Postulates, definition

No direct evidence has yet been obtained to support this hypothesis, but on the other hand no evidence Is known that Is contrary to the above postulate. Definitive evidence Is clearly needed. 

At first, the dimeric nature of the base isolated from 3-ethyl-2-methyl-4-phenylthiazolium was postulated via a chemical route. Indeed the adduct of ICH, on a similar 2-ethylidene base is a 2-isopropylthiazolium salt in the case of methylene base it is an anilinovinyl compound identified by its absorption spectrum and chemical reactivity (45-47). This dimeric structure of the molecule has been definitively established by its NMR spectrum. It is very similar to the base issued from 2.3-dimethyl-benzo thiazolium (48). It corresponds to 2-(3 -ethyl-4 -phenyl-2 -methylenethiazolinilydene)2-methyl-3-ethyl-4-phenylthiazoline (13). There is only one methyl signal (62 = 2.59), and two series of signals (63= 1.36-3.90, 63= 1.12-3.78) correspond to ethyl groups. Three protons attributed to positions T,5,5 are shifted to a lower field 5.93, 6.58, and 8.36 ppm. The bulk of the ten phenyl protons is at 7.3 ppm (Scheme 22). 

The next step in the development of a model is to postulate a perfect network. By definition, a perfect network has no free chain ends. An actual network will contain dangling ends, but it is easier to begin with the perfect case and subsequently correct it to a more realistic picture. We define v as the number of subchains contained in this perfect network, a subchain being the portion of chain between the crosslink points. The molecular weight and degree of polymerization of the chain between crosslinks are defined to be Mj, and n, respectively. Note that these same symbols were used in the last chapter with different definitions. 

No definitive evidence has appeared that identifies the source of the color generated duriag thermooxidatioa (95). However, two laboratories have postulated that the reactioas leading to the formation of the color chromophores are aldol-type reactioas, either via the reactioa of aldehydes direedy (96)... 

The polyions postulated in solution all have known structural analogues in crystalline borate salts. Investigations of the Raman (66) and B nmr (67) spectra of borate solutions have confirmed the presence of three of these species the triborate (3), B202(0H) 4, tetraborate (4), [B40 (0H) 4], and pentaborate (5) B O (OH) 4, polyanions. Skeletal stmctures were assigned based on coincidences between the solution spectra and those soHd borates for which definitive stmctural data are available (52). These same ions have been postulated to be present in alkah metal borate glasses as well. 

Five oxidation states of At have been definitely established (-1, 0, +1, V, VII) and one other (III) has been postulated. The standard oxidation potentials connecting these states in 0.1 M acid solution are E°fV) ... 

Other postulates required to complete the definition of will not be listed here they are concerned with the existence of a basis set of vectors and we shall discuss that question in some detail in the next section. For the present we may summarize the above defining properties of Hilbert space by saying that it is a linear space with a complex-valued scalar product. 

The importance of twinned crystals in demonstrating that nucleation is the relevant growth mechanism has been realized since 1949 [64, 99]6. They were first investigated extensively in polymer crystals by Blundell and Keller [82] and they have recently received increased attention as a means of establishing, or otherwise, the nucleation postulate for lamellar growth [90, 91, 95,100-102]. The diversity of opinion in the literature shows that it is very difficult to draw definite conclusions from the experimental evidence, and the calculations are often founded upon implicit assumptions which may or may not be justified. We therefore restrict our discussion to an introduction to the problem, the complicating features which make any a priori assumptions difficult, and the remaining information which may be fairly confidently deduced. 

Generally speaking, the investigator carries out such simulations to show whether the postulated scheme matches the data. To carry out the simulations, the researcher fixes the rate constants of some steps at their established values and evaluates the ones that are unknown by iterative adjustment, the criterion being the quality of the match. Obviously, one is not likely to produce a definitive answer if too many steps have rate constants that are allowed to be adjusted at will. One may also be tempted to adjust one (more ) of the supposedly established rate constants. This action is perilous, without independent cause for suspicion. In that event, one should very seriously consider replicating the original experiments that defined that step. Not to do so invites the construction of an unsound house of cards. ... 

These new statistical procedures permit reexamination of a number of reaction series to reach more definite conclusions than formerly concerning the occurrence, accuracy, and significance of isokinetic relationships and possible values of the isokinetic temperatures. In this section, the consequences of these findings will be discussed and confronted with theoretical postulates or predictions. 

Combustion has a very long history. From antiquity up to the middle ages, fire along with earth, water, and air was considered to be one of the four basic elements in the universe. However, with the work of Antoine Lavoisier, one of the initiators of the Chemical Revolution and discoverer of the Law of Conservation of Mass (1785), its importance was reduced. In 1775-1777, Lavoisier was the first to postulate that the key to combustion was oxygen. He realized that the newly isolated constituent of air (Joseph Priestley in England and Carl Scheele in Sweden, 1772-1774) was an element he then named it and formulated a new definition of combustion, as the process of chemical reactions with oxygen. In precise, quantitative experiments he laid the foundations for the new theory, which gained wide acceptance over a relatively short period. 

A possible role for shape resonances has been postulated in a number of the photoionization studies mentioned above [52, 53, 57, 60], although it has to be noted that except for camphor [57], the evidence for the existence of the shape resonance is not definitive. (It also then remains an open question how any such resonances, inferred from fixed geometry calculations, would manifest themselves in practice in large, and sometimes floppy, molecules, such as these chiral species.)... 

The textbook definition of a reactive intermediate is a short-lived, high-energy, highly reactive molecule that determines the outcome of a chemical reaction. Well-known examples are radicals and carbenes such species cannot be isolated in general, but are usually postulated as part of a reaction mechanism, and evidence for their existence is usually indirect. In thermal reactivity, for example, the Wheland intermediate (Scheme 9.1) is a key intermediate in aromatic substitution. 

In the course of the tempestuous development of organophosphorus chemistry, interest has only recently been focused on compounds of formally quinquevalent phosphorus having coordination number 3, such as 1, 2, or 3, although one of the other species of this kind has long been postulated as reactive intermediate of solvolysis of phosphorylation reactions. Definite evidence of even proof of the existence of such coordinatively unsaturated phosphorus compounds, however, has been obtained only recently in mechanistic studies, by trapping reactions with suitable cycloaddends, or actually by direct isolation. 

Clearly, mechanistic investigations can provide circumstantial evidence for the participation of particular intermediates in a reaction but, here, we are concerned with the definitive observation of these species. If the intermediates are relatively stable then direct spectroscopic observation of the species during a room-temperature reaction may be possible As a rather extreme example of this, the zero-valent manganese radicals, Mn(CO>3L2 (L phosphine) can be photochemically generated from Mh2(CO)gL2, and, in the absence of O2 or other radical scavengers, are stable in hydrocarbon solution for several weeks (2, 3) However, we are usually more anxious to probe reactions in which unstable intermediates are postulated. There are, broadly speaking, three approaches - continuous generation, instantaneous methods and matrix isolation. 

The idea is developed by postulating a function of the extensive parameters that tends to a maximum for any composite system that approaches a state of equilibrium on removal of an internal constraint. This function, to be called the entropy S, is defined only for equilibrium states where it assumes definite values. The basic problem of thermodynamics may therefore be considered solved once the entropy is specified in terms of a fundamental relation as a function of the extensive parameters. ... 

The previous general continuous-time formulations are mostly oriented towards arbitrary network processes. On the other hand, different continuous-time formulations focused their attention on particular features of a wide variety of sequential processes. One of the first contributions following this direction is based on the concept of time slots, which stand for a set of predefined time intervals with unknown durations. The main idea is to postulate an appropriate number of time slots for each processing unit in order to allocate them to the batches to be processed. The definition of the number of time slots required is not a trivial decision and represents an important trade-offbetween optimality and computational performance. Other alternative approaches for sequential processes were developed based on the concept of batch precedence. Model variables defining the processing sequence of batch tasks are explicitly embedded into these formulations and, consequently,... 

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