Mutatis mutandis

The principles underlying this question are, mutatis mutandis, identical for all cases, so that as a typical illustration the case of the peppermint plant may be selected, as this has b en worked on by several independent investigators very exhaustively. 

Mutatis mutandis the same terminology is applied to the surface of p-type semiconductors. So if the bands bend upward, we speak of an enrichment layer if they bend downward, of a depletion layer. 

These activities may introduce many hazards, such as contaminants, materials of repair corrodible, combustible or catalytic in the given environment, blocked vents, open valves etc. into the restarted plant, while shutdown and startup are, in any event, the most dangerous periods. Many examples of reactive hazards thus introduced are to be found in [1], Mutatis mutandis, this is also true of the laboratory this Handbook contains many incidents consequent upon stopping a reaction and/or its agitation to sample, change cooling bath, etc. 

As mentioned before (see Section 11.1), the lifecycle of a specialty chemical lends itself for the identification of business opportunities. This is particularly the case for PFCs, but, mutatis mutandis, it also applies for agrochemicals and other target products. 

The key to get a diabatic electronic state is a strict constraint i.e. keep local symmetry elements invariant. For ethylene, let us start from the cis con-former case. The nuclear geometry of the attractor must be on the (y,z)-plane according to Fig.l. The reaction coordinate must be the dis-rotatory displacement. Due to the nature of the LCAO-MO model in quantum computing chemistry, the closed shell filling of the HOMO must change into a closed shell of the LUMO beyond 0=n/4. The symmetry of the diabatic wave function is hence respected. Mutatis mutandis, the trans conformer wave function before n/4 corresponds to a double filling of the LUMO beyond the n/4 point on fills the HOMO twice. At n/4 there is the diradical singlet and triplet base wavefunctions. 

This chapter focuses primarily on the influence of anion-anion repulsion and on the anion bonding strength. The other factors are described briefly in Section 6.4 but are developed in more detail in later chapters. The special case of is discussed in Chapter 7 and effects that depend on details of the electronic structure of the cation are treated in Chapter 8. The influence of space and symmetry are discussed in Part III. For simplicity, unless otherwise stated, the discussion is confined to compounds in which the anion is oxygen or an oxyanion. Any conclusions will be applicable, mutatis mutandis, to other kinds of anion. 

All of the results of Section 6.1 apply, mutatis mutandis, to irreducible Lie algebra representations. For example, if T is a homomorphism of Lie algebra representations, then the kernel of T and the image of T are both invariant subspaces. This leads to Schur s Lemma for Lie algebra representations. 

The proofs in Chapter 7 apply to Proposition 9.3 as well, mutatis mutandis. Fock uses a stereographic projechon from the three-sphere 5 to Euclidean... 

If the proof in section 2 is studied carefully, it will be seen that there is nothing in the derivation of this law which could not be applied mutatis mutandis to any kind of energy representable in the form mec2. For, apart from general considerations of probability, the only condition assumed in the proof was that the total kinetic energy could be expressed as a sum of three quadratic terms— equation 1 of section 2 multiplied by I/2m expresses this condition. 

It is important to note that, with the exception of the extraordinarily large aperture size requirement, the criteria for a fusion laser frequency convertor are generally applicable to any high power laser. Moreover, many of the ideas presented here are applicable, mutatis mutandis, to the search for NLO crystals for any specific application, for example, diode laser doubling. 

Nucleophilic and electrophilic catalysis occur when a nucleophile or electrophile reacts with the substrate to form an adduct which provides a more favourable alternative mechanism to that of the uncatalysed reaction. The intermediate can be formed as a transient species present in only a small concentration compared with the reactant or product, or it can build up to a measurable concentration. In this section, we exemplify the techniques used in their investigation using nucleophilic reactions. The same techniques can be used for reactions undergoing electrophilic catalysis, mutatis mutandis. 

Unsaturated molecules/ions other than hydrocarbons and their simplest derivatives can function as ligands, using their n bonding and antibonding MOs in the manner (mutatis mutandis) described above for ethylene. C02, R2CO, CS2 and SOz provide examples ... 

These methods are, mutatis mutandis, applicable to the formation of E-H and E-X (X = halogen) bonds in compounds other than binary hydrides and halides. 

Lastly, let us mention that the integral equation method applies mutatis mutandis to the case of multiple cavities (i.e. to the case when C has several connected components). This situation is encountered when studying chemical reactions in solution. 

Of course, the (3S)-compounds would also be formed if D-valine would be employed as chiral auxiliary. Hence, this method with valine as chiral auxiliary reagent solves the problem of enantioselective synthesis of a-methyl amino acids satisfactorily. Probably it can also be used — mutatis mutandis — for the asymmetric synthesis of a variety of a-alkyl amino acids, provided, the corresponding bis-lactim ether (type I) with valine as C-6 is regiospecifically metallated by butyl-lithium. This, for instance, is not be case with the mixed bis-lactim ether (20c) of cyclo(L-Leu-D,L-Ala)17). 

The living organism has already been compared with a crystal, and the comparison is, mutatis mutandis, justifiable. 

Gibbs s analytical proof of the adsorption formula is, mutatis mutandis, analogous to the analytical deduction of the Gibbs-Duhem relation both depend on the integration of the formula for the increment in energy, followed by differentiation and comparison of the result with the original formula. 

The first unipolar transistor was a JFET the layout of an n-channel JFET is given in Fig. 9.31. The mechanism of function is similar to the MOSFET The n-channel is narrowed by the electric field applied to the gate and the body. The operational characteristics, mutatis mutandis, resemble those of the MOSFET discussed above. 

This organizational point is of utmost importance and should be examined a little more closely, for the relevant considerations apply mutatis mutandis for all the various versions of the massacre. 

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