Ordinary system

The calculated isotope effects for the solvolyses of t-butyl chloride-dg (previously estimated by Bartell, 1961a) and acetyl chloride-ds were much weaker than the experimentally observed ones. The authors conclude (Karabatsos et al., 1967) that in ordinary systems where hyperconjugation (from the j8-position) is possible, the effect of non-bonded interactions accounts for only a small part (less than 10%) of the observed isotope effect. 

It is evident from these two examples, that the chemistry of low pressure plasmas is fundamentally different from the chemistry of ordinary systems. Unfortunately, the actual chemical composition of these plasmas is not known in most cases. The high degree of dissociation indicates that only simple (diatomic ) species which are generated by fast reactions on the walls of the discharge tube may survive in the plasma. This fact has to be kept in mind in any theoretical consideration of chemical processes taking place in such systems. 

Evolvability and adaptability are usually crucial, but an additional dependability challenge. A particular problem is that, just as with ordinary systems, whatever analysis was undertaken in order to establish that an infrastructure is likely to be adequately dependable, may have to be redone virtually from scratch for a modified version of the infrastructure. (Ideally the amount of reworking of the dependability analysis would be commensurate with the extent of the change.)... 

Indeed, the values of the derivatives dx/dt and dy/dt at t = 6 can readily be determined (for example, by graphical differentiation) from the experimental data. Then, the system (2.46) transforms into an ordinary system of two algebraic equations with two unknown quantities k[A2 and k[B2 ... 

Clearly b must be negative for ordinary systems have possible states of infinite energy, though not of negatively infinite energy, and if b were positive, would become infinite for the states of infinite energy, an impossible situation. We may easily evaluate the constant a in terms of... 

Electronic configurations of ions are obtained in much the same way as those of elements. The fluorine atom has nine electrons, so the F ion (with ten electrons) would have the same configuration as Ne gas. Similarly, the sulfide ion (S2 ) would have the argon structure. All monatomic negative ions in ordinary systems have rare gas configurations (except for a negative ion of rhenium which has been reported). 

Microwave spectroscopy on related heterocycles like 1,2,5-oxa-diazole and 1,3,4-thiadiazole has led to an interesting ranking of these molecules in order of decreasing aromaticity as 1,2,5-thiadiazole > thiophene > 1,3,4-thiadiazole > 1,2,5-oxadiazole. The almost normal O—N bond distance in the oxadiazole indicates this molecule to consist essentially of an ordinary system of two conjugated double bonds without any sizable degree of aromaticity. This is further borne out by a comparison of the C—N bond lengths of the two molecules (see Table V). 

Each term from the right side of this representative equation of the model has a particular meaning. The first term shows that the number of the reactant species molecules in the k cell decreases as a result of the consumption of species by the chemical reaction and the output of species from the cell. The second term describes the reduction of the number of molecules as a result of the transport to other compartments. The last term gives the increase in the number of the species in the k compartment because of the inputs from the other cells of the assembly. With reference to the mathematical formalism, our model is described by an ordinary system of differential equations. Indeed, for calculations we must specify the initial state of the probabilities. So, the vector P] (0), k = 1, N must be a known vector. The frequencies Oj wUl be established by means of the cellular... 

For ordinary systems which can be described by equation (1) we have to use... 

Ethane-Deuteroethanes. Chromatographic separation of ethane and perdeuteroethane was first reported by Van Hook and Kelly (32) using packed columns loaded with methylcyclopentane at subambient temperatures. These authors also reported the partial resolution of protio-ethane from mono and di-deuteroethanes. The chromatographic properties of the perdeutero-ordinary system were further investigated on a variety of liquid substrates using packed column GLC techniques by Van Hook and Phillips (34) and on an open tubular etched glass column with a wetted wall (subsequently called wet glass in this paper) by Bruner, Cartoni, and Liberti (8). 

What is undoubtedly true is that for practical purposes the chaos can be regarded at least as very nearly complete. That this is so irrespective of the origin of the present order of things is attested by such simple experiences as the shuffling of a pack of cards, which show how rapidly all vestiges of order become undetectable. While forgoing any attempt at a rigid application of the laws of dynamics to the question, we may therefore introduce as a specific postulate the assumption of molecular chaos for ordinary systems endowed with... 

It had long been the desire of soap-makers to possess some process of saponification less tedious and costly than the ordinary systems of soap-boiling. It was well own that caustic alkalies would convert into saponaceous matter fats and oils, without the application of heat, and it was also well known that during the process of saponification by the ordinary system of boiling over caustic leys, a considerable amount of glycerine was set free, and which, being a substance soluble in water, passed away with the spent or waste leys, causing a direct and positive loss in the manufacture. 

Eawes s System.—One of the most ingenious practical attempts to modify the ordinary system of soap-making was that devised by Mr. William Hawes, a gentleman who had long been connected with the soap trade, and was indeed a member of one of the largest and most enter prising firms in London. The process is well known as the COLD PROCESS, and is thus described by the inventor ... 

Kottula s Soaps.—K. departure from the ordinary system of Boap-raaking was introduced by Dr. Hottnla about twenty five years ago, and at the time attracted much attention. In conducting his process, Kottula adds to ordinary curd, mottled, yellow, or other soaps, made in the ordinary way, fatty matters, lime liquor, concentrated soda leys and alum, with the object of producing a cheaper neutral soap than he believes was hitherto produced. The fatty matters he employs are such as are commonly used by soap-makers. He first boils soda leys until they have acquired the strength of about 30 B., and then adds to them alum, in the proportion of about lbs. to each owt. of ley. He then prepares a lime liquor by adding to any requisite quantity of water as much lime as it will absorb or take up, and to this lime solution he adds sal ammoniac in the proportion of about half a pound to each owt. of the solution. Sometimes he omits the sal ammoniac. 

Steel frames were used by Evans and Marathe (1968) which deformed together with a specimen to control its deformations (Figure 8.8b). In such a frame, an explosive failure of the specimen such as would occur in an ordinary system where the specimen is placed under direct loading is impossible (Figure 8.8c). Balavadze explained the high extensibility of his specimens by the more uniform distribution of internal stresses in the specimen when failure cannot be caused by rapid crack propagation from the weakest region. 

In our ordinary system of writing numbers, the value of any digit depends on its position in the number. The value of a digit in any position is ten times the value of the same digit one position to the right, or one tenth the value of the same digit one position to the left. For example,... 

The minimum a value required for the occurrence of a double critical point is considerably higher for v = 0.4 than for v = 0.5. A more detailed mathematical analysis [53] of (63) yields a border line for the combination of parameters, which separates the normal firom anomalous behavior. For ordinary systems, the combination of a and v values required to produce multiple critical points has so far not been observed. However, for water/PVME systems, such data may well be realistic... 

Van Rees employed in the preceding partial re-immersement when, after having obtained the ordinary system on an arbitrary frame, he re-immersed it by a few millimetres on one of its faces, then it was withdrawn, the film across the base which then goes up between the others, always leads to the formation of an interior film polyhedron. This polyhedron generally has the same number of faces as that which is represented by the frame, and these faces are always more or less convex. 

By a means that I will indicate, one determines, in the systems of certain frames, a modification of another kind, and rather curious if, after having formed the ordinary system of the cube, one bursts the central quadrangular film, the system immediately makes an arrangement very different, and also regular, although it presents a hole in its middle one brings about a similar result, but with two holes, by bursting, in the octahedral system (fig. 75), initially the upper quadrilateral, then the film which replaces the lower quadrilateral. 

To refer to H" as a general functional entity can only mean that any somce will do, a conclusion which is out of harmony with reality. Energy requirements prevent the formation of the free proton in ordinary systems. Homolytic fission giving the hydrogen atom is much less energy demanding. 

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