Origin, definition

Within the scope of the original definition, a very wide variety of ionomers can be obtained by the introduction of acidic groups at molar concentrations below 10% into the important addition polymer families, followed by partial neutralization with metal cations or amines. Extensive studies have been reported, and useful reviews of the polymers have appeared (3—8). Despite the broad scope of the field and the unusual property combinations obtainable, commercial exploitation has been confined mainly to the original family based on ethylene copolymers. The reasons for this situation have been discussed (9). Within certain industries, such as flexible packaging, the word ionomer is understood to mean a copolymer of ethylene with methacrylic or acryhc acid, partly neutralized with sodium or zinc. 

FIGURE 8.8 Tfie original definition of "ventilation efficiency."... 

The original definition of natural orbitals was in terms of the density matrix from a full Cl wave function, i.e. the best possible for a given basis set. In that case the natural orbitals have the significance that they provide the fastest convergence. In order to obtain the lowest energy for a Cl expansion using only a limited set of orbitals, the natural orbitals with the largest occupation numbers should be used. 

In 1964 the Conference Generate des Poids et des Mesures (CGPM) decided to accept the term litre as a special name for the cubic decimetre, and to discard the original definition. With this new meaning of the term litre (L), the millilitre (mL) and the cubic centimetre (cm3) are identical. 

At this stage it should be pointed out that the original definition of pH = —log cH (due to Sorensen, 1909 and which may be written as pcH) is not exact, and cannot be determined exactly by electrometric methods. It is realised that the activity rather than the concentration of an ion determines the e.m.f. of a galvanic cell of the type commonly used to measure pH, and hence pH may be defined as... 

When chemists see a pattern in the reactions of certain substances, they formulate a definition of a class of substance that captures them all. The reactions of the substances we call acids and bases are an excellent illustration of this approach. The pattern in these reactions was first identified in aqueous solutions, and led to the Arrhenius definitions of acids and bases (Section J). However, chemists discovered that similar reactions take place in nonaqueous solutions and even in the absence of solvent. The original definitions had to be replaced by more general definitions that encompassed this new knowledge. 

Since these loss functions express quality costs on a common and commensurate basis, extending the learning methodology of Section V to a situation with P objectives is straightforward. All one has to do is replace the original definition of the y performance metric [Eq. (23)] by the following more general version ... 

Note that just three points have been used to define our plane (see 2.1.6.). The original definition was given by Whewell in 1825 and by Grassman in 1829, but was popularized by Miller in 1839. Since three points of a lattice can be used to define a plane, it is obvious that such... 

Thus, for the purposes of this chapter, a hydrogel is considered to be a polymeric material that can absorb more than 20% of its weight in water while maintaining a distinct three-dimensional structure. This definition includes dry polymers that will swell in aqueous environments in addition to the water-swollen materials which inspired the original definitions [3], A hydrogel that dries without significant collapse of the macroscopic structure and which absorbs water into... 

These last two facts can be obtained from Minsky s result that two counter machines are universal and FACT III justifies the original definitions of Ianov and Rutledge. Of course, the programs involved are in general complex, unnatural and highly inefficient. 

We remind our readers here that AE, as we have been using it in this derivation is, as you will recall, the difference between AE and AE 0 in equation 41-4 and the expected value in the statistical nomenclature is therefore 21/2 times as large as AE (due to the fact that it is the result of the difference between random variables with equal variance), a difference that should be taken note of when comparing results with the original definition of S/N in equation 41-2. 

Tools that support model frameworks and templates should allow you to unfold each application of a model framework so as to see the full resulting model with all the substitutions made. Ideally, the tool should keep the definitions of the framework, the original definitions of the types to which it is applied, and each diagram in which the framework is applied. If the user changes any of these, the resulting unfolded model should change in step. Furthermore, the tool should allow you to define your own frameworks in the same notation as the models themselves. 

Among current popular tools, there is some support for templates in a restricted way. Typically, the template works more like a script a series of operations that is applied once to a model, adding the necessary attributes and operations. This technique has the disadvantage that the simpler original definitions are lost and changes are less easy to make. It is also less easy to see what the template is about, because it is written in a scripting language. 

The original definition was established as 1 /2 of the second derivative however, the one given in Equation 2.6 is more convenient and it has become the most common one in the recent literature. 

The specific heat capacity commonly has units of J/g-K. Because of the original definition of the calorie, the specific heat capacity of water is 4.184 J/g-K. If the specific heat capacity, the mass, and the change of temperature are all known, the amount of energy absorbed can easily be calculated. 

This index clearly corresponds with case 1(c) of Table 2, i.e., an ME computed as the sum of absolute deviations and related to the sum of the reference data. In the original definition according to Eq. (lib), R and T are supplied as percentages and a factor of 100 is included so that the results can be expressed on a percentage scale. 

Both definitions are identical, but Eq. (12a) expresses all relative quantities (R, T, f2) as fractions, whereas the original definition according to Eq. (12b) expresses them as percentages. This index has found much attention in the subsequent literature (20,21), but some objections have been raised against the use of percentages and the similarity scale in the definition of f2, which is in opposition to the dissimilarity scale used generally in statistics (22). 

The experimental activation volume is unambiguously determined from the slope of In kvs.p but its interpretation is not necessarily that of the original definition, the difference between the volumes of the activated complex and the reactants. In most cases the activation volume is a linear combination of volume changes in steps 1 and 2. In other cases one may have linear combinations of 3 and 4 volume contributions to AV. This will be treated in detail in the next section. 

The interpretation according to the original definition is indicated in Fig. 2b, as if the catalytic volume change had become smaller, without noticing that there is a significant contribution from the binding volume. It is clear that there is much more information to extract... 

As frequently happens in science, simplicity gives way to complexity when our horizons are broadened by further research. There are now several definitions of pheromone available in the relevant literature, each more elegant than the other. However, we do not have to worry much about the arcane issues that amuse and challenge researchers in the field. For our purposes, we can pretty much do with the original definition, expanded to include a classification system. 

If a particle appears bent, the designationis obviously appropriate, in accordance with the original definition, and the particle probably possesses enhanced mechanical strength. However, the tena fiber is usually applied to any small elongate inorganic particles without consideration of flexibility or mechanical strength. 

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