Definitions differences

We must now mention, that traditionally it is the custom, especially in chemo-metrics, for outliers to have a different definition, and even a different interpretation. Suppose that we have a fc-dimensional characteristic vector, i.e., k different molecular descriptors are used. If we imagine a fe-dimensional hyperspace, then the dataset objects will find different places. Some of them will tend to group together, while others will be allocated to more remote regions. One can by convention define a margin beyond which there starts the realm of strong outliers. "Moderate outliers stay near this margin. 

Solubilisation is usually treated in terms of the pseudophase model, in which the bulk aqueous phase is regarded as one phase and tire micellar pseudophase as another. This allows the affinity of the solubilisate for the micelle to be quantified by a partition coefficient P. Different definitions of P can be found in the literature, differing in their description of the micellar phase. Frequently P is... 

The next step in the development of a model is to postulate a perfect network. By definition, a perfect network has no free chain ends. An actual network will contain dangling ends, but it is easier to begin with the perfect case and subsequently correct it to a more realistic picture. We define v as the number of subchains contained in this perfect network, a subchain being the portion of chain between the crosslink points. The molecular weight and degree of polymerization of the chain between crosslinks are defined to be Mj, and n, respectively. Note that these same symbols were used in the last chapter with different definitions. 

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) ... 

However, several different definitions are also in current use ... 

In the previous seetion a study was eited in whieh DOE agreed that safety eulture at some of its faeilities needed to improve. The DOE is not alone in its efforts to improve safety eulture. Private industry is also entering a movement to improve safety eulture. Safety eulture is being mentioned more often, and in mixed eireles. However, safety eulture is rarely defined. In an effort to deseribe what safety eulture is, let s look at some different definitions. 

Local ventilation is used to diminish or, preferably, to prevent exposure to contaminants (including heat). This includes protection of persons, products, or animals from hazardous and/or nuisance contaminants. This task is not specific for local ventilation and different definitions exist. One is the following ... 

There are several different definitions relating to second moments in the literature, and it is necessary to take care when applying seemingly simple formulae that involve such quantities. Not only that, authors often use the same name for the different definitions. 

The expressions in Eq. 1 and Eq. 6 are two different definitions of entropy. The first was established by considerations of the behavior of bulk matter and the second by statistical analysis of molecular behavior. To verify that the two definitions are essentially the same we need to show that the entropy changes predicted by Eq. 6 are the same as those deduced from Eq. 1. To do so, we will show that the Boltzmann formula predicts the correct form of the volume dependence of the entropy of an ideal gas (Eq. 3a). More detailed calculations show that the two definitions are consistent with each other in every respect. In the process of developing these ideas, we shall also deepen our understanding of what we mean by disorder. ... 

However, these investigations also point out that we need a proper definition of space-time yields for micro reactors. This refers to defining what essentially the reaction volume of a micro reactor is. Here, different definitions lead to varying values of the respective space-time yields. Following another definition of this parameter for ethylene oxide formation, a value of only 0.13 t h m is obtained -still within the industrial window [159, 162, 163]. 

Formulae (21) and (26) use different definitions of the composition unit N, but, actually, these two approaches are the same. In fact, when a phase is crystalline. Equation (26) combined with Equation (24) gives [52] ... 

It should be mentioned here that a different definition of the diffusion coefficient is often used in chemical engineering problems, which is more appropriate for the description of reactant or tracer transport. It takes into account the fact that the total fluid contained in a porous substance of porosity e is reduced by this factor relative to the bulk, so that an effective diffusion coefficient D of the reactants is defined such that... 

Yield is a measure of the performance of a reactor or plant. Several different definitions of yield are used, and it is important to state clearly the basis of any yield figures. This is often not done when yield figures are quoted in the literature, and the judgement has to be used to decide what was intended. 

Because of this formation, a different definition of the enthalpy must be introduced for the interphase, differing from the usual expression for a homogeneous phase ... 

Proportional gain, integral and derivative time constants to PI and PID controllers. Different settings for load and set point changes. Different settings for different definitions of the error integral. The minimum ITAE criterion provides the least oscillatory response. 

As V is a unitary matrix, Y = VTX is just an equivalent set of Cartesian coordinates, and = UTZ is just an equivalent set of internal coordinates, simply linear combinations of the Zn. The i, , N-6, change independently, in proportion to changes in linear combinations of the Cartesian coordinates. So, locally, we have defined 3N — 6 independent internal coordinates. Every different configuration of the molecule, X, will have a different B matrix, and hence a different definition of local internal coordinates, defined automatically. 

In the literature slightly different definitions of the multipole expansion are found, depending on how the pre-factor (2( — l)/2 is distributed between expansion equation and the definition of die coefficients. Cf. (Ward [251], eq. 5.2)... 

Physical Properties. To determine or calculate particle size, it is important to be aware of the following different definitions and related properties (Geldart and Abrahamsen, 1981 Allen, 1975). 

A definition of Chemometrics is a little trickier of come by. The term was originally coined by Kowalski, but nowadays many Chemometricians use the definition by Massart [4], On the other hand, one compilation presents nine different definitions for Chemometrics [5, 6] (including What Chemometricians do , a definition that apparently was suggested only HALF humorously ). But our goal here is not to get into the argument over the definition of the term, so for our current purposes, it is convenient to consider a perhaps somewhat simplified definition of Chemometrics as meaning multivariate methods of data analysis applied to data of chemical interest . 

For a surface 5 the variety D2(S) is considered in the literature (using a slightly different definition). It is called the variety of second order data on S and denoted... 

Many different definitions of sustainability have evolved over the past decades (Pretty 2007). Despite this ambiguity, Klauer (1999) for instance stated that common ground of all definitions of sustainability is the preservation of a system... 

The impact of the root to shoot ratios on calculated maintenance requirements is important because root to shoot ratios are highly variable and almost always underestimate below-ground biomass. Amos and Walters (2006) reported that the net below-ground C deposition in com at physiological maturity was 29% 13% of the shoot biomass (leaves, stems, and husks) in 41 studies. The use of these values is further complicated by the use of different definitions for root to shoot ratio. Converting Amos and Walters (2006) units to units used by Johnson et al. (2006) would reduce the reported values from 0.29 to 0.15 (harvest index 50%). 

Denser-than-air puff or plume Britter and McQuaid use the ratio of the source duration to the travel time to distinguish between plumes and puffs with a slightly different definition of travel time tt = xe/(0.4ur). The release can be considered a plume if ts > tt, where ts is the source time scale defined above, and the release can be considered a puff if ts < tJ4. For tt/4 plume models are entirely appropriate the predicted concentration is considered the largest of the puff and plume predictions. 

Stating a definition of safety is often overlooked in safety research, and the concept of safety is not as obvious as it may seem, often being associated merely with the absence of risk. Literature contains many different definitions of risk (see for different examples of definitions Adams (Adams, 1995) Lees (Lees, 1996), IEC 61508 (IEC 61508, 2000)). The IEC (IEC 61508, 2000), defines risk as a combination of the probability of an occurrence of harm and the severity of this harm. Harm is... 

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