing has provided a limit for the maximum number of folds that might be needed for the life of an organism by providing an upper limit to the number of proteins in the genome. Fortunately, the number of unique folds is likely to be considerably less than the total number of proteins since many proteins of dissimilar function have been found to contain the same fold. 

When two dissimilar metals are connected, as illustrated in Fig. V-16, ]here is a momentary flow of electrons from the metal with the smaller work function to the other so that the electrochemical potential of the electrons becomes the same. For the two metals a and /3... 

Once we have the measures, we have to apply them to chemical objects. Objects of interest to a chemist include molecules, reactions, mbrtures, spectra, patents, journal articles, atoms, functional groups, and complex chemical systems. Most frequently, the objects studied for similarity/dissimilarity are molecular structures. 

Separation. In this function, the geotextile serves to separate two dissimilar materials (Fig. 3), eg, two different soils, landfill material and the native soil, stone material and subgrade sod, old and new pavement, foundation sods and various types of wads, or one of many other similar situations. In some instances, it is difficult to distinguish between the separation and stabilization functions because in both situations the geotextde is serving as a separator. However, in stabilization some additional phenomena occur. 

Materials of Construction The most common material of construction for heat exchangers is carbon steel. Stainless-steel construction throughout is sometimes used in chemical-plant service and on rare occasions in petroleum refining. Many exchangers are constructed from dissimilar metals. Such combinations are functioning satisfactorily in certain sei vices. Extreme care in their selection is required since electrolytic attack can develop. 

The refractive index of the sample can be written as a complex number 2 = n2 — ik2. At wavelengths where the sample is not absorbing, 2, the absorption constant, equals zero. However, kj is non-zero at wavelengths where the sample is absorbing. In transmission spectroscopy, the intensity of an absorption band depends almost entirely on k2 while in ATR the intensity of the same band is a complex function of 2 and 2- Nevertheless, the statement made previously still holds. There will be absorption bands in ATR at wavelengths where 2 0. Thus, bands are expected at the same wavelengths in transmission and in ATR but their intensities may be dissimilar. 

Associative symbiosis Close but relatively casual interaction between two dissimilar organisms or biological systems. The association may be mutually beneficial but is not required for accomplishment of a particular function. 

Dissimilar metals should be in contact (either directly or by means of a conductive path such as water, condensation, etc.) only when the functional design so dictates. 

Note that in ISO/TS 16949 documented procedures are needed where the product identity is not inherently obvious - the where appropriate condition has been removed. If products are so dissimilar that inadvertent mixing would be unlikely to occur, a means of identifying the products is probably unnecessary. Inherently obvious in this context means that the physical differences are large enough to be visible to the untrained eye. Therefore functional differences, no matter how significant - as well as slight differences in physical characteristics, such as color, size, weight, appearance - would constitute an appropriate situation for documented identification procedures. 

A compatibilizer is sometimes used to overcome the interfacial tension between the two phases of dissimilar polymers. It enables a fine dispersion of highly cross-linked rubber particles. The function of the compatibilizer is to provide greater, but not total, thermodynamic compatibility between the two polymers [8]. 

These are active transducers in the sense that they act as a generator of EMF whose magnitude is a function of the temperature of the junction of two dissimilar metals. Rare-metal combinations are used for high accuracy and at high temperatures, but for most engineering applications one of the following is suitable, depending on the temperature ... 

Titanium in contact with other metals In most environments the potentials of passive titanium. Monel and stainless steel, are similar, so that galvanic effects are not likely to occur when these metals are connected. On the other hand, titanium usually functions as an efficient cathode, and thus while contact with dissimilar metals is not likely to lead to any significant attack upon titanium, there may well be adverse galvanic effects upon the other metal. The extent and degree of such galvanic attack will depend upon the relative areas of the titanium and the other metal where the area of the second metal is small in relation to that of titanium severe corrosion of the former will occur, while less corrosion will be evident where the proportions are reversedMetals such as stainless steel, which, like titanium, polarise easily, are much less affected in these circumstances than copper-base alloys and mild steel. 

Grafting two dissimilar plastics often involves a third plastic whose function is to improve the compatibility of the principal components. This compatibilizer material is a grafted copolymer that consists of one of the principal components and is similar to the other component. The mechanism is similar to that of having soap improve the solubility of a greasy substance in water. The soap contains components that are compatible with both the grease and the water. 

For those dilute mixtures where the solute and the solvent are chemically very different, the activity coefficient of the solute soon becomes a function of solute mole fraction even when that mole fraction is small. That is, if solute and solvent are strongly dissimilar, the relations valid for an infinitely dilute solution rapidly become poor approximations as the concentration of solute rises. In such cases, it is necessary to relax the assumption (made by Krichevsky and Kasarnovsky) that at constant temperature the activity coefficient of the solute is a function of pressure but not of solute mole fraction. For those moderately dilute mixtures where the solute-solute interactions are very much different from the solute-solvent interactions, we can write the constant-pressure activity coefficients as Margules expansions in the mole fractions for the solvent (component 1), we write at constant temperature and at reference pressure Pr ... 

The number-average molecular weight of a polymer may be controlled by offsetting the stoichiometry of two dissimilar mutually reactive difunctional monomers. The polymer will have the same endgroup functionality as that of the monomer used in excess. For a generic polymer made from a difunctional monomer AA with A functional groups and an excess of difunctional monomer BB widt B functional groups, r is defined as... 

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