Importance identity

One important question is that of the order in which the basic mechanisms of evolution processes, leading eventually to the emergence of life, occurred. As far as the development of the genetic code is concerned, it is not clear whether the code evolved prior to the aminoacylation process, i.e., whether aminoacyl-tRNA synthetases evolved before or after the code. A tRNA species which is aminoacy-lated by two different synthetases was studied if this tRNA had important identity elements such as the discriminator base and the three anticodon bases for the two synthetases, this would be evidence that the aminoacyl-tRNA synthetases had developed after the genetic code. Dieter Soil s group, which is experienced in working with this family of enzymes, came to the conclusion that the universal genetic code must have developed before the evolution of the aminoacylation system (Hohn et al, 2006). 

Integration of the operator of Eq. (10) over Xc and pc results in the following important identity ... 

Ansatzes (53)-(55) are given in explicitly covariant form. This fact enables us to perform symmetry reduction of Eqs. (46) in a unified way. First, we give without derivation three important identities for the tensor [35] ... 

Of particular interest in the present context is the entropy S = —(dA/dT)VytL, which can be shown to satisfy the important identity (see Sidebar 13.6)... 

The following important identity holds for any two operators A and B under the condition that, as in 3 above, both commute with their commutator ... 

The relationship between the potential of mean force and the free-energy surface as given in Eq. (108) leads to some important identities. The parabolic expansion for the potential of mean force is denoted... 

But the ratio of dy to dx means, in this instance, (dy/dx), since z was constrained to a constant value. Thus, we obtain the important identity... 

It is apt at this stage to redefine the modem safety management terms and definitions used in this book. There still exists confusion in the safety industry concerning the words accident and incident. The term incident is so widely used and misused that the term near miss has almost become obscure. Because near-miss incident recording is one of the main elements in a world s best practice (i.e., meeting the highest international safety standards) SMS, it s important that it be redefined and renamed so that its important identity can be maintained and recognized. 

The last expansion helps in proving the important identity 1... 

Density requirements may also be set by the mentioned Pharmacopoeias, for the relative density of a liquid or solution. For alcoholic solutions such a requirement may be useful to determine whether the correct quality and the correct volume of ethanol have been used in the preparation process. The same is true for other preparations of which the density deviates strongly from water, for example because of the presence of dissolved substances. Preparations that, for example, contain a high percentage of sorbitol or glycerol are well characterised by their density and a determination of the density actually becomes an important identity criterion. The requirements for the relative density are not strictly defined, because the nature and amotmts of the excipients may have a significant impact oti the density of a product. As guidance a precision of maximally three decimal places may be appropriate, with limits of 0.020 unless there is practical information available that requires wider or stricter limits. 

The important identity in Eq. (2.107) relates the energy density of the electromagnetic field with the currents flowing in the system and is sometimes denoted as Foynting s theorem. Inserting these results in Eq. (2.106) and taking the arbitrariness of the volume V into account, we find... 

Application of the Laplacian to a vector field A has to be understood as acting separately on each component. The result is then again a three-vector, of course. We note some important identities for the above vector operations. 

A mathematical identity is an equation that is valid for all values of the variables contained in the equation. There are several useful identities involving partial derivatives. Some of these are stated in Appendix B. An important identity is the cycle rule, which involves three variables such that each can be expressed as a differentiable function of the other two ... 

There exists an important identity between an extensive variable and the corresponding partial molar quantities. (The so called Euler s theorem )... 

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