Relative definition

MINERALOGY. The science of mineralogy is concerned with the formation, occurrence, properties, composition, and classification of minerals. Vnrinus definitions of a mineral have been proposed. Possibly, the most acceptable may be. "a naturally occurring inorganic substance, usually crystalline, possessing a relatively definite chemical composition and physical characteristics. It should be pointed out that some naturally formed organic substances, particularly of an economic resource nature, are sometimes classified as minerals. 

Concepts and terminology of adsorption processes on solid adsorbents are discussed by D. H, Everett, Reporting data on adsorption from solution at the solid/solution interface, Pure Appl. Chem. 58 967 (1986). See also D. H. Everett, Manual of Symbols and Terminology for Physicochemical Quantities and Units. Appendix II Definition, Terminology and Symbols in Colloid and Surface Chemistry, Butterworths, London, 1972 [published in Pure Appl. Chem. 31 577 (1972)]. The need for a relative definition of the amount of adsorbed substance stems from the fact that the actual position of an interface cannot be specified with absolute precision, even conceptually. 

Table 2.11 lists the principal types of solid base catalysts. We should remember, however, that base catalyst is a relative definition and thus the materials listed in Table 2.11 do not necessarily function as a base in all cases. Some of these materials may act as an acid if the reactants are strongly basic. The terms, acid and base, should be used according to the function. The materials may be called solid base catalysts only if acting as a base toward the reactants by abstraction of a proton (Bronsted base) or by donation of an electron pair (Lewis base) to form anionic intermediates that undergo catalytic cycles. 

The energy difference provided by MO calculations, with or without the inclusion of solvent, serves as a direct measure of the anomeric energy, AE(AE3), when its absolute definition by Eq. 4 is used. However, the more-frequent use of a relative definition by Gibbs energy difference in Eq. 1 warrant an attempt to recalculate the AE(AE3) data to the values AG(AE 1). Such a procedure is, of necessity, an approximation, because the assumption that AG° = AE(AE3) neglects the entropy and volume changes of conformers owing to absence of suitable information, and the cyclohexane-based and solvent-independent A values must be used. 

In addition to this absolute sense, Avicenna gives two further, relative definitions for continu-ity , namely contiguity, that is, when two bodies share a common boundary, in the sense that their surfaces are in contact and attachment, that is, when two bodies are attached to one another, either by adhesion or interconnection (Avicenna, Mantlq, II.III.4,116-117 Tabrfyydt, I.III.2,269-271 cf. Stone, Simplicius and Avicenna , 102). 

The preceding definitions of economic potential and total annual cost can be simplified if it is accepted that they will be used to compare the relative merits of difierent structural options in the flowsheet and difierent settings of the operating parameters. Thus items which will be common to the options being compared can be neglected. 

In the case of motor fuels, when the content of the material added is relatively high, we will use the term components of the mixture. Thus the ethers, used in the formulation of motor fuels in significant proportions, will not be Included in our definition. 

Reservoir fluids (oil, water, gas) and the rock matrix are contained under high temperatures and pressures they are compressed relative to their densities at standard temperature and pressure. Any reduction in pressure on the fluids or rock will result in an increase in the volume, according to the definition of compressibility. As discussed in Section 5.2, isothermal conditions are assumed in the reservoir. Isothermal compressibility is defined as ... 

Final state analysis is where dynamical methods of evolving states meet the concepts of stationary states. By their definition, final states are relatively long lived. Therefore experiment often selects a single stationary state or a statistical mixture of stationary states. Since END evolution includes the possibility of electronic excitations, we analyze reaction products in terms of rovibronic states. 

Asymmetry in a similarity measure is the result of asymmetrical weighing of a dissimilarity component - multiplication is commutative by definition, difference is not. By weighing a and h, one obtains asymmetric similarity measures, including the Tversky similarity measure c j aa 4- fih + c), where a and fi are user-defined constants. The Tversky measure can be regarded as a generalization of the Tanimoto and Dice similarity measures like them, it does not consider the absence matches d. A particular case is c(a + c), which measures the number of common features relative to all the features present in A, and gives zero weight to h. 

Two other atomic properties have been used in the definition of atom type, thereby increasing its fuzziness relative to that in the ap and tt descriptors - atomic log P contribution (yielding hydrophobic pairs, hps, and torsions, hts) and partial atomic charges (charge pairs, cps, and charge torsions, cts). 

The explicit definition of water molecules seems to be the best way to represent the bulk properties of the solvent correctly. If only a thin layer of explicitly defined solvent molecules is used (due to hmited computational resources), difficulties may rise to reproduce the bulk behavior of water, especially near the border with the vacuum. Even with the definition of a full solvent environment the results depend on the model used for this purpose. In the relative simple case of TIP3P and SPC, which are widely and successfully used, the atoms of the water molecule have fixed charges and fixed relative orientation. Even without internal motions and the charge polarization ability, TIP3P reproduces the bulk properties of water quite well. For a further discussion of other available solvent models, readers are referred to Chapter VII, Section 1.3.2 of the Handbook. Unfortunately, the more sophisticated the water models are (to reproduce the physical properties and thermodynamics of this outstanding solvent correctly), the more impractical they are for being used within molecular dynamics simulations. 

Furthermore, it is the system. Hydrate I/Hydrate II (or Anhydrous Salt), that possesses a definite pressure at a particular temperature this is independent of the relative amounts, but is dependent upon the nature of the two components in equilibrium. It is incorrect, therefore, to speak of the vapour pressure of a salt hydrate. ... 

The above definition implies that the reactivity of an aromatic compound depends upon the reaction which is used to measure it, for the rate of reaction of an aromatic compound relative to that for benzene varies from reaction to reaction (table 7.1). However, whilst a compoimd s reactivity can be given no unique value, different substitution reactions do generally set aromatic compoimds in the same sequence of relative reactivities. 

Streitwieser pointed out that the eorrelation whieh exists between relative rates of reaetion in deuterodeprotonation, nitration, and ehlorination, and equilibrium eonstants for protonation in hydrofluorie aeid amongst polynuelear hydroearbons (ef. 6.2.3) constitutes a relationship of the Hammett type. The standard reaetion is here the protonation equilibrium (for whieh p is unity by definition). For eon-venience he seleeted the i-position of naphthalene, rather than a position in benzene as the referenee position (for whieh o is zero by definition), and by this means was able to evaluate /) -values for the substitutions mentioned, and cr -values for positions in a number of hydroearbons. The p -values (for protonation equilibria, i for deuterodeprotonation, 0-47 for nitration, 0-26 and for ehlorination, 0-64) are taken to indieate how elosely the transition states of these reaetions resemble a cr-eomplex. 

The kinetic chain length has a slightly different definition in the presence of chain transfer. Instead of being simply the ratio Rp/R, it is redefined to be the rate of propagation relative to the rates of all other steps that compete with propagation specifically, termination and transfer (subscript tr) ... 

In a medium where the relative dielectric constant is e, the force between fixed chages at a definite separation is decreased by the dimensionless factor e. This is true regardless of the system of units and is incorporated into Eqs. (10.101) and (10.102) by dividing the right-hand side of each by e. ... 

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