Process formalisms

From the calculus, the limit process formally gives... 

Bearman, Kirkwood, Fixman). Transport Processes, Formal Statistical Theory of 1 1... 

The first chair of theoretical physics in France was the professorship established for Pierre Duhem in 1894 at the Bordeaux Faculty of Sciences. 1 Duhem was well known in French scientific circles not only as a physicist but as a physicist of exceptional mathematical skills who addressed himself early in his scientific studies to chemical problems. He wrote a controversial doctoral thesis (1886) in which he developed the concept of thermodynamic potential for chemistry and physics, and he later developed a treatment of equilibrium processes formally analogous to the mechanics of Lagrange. The goal was to make mechanics a branch of the more general science of thermodynamics, a science that embraces "every change of qualities, properties, physical state, chemical constitution. "2... 

Treatment of a-cyclopropyl acyl silanes with sulphuric or triflic acids results in rearrangements to give cyclobutanones and 2-silyl-4,5-dihydrofurans, respectively, in processes formally involving intramolecular nucleophilic attack at the acyl silane moiety (Scheme 80)190. 

Some /J-heteroatom substituted a,/J-unsaturated acyl silanes react with methyl ketone enolates in a stepwise stereoselective cyclopentannelation process, formally a [3 + 2] annelation, which may proceed through aldol reaction followed by Brook rearrangement and cyclization (Scheme 111)223. 

Operational qualification is the step in a validation process that will ensure the reproducibility and acceptability of the packaging process. Formally, it is an investigation of the control of variables in any given individual piece of equipment or in a given subprocess. In this way it is possible to verify that the sequencing of events is in the proper order and that the process equipment is operating consistently within the design limits. 

The final stage of this investigation was to study the reaction of the hydroxy dimer 7 with phenylboronic acid to test whether 7 is able to undergo efficient phenylation. The reaction with PhB(OH)2 was found to proceed smoothly and, when conducted in the presence of PPh3, gave the stable four-coordinate complex 4 which had already been characterised, Scheme 12.4. As 4 was already known to be effective as a pro-catalyst (see above), this process formally closed the circle to constitute a very convincing and conclusive collection of experiments. 

The pentamer of tetrafluoroethene (66) (Scheme 29) is an unusual example of type (96) and reacts readily with nucleophiles [129] (Scheme 65). In contrast, (66) undergoes a remarkable reaction with aqueous triethylamine, producing the dihydrofuran derivative (101) and the process formally involves a direct intramolecular displacement of fluorine from a saturated site and a mechanism has been advanced (Scheme 66) which accounts for the product formed [126]. Understandably, this process is not easily accepted [3, 130] because it has essentially no precedent. Indeed, it is well established that nucleophilic displacement from saturated sites in fluorocarbons occurs only in exceptional circumstances. Consequently, other mechanisms have been advanced, which seem no more convincing [3, 130]. It should be remembered that the major point in favour of the step (100) to (101) (Scheme 66) is that the nucleophile is generated in close proximity to the reaction centre because of the special geometry of this situation. Consequently, much of the otherwise high energy/entropy barrier has already been overcome in this case. 

CT transitions occur in Mo(IV) oxo-molybdenum-bis(dithiolene) complexes since the dxy acceptor orbital is completely filled. Therefore, it has been proposed that a thermally induced intramolecular electron/charge transfer (valence tautomeric) process is operable in [MovO(qdt)2J1 and responsible for the observed thermochromism. Such a S —> Mo dXi CT process formally results in the conversion of [Mo 0(qdt)2] to the Mo(IV) species LMoIV0(qdt Kqdt) 1 (Fig. 46), which is consistent with the attenuation of both the S —> Mo dxy CT and the dianionic qdt n —> n bands. 

The latter compounds are prone to an intramolecular nitroaldol (Henry) reaction, yielding nitrocyclohexanola (53) in less than 1 h. The formation of (53) can be easily observed by thin-layer chromatography (TLC), thus treatment of (53) with 4N hydrochloric acid favors the elimination of both water and a further molecule of nitrous acid, allowing the one-pot synthesis of target molecules (54) in 42-77% overall yields. It is important to note that this one-pot process formally includes five different transformations (i) Michael addition, (ii) nitrous acid elimination, (iii) intramolecular nitroaldol reaction, (iv) water elimination, and (v) elimination of a further molecule of nitrous acid. 

The restrictions associated with four-coordinate complexes are reversed when the band of d orbitals is filled with metal valence electrons (e.g., d systems). In these situations, ligand field restrictions are encountered from the tetrahedral complex and not the square planar. This departure from the quaUtative picture based on pure d orbitals is primarily due to hybridization factors in these systems. The square planar complex requires an empty d orbital (in the plane) to construct the four hybrid orbitals in the square plane. The [2-f2] transformation from the square planar complex thus returns two valence electrons (formally from a p orbital) to this orbital generating a filled d band in the process. The process proceeds without an orbital crossing. The tetrahedral system, in contrast, starts with a filled d band. The [2- -2] process formally moves a pair of d electrons into a p orbital. This process thus involves an orbital crossing and therefore encounters ligand field restrictions. 

This process, formally related to the Diels Alder reaction, may also proceed by various mechanisms (Scheme 6.257)1421 1443 similar to those of [2 + 2] cycloaddition (Scheme 6.251), such as a concerted process or formation of charge-transfer (exciplex, 532), biradical (533), zwitterion (534) or perepoxide (535) intermediates. A concerted pathway1444 and exciplex1445 intermediacy was proposed to be involved in most cases. The [4 + 2] photooxygenation may be accompanied by other related processes (e.g. [2 + 2]). 

The second major modification was developed by Mukaiyama and coworkers (4) and Hosomi and Sakurai (5). These workers found that weakly nucleophilic silyl enol ethers and allylsilanes add to a,/ -unsaturated ketones that have been precomplexed with a Lewis acid. This process formally mimics the protic-acid-catalyzed Michael addition but allows for regiocontrol over enol generation. 

The equation above is equivalent in format to Eqn 13-27. But in general it cannot be expected that the slider will remain in a configuration which l eeps I constant throughout the course of the wear process. Formal differentiation of Eqn 13-36 gives... 

Investigation Processes Formal investigations (root cause analysis as warranted) Communication of causes and corrective actions Follow-up actions for verification that corrective actions were implemented... 

Fig. 2 illustrates correspondence between the requirements and verification assessment criteria. As a result under A SW verification assessment the fulfillment of all requirements mentioned above must be checked. The model base for the verification assessment process formalization is [9] ... 

We have hypothesized that the second electrochemical process formally refers to NO° reduction. It seems to be more convenient to attribute the second reduction process in the CV of ds/tra 5-[Ru(bpy)2L(NO)] complexes as delocalized charge, which should be more representative for a system with different contributions from an L spectator Hgand and a nitrogen oxide ligand. 

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