Second definition

In order to define how the nuclei move as a reaction progresses from reactants to transition structure to products, one must choose a definition of how a reaction occurs. There are two such definitions in common use. One definition is the minimum energy path (MEP), which defines a reaction coordinate in which the absolute minimum amount of energy is necessary to reach each point on the coordinate. A second definition is a dynamical description of how molecules undergo intramolecular vibrational redistribution until the vibrational motion occurs in a direction that leads to a reaction. The MEP definition is an intuitive description of the reaction steps. The dynamical description more closely describes the true behavior molecules as seen with femtosecond spectroscopy. 

To convert the words of the second definition of risk into mathematics, let chance" be probability, "loss" be consequences, and... 

The second definition is a conceptual definition. It defines the class in terms of an explanation of why the class has its properties. To see the difference—and the relative merit—of the two kinds of definition, let us consider an analogy. 

The second definition might be called a conceptual definition. It offers an explanation of why the athlete enjoys special success in his sport. It is one step removed from things that show on the scoreboard. 

In Chapter H, we introduce a second definition of acids and bases, the Lewis definition, which focuses attention on electron movement rather than proton movement Until then, acid-base always means proton transfer."... 

Following the first definition, a space-time yield of 0.781 h m using a OAOR-modified silver is obtained, which exceeds the industrial performance considerably (0.13-0.26 t h m ) [4]. Following the second definition and hence orienting more on outer than on inner dimensions, a space-time yield of 0.13 t h m is obtained, still within the industrial window. 

This second definition explains why autoignition appears after a certain time and that according to the set period of time there can be a different ATT for the same substance. 

The above definition of the enthalpic effects of conjugation is not unique. A second definition decouples the two double bonds by an alternative hydrogenation process (equation 19). 

The term race primarily means an ethnical stock a great division of mankind having in common certain distinguishing physical peculiarities, and thus constituting a comprehensive class appearing to be derived from a distinct primitive source. A second definition is a tribal or national stock a division or subdivision of one of the great racial stocks of mankind, distinguished by minor peculiarities. The word race connotes descent.23... 

In the above arrangement, "Also known as. . applies only to the first definition "Symbolized. . applies only to the second definition. 

This critical position of equilibrium can be defined in two fundamentally different ways. The first is that the system A-B with composition xo has reached an equilibrium where its Gibbs energy is at a minimum. The second definition is that phases ai and Q2 with compositions x and x are in equilibrium because the chemical potentials of A and B are equal in both phases. The importance of these two definitions becomes clearer if we consider how it would be possible to write a computer programme to find x and xf. ... 

The second definition of the purpose of a carrier was to remove the overburden of material above a surface above the device plane. For present purposes, we define the device level as the boundary between the material one wishes to remove and the material one wants to keep. It is not necessarily planar, and it moves up with each layer. For oxide CMP, this layer lies within the topmost film layer. For metal CMP, this surface is defined by the topmost surface of the dielectric into which lines and vias are etched for a damascene process. This definition must accommodate a wafer with a modest amount of bow, tilt, warp, and total thickness variation. Furthermore, it must accommodate very modest amounts of bow, warp, tilt. 

Well, the second definition is the correct one. The first definition is not only incorrect, it is also the common mistake that many people make. We will explore later in Section 9.3.1 why this definition causes so many problems and misunderstandings. For the moment, however, we will explore in more detail the correct definition. It is worthwhile expanding on the various components of the definition ... 

Freezing point is the temperature at which, a liquid or solution solidifies. It is the temperature at which the liquid and solid states of a substance are in equilibrium at a given pressure (usually atmospheric). The second definition may be applied to Melting (or Freezing) Point, which may also be defined as the temperature at which a solid changes to a liquid. For pure crystalline substances, mp is usually identical with ft p, while for many mixtures, they are not identical. For example, fats and waxes do not solidify until they have been cooled several degrees below their, mp s. 

This supplies a second definition of surface tension It equals the work per unit area required to produce a new surface. In terms of this definition, the units of 7 are energy per area — J m 2 in SI or erg cm"2 in the cgs system. 

This is precisely the same as the force that a unit positive charge would experience at the same location. Since force is the negative gradient of the potential, Equation (7) also supplies a second definition of field ... 

The first definition of the word has a more scientific ring to it than the second, the second being related to some extent to the rather more nebulous concept of beauty, for example John Bulwer wrote in 1650 True and native beauty consists in the just composure and symetrie of the parts of the body .f It is nonetheless interesting that when we go deeper into the scientific meaning of symmetry we find that the underlying mathematics involved has itself a beauty and elegance which could well be described by the second definition. 

The Michaelis constant, KM, for an enzyme-substrate interaction has two meanings (1) Ku is the substrate concentration that leads to an initial reaction velocity of V" /2 or, in other words, the substrate concentration that results in the filling of one-half of the enzyme active sites, and (2) KM = (k2 + ki)/kv The second definition of Ku has special significance in certain... 

As cell solution for this example one uses, in two different experiments, the unknown solution (x) and a standard buffer solution (s), whose pH (pH ) has been estimated so as to approach the second definition. Comparing the e.m.f. s gives... 

With this definition a reproducible number will always result. On the other hand the pHx so obtained does not correspond exactly to the second definition since it contains the uncertainty in the definition of yH and in addition an unknown difference in the liquid junction potential which may be important, especially if the solution is not very dilute. If similar solutions are compared, however, differences in pH may give accurate ratios between H+ activities or concentrations. 

It should be noted that U differs from the usual definition of the Hubbard XJ, involving the lowest multiplet in each -configuration f/ n = E mn(n + 1) + Elmn(n — 1) — 2 mm(w). This second definition is inconvenient here, since it depends wildly on n. 

In applied molecular evolution, fitness generally has one of two meanings (i) It can refer specifically to how well a molecule performs a desired function, typically the affinity of a ligand for a given receptor or its catalytic activity for a given reaction, (ii) It can refer to the rate at which a molecule in a population of molecules is copied over one iteration, similar to the notion of enrichment in die molecular diversity literature. This second definition is more complex, as fitness depends not only on the properties of a molecule but also on the properties of the rest of the population. Since fitness then changes each iteration as the population changes, the whole fitness landscape metaphor is weakened. For these reasons, I will restrict myself to the first definition of fitness. 

This second definition is useful when ion and electron movement is involved in chemical reactions. Chemical reactions involving ionic compounds are best interpreted by this definition. Consider the attack of dilute hydrochloric acid on metallic zinc. The zinc dissolves and forms zinc chloride solution and the hydrogen gas fizzes off ... 

Because there is no oxygen involved in this reaction, it is difficult to see what is happening to the zinc. The second definition is more helpful in interpreting this reaction. Looking at the ions present ... 

The second definition we wish to introduce is the number average length of A (and B) runs. This is simply defined in Equation 6-37. 

This second definition of theta point is used to describe a solvent. In a solvent where Xi < 1/2, we have a better than theta solvent conditions with a second virial coefficient B2, which is positive. In a solvent where Xi > 1/2 we have less than theta solvent conditions with a second virial coefficient B2, which is negative. 

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