Equality small variations

Since the first bracket on the right-hand side is a constant and the second is an integer, it is evident that, for any particular /, some leeway must exist in the value of the ratio rj/G for the equality to be satisfied. Here too, the presence of screw helicity must affect either / , or G, or both. In view of the fairly small variations of G allowed if the hybridization of the C atoms is to remain sp, and since the deformation of the C orbitals decreases as the radius of the cylindrical sheets increases, the distance between successive cylinders must decrease and probably tend towards a value characteristic of turbostratic graphite. 

However, at the time the bulk samples were collected, NDMA was present in the air at all test sites in the tannery. The airborne data (see Table III), shows that dimethylamine (DMA) was always present. The amount of airborne NDMA was always approximately equal to 1% of the amount of airborne DMA. The apparent lack of correlation of the NDMA levels with nitrosating capacity is probably due to the relatively small variation in the measured NO levels. 

Similar molecular weight poly(DMA-co-EPl), 1750 daltons, ca. 13 repeat units, and poly(TMDAB-co-DCB), 1500 daltons, ca. 11 repeat units were compared. The two condensation polymers appeared to be about equally effective in preventing the swelling of Wyoming bento-nite. Any small differences are probably due to repeat unit chemical structure differences rather than the small variations in polymer molecular weight. The presence of the hydroxyl group and the smaller N - N distance in poly(DMA-co-EPl) could affect polymer conforma-tion in solution, geometry of the polymer - clay complex, and surface properties of the polymer - clay complex as compared to poly(TMDAB-co-DCB). 

An alternative way to describe the phenomenon is to consider that the ground state of a chain is already divided into domains at any temperatures. In order for the system to follow a small variation of the magnetic field some domains have to reverse their spin orientation. This occurs through a random walk of the DWs, that is, equal probability for the DW to move backward or forward, which implies that the DW needs a time proportional to d2 to reach the other end of a domain of length d. Given that d scales as the two spins correlation length, ., which, for the Ising model, is proportional to exp(2///rB7 ), for unitary spins, the same exponential relaxation is found... 

The change in the response from an analyte relative to a small variation in the amount being determined. The sensitivity is equal to the slope of the calibration curve, being constant if the curve is linear. 

The plateau of the ionization efficiency curve around 70 eV makes small variations in electron energy negligible in practice El works equally well at 60-80 eV. 

The three successive portions of the plot have slopes equal to zero, aFjRT and FjRT respectively, in terms of a In A + versus diagram. The (small) variation of a with the driving force has been omitted for clarity. Thus, if experimental points arising from a family of electron donors are available... 

The last relation is valid for relatively small variations of the flow across the distributor. The value of Mio can be considered equal to 5%, in general. Ap0 can be calculated from eqs. (3.341) and (3.338), and u0 can also be determined from eq. (3.340). Subsequently, the total cross-section A0 of the openings can be calculated. 

If the aim is to determine the stability limit of the trickling flow (that is, the limit of existence of a truly stationary flow), one may neglect the effective viscosity terms in Eqn. (5.2-9) and Eqn. (5.2-10). Furthermore, in trickling flow, all derivatives with respect to time or height (z) are equal to zero a stability analysis of the solution of the system of equations against small variations of t or z yields an algebraic equation which permits to calculation of the limit of liquid mass-flow-rate for a given gas flow rate. 

Conclusions drawn from the study of nitration are subject to many serious reservations. As discussed in Section III, the several sets of experimental conditions employed for nitration are not equally selective. Experimental discrepancies contribute further uncertainty. In addition, the nature of the transition state for nitration may limit its utility as a model for other substitution processes. This difficulty is developed by small variations in the degree of electron deficiency in the aromatic fragment of the transition state (Stock and Himoe, 1962). In view of these limitations, a plot of the composite data for nitration under several conditions versus the cr+-constants (Fig. 16) is most encouraging. The reaction constant is — 6.0. 

The potentials of both individual electrodes are dependent on the hydroxyl ion activity (or concentration) of the potassium hydroxide solution employed as electrolyte. It is evident, however, that in theory the E.M.F. of the complete cell, which is equal to — E+, should be independent of the concentration of the hydroxide solution. In practice a small variation is observed, viz., 1.35 to 1.33 volts for n to 5 N potassium hydroxide this is attributed to the fact that the oxides involved in the cell reactions are all in a hydrousor hydrated form, with the result that a number of molecules of water are transferred in the reaction. The equations for the potentials of the separate electrodes should then contain different terms for the activity of the water in each case the e.m.f. of the complete cell thus depends on the activity of the water in the electrolyte, and hence on the concentration of the potassium hydroxide. 

If the temperature T underwent alone a small variation (T — T), the velocity would undergo an increase B (T —T), where B is a coefficient depending on the mass m, the temperatme T, and the other conditions of the system we know that, if the reaction is unlimited, or if the value fiolm which limits the reaction does not decrease as the temperature increases, a rise of temperature produces, other things being equal, an increase in the velocity of reaction in these conditions the coefficient B is positive. 

The pyrolysis time (THT) in this example is 1.0 s. At temperatures up to 560° C, process (2) will dominate the pyrolysis, while at temperatures higher than 560° C, the pyrolysis will be dominated by process (1). If the pyrolysis products for process (1) are different from those for process (2), it can be seen that a small variation in the temperature profile may significantly modify the analytical results producing more of the products from process (1) or more from process (2). Therefore, the importance of TRT is more significant when rapid degradation reactions occur during pyrolysis. Equal TRT values are essential for the reproducibility of analytical pyrolysis mainly for fast processes. 

At any given ionic strength, the activity coefficients of ions of the same charge are approximately equal. The small variations that do exist can be correlated with the effective diameter of the hydrated ions. 

For a given family of compounds, there exists a certain relationship between the proton affinity and the core ionization energy of the atom which is protonated . The latter could be approximated by the Is-orbital energy, e(ls), of the relevant atom of the conjugate anion, which is relatively stable with respect to the small variations in the basis sets. Calculations demonstrated that for phenol derivatives, a linear relationship (equation 30) equally exists ... 

Let us begin by asking whether the backbone of a protein can be described as a tube. Figure 12.5 indeed shows that, in its native state, the protein backbone can be thought of as the axis of a tube of approximate radius of cross-section (A) equal to 2.7 A. Interestingly, the tube radius shows small variations, especially in the vicinity of backward bends [36]. 

For very low oxygen pressures, the small variation of a implies that the sample has almost a stoichiometric composition and contains nearly equal amounts of n and p carriers. 

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