Alternative definitions

The avadabihty of multiple pH(5) reference solutions makes possible an alternative definition of pH( ... 

It was agreed at the workshop that endocrine disrupting activity could only be adequately defined in terms of effects in intact animals, be they juvenile or adult, or in the offspring of exposed parents. For many chemicals, evidence of endocrine disrupting activity has been obtained only by the use of in vitro models, such as hormone binding assays. It was accepted, therefore, that chemicals active in such models should be considered only as potential EDs and should be distinguished from those established as active in vivo. For such chemicals, an alternative definition was recommended ... 

An alternative definition of the cost function was proposed by Huo and Straub [35] based on an earlier suggestion of Berkowitz et al. [42],... 

The dietionary defines culture as The totality of soeially transmitted behavior patterns, arts, beliefs, institutions, and all other produets of human work and thought typieal of a population or eommunity at a given time. An alternative definition is The aet of developing the soeial, moral, and intelleetual faeilities through edueation [3]. 

This appendix contains a glossary of nearly 200 common and uncommon terms and phrases used in ISO/TS 16949 and the Rules for Achieving lATF Recognition. It contains many terms and phrases not defined in ISO 8402 or ANSI/ASQC A3. Some alternative definitions are provided for clarification. The explanations are given for the context in which the terms are used. 

Human Error Probability The probability that an error will occur during the performance of a particular job or task within a defined time period. Alternative definition The probability that the human operator will fail to provide the required system function within the required time. 

This approach to separating the different types of interaetions eontributing to a net solvent effeet has elieited much interest. Tests of the tt, a, and p seales on other solvatochromie or related proeesses have been made, an alternative tt seale based on ehemieally different solvatochromie dyes has been proposed, and the contribution of solvent polarizability to ir has been studied. Opinion is not unanimous, however, that the Kamlet-Taft system eonstitutes the best or ultimate extrathermodynamie approaeh to the study of solvent effeets. There are two objections One of these is to the averaging process by which many model phenomena are eombined to yield a single best-fit value. We eneountered this problem in Section 7.2 when we eonsidered alternative definitions of the Hammett substituent eonstant, and similar eomments apply here Reiehardt has diseussed this in the eontext of the Kamlet-Taft parameters. - The seeond objeetion is to the elaim of generality for the parameters and the eorrelation equation we will return to this eontroversy later. 

The equivalent weight of an ion (or an element) is the ratio of its formula weight to its valence. According to an alternative definition that is also suitable for compounds, an equivalent weight represents the amount of a substance which will react with one atomic weight of hydrogen or its chemical equivalent. 

A random process can be (and often is) defined in terms of the random variable terminology introduced in Section 3.8. We include this alternate definition for completeness. Limiting ourselves to a single time function X( ), it is seen that X(t) is completely specified as a random process by the specification all possible finite-order joint distribution functions of the infinite set of random variables T, — oo < t < oo, defined by the equations... 

Before discussing such theories, it is appropriate to refer to features of the reaction rate coefficient, k. As pointed out in Sect. 3, this may be a compound term containing contributions from both nucleation and growth processes. Furthermore, alternative definitions may be possible, illustrated, for example, by reference to the power law a1/n = kt or a = k tn so that k = A exp(-E/RT) or k = n nAn exp(—nE/RT). Measured magnitudes of A and E will depend, therefore, on the form of rate expression used to find k. However, provided k values are expressed in the same units, the magnitude of the measured value of E is relatively insensitive to the particular rate expression used to determine those rate coefficients. In the integral forms of equations listed in Table 5, units are all (time) 1. Alternative definitions of the type... 

An alternative definition of the Griineisen parameter is in terms of thermodynamic properties [87]... 

We will also use an alternative definition of stability of a scheme with respect to the right-hand side ... 

Before proceeding further it is well to consider the term cement, for its definition can be the source of some confusion. Both the Oxford English Dictionary and Webster give two alternative definitions. One defines a cement as a paste, prepared by mixing a powder with water, that sets to a hard mass. In the other a cement is described as a bonding agent. These two definitions are quite different. The first leads to a classification of cements in terms of the setting process, while the second lays emphasis on a property. In this book the term cement follows the sense of the first of these definitions. 

For a linear plan the pseudo-overall yield as defined above is numerically close to the multiplicative product of the reaction yields. The difference between the two values diminishes as the reaction yields approach 1 as would be expected. However, for complex plans with several converging branches this alternative definition becomes less useful. For the triclosan branch equation (4.16) yields 0.405 (40.5%) for the pseudo-overall yield. 

For the sake of completeness we mention here an alternative definition of eigenvalue decomposition in terms of a constrained maximization problem which can be solved by the method of Lagrange multipliers ... 

An alternative definition, but equally useful, of the associated Legendre polynomials is of die form... 

An alternative definition involves the use of a generating function. This method is especially convenient for the evaluation of certain integrals of the Hermite polynomials and can be applied to other polynomials as well. For the Hermite polynomials the generating function can be written as... 

We would be remiss if we did not indicate that some authors have defined yet another Thiele-type modulus ( ) for this problem as <. = 0s/3 and they have developed their analysis according to this parameter. In using plots of f] versus S9 one must be careful to determine which of the two alternative definitions has been adopted for s. Otherwise his value for rj may be considerably in error. A variety of other symbols for dimensionless groups akin to the Thiele modulus have been employed by different authors. 

Using our results concerning consistent paths, we can given alternative definitions of free schemes. 

There are alternative definitions of "weak translatability". The following definition is rather "strong". "Weaker" versions cunit condition (3). 

That branch of chemistry which deals with the compounds of the element carbon the simpler carbon-containing compounds (such as calcium carbonate) are usually classed with inorganic chemistry and an alternative definition of organic chemistry is the chemistry of the hydrocarbons and their compounds. 

These definitions are interpreted as follows environment atoms recognize the average weighted states of the ligands each ligand recognizes only the environment atoms and itself with the full scale for estimation of its effective Bom radius. Alternate definitions of the electrostatic solvation energy and the effective Bom radius at the intermediate states are also possible.81... 

A The amount of solute in the concentrated solution doesn t change when the solution is diluted. We take advantage of an alternate definition of molarity to answer the question millimoles of solute/milliliter of solution. 

Equation (5.86c), written as a strict equality, may also be taken to define the NRT transition state as an alternative to (and slightly different from) the usual definitions based on energetic, saddle-point-curvature, or density-of-states criteria. Note that this NRT alternative definition can be employed for non-IRC choices of reaction coordinate, and remains valid even in the case of barrierless processes (such as many ion-molecule or radical-recombination reactions) for which the reaction profile does not exhibit an energy maximum as in Fig. 5.52. The NRT definition is practically identical to the usual saddle-point definition of the transition state in the present examples. 

Equation 24.14 provides an alternative definition of the electronic responses they are derivatives of the energy s relative to the field E. Note that the response of order n, the nth derivative of the response to the perturbation, is the n + 1th derivative of the energy relative to the same perturbation. Hence, the linear response a t is a second derivative of the energy. Because the potential (E) and the density (p) are uniquely related to each other, the field can be formulated as a function of the dipole moment p. The expansion of the field in function of p can be obtained from Equation 24.12 which can be easily inverted to give... 

In the same year, Lewis proposed an alternative definition According to Lewis, an acid is ary species that can accept a pair of electrons because of the presence of an incomplete electronic grouping. Hence, a Lewis base is any species that possesses a nonbonding electron pair that can the donated to form a coordination or dative bond. The Lewis acid-base interaction is given by... 

Alternative definitions lack the (— l)m term. P,(x) is therefore a concise expression for P,°(x). Note that, because of the derivative term in equation (2.6.14), if m > l, P,m(x) = 0. Advanced calculus would show orthogonality properties with... 

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