Negligibly small

When the non-adiabatic coupling terms x and x are considered negligibly small and dropped from Eq. (B.15), we get the uncoupled approximate Schrbdinger equation... 

In what follows, we assume that the second term in Eq. (158a) is negligibly small and as a result x q, 0) becomes independent of q. Thus... 

To summarize our findings so far, we may say that if indeed the radial component of a single completely isolated conical intersection can be assumed to be negligible small as compared to the angular component, then we can present, almost fully analytically, the 2D field of the non-adiabatic coupling terras for a two-state system formed by any number of conical intersections. Thus, Eq. (165) can be considered as the non-adiabatic coupling field in the case of two states. 

Phosphorus(V) oxide is an extremely effective desiccating agent, reducing the vapour pressure of water over it to a negligibly small... 

Chain transfer to initiator or monomer cannot always be ignored. It may be possible, however, to evaluate the transfer constants to these substances by investigating a polymerization without added solvent or in the presence of a solvent for which Cgj is known to be negligibly small. In this case the transfer constants Cjj and Cj determined from experiments in which (via... 

In the forced convection heat transfer, the heat-transfer coefficient, mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, on fluid velocity, which has been observed empirically (1—3), for laminar flow inside tubes, is h for turbulent flow inside tubes, h and for flow outside tubes, h. Flow may be classified as laminar or... 

The dehvery port can be sized sufficiently large that the back pressure is negligibly small. Equation 4 then reduces to equation 5, where k represents the osmotic water permeabihty of the membrane and S represents the solubihty of the dmg at saturated concentration. 

If the system under consideration involves use of the sorbent for only a single feed step or reuse after uniform regeneration, as in many apphcations with activated carbons and ion exchangers, then one of two paths is often followed at this point to simplify Eq. (16-124) further. The second term on the left-hand side of the equation is often assumed to be negligibly small (usually a good assumption), and time is redefined as... 

The metallized film capacitors have the characteristic of self-healing. On a small dielectric failure the capacitor element is not rendered completely unserviceable. After clearing the fault, the affected capacitor element returns to the circuit and the capacitor unit functions normally. Only the punctured area is eliminated from the element and causes a negligibly small reduction in its capacitance value. Such a characteristic is termed self-healing and such capacitors are known as the self-healing type. 

It is not necessary for a compound to depart from stoichiometry in order to contain point defects such as vacant sites on the cation sub-lattice. All compounds contain such iirndirsic defects even at the precisely stoichiometric ratio. The Schottky defects, in which an equal number of vacant sites are present on both cation and anion sub-lattices, may occur at a given tempe-ramre in such a large concentration drat die effects of small departures from stoichiometry are masked. Thus, in MnOi+ it is thought that the intrinsic concentration of defects (Mn + ions) is so large that when there are only small departures from stoichiometry, the additional concentration of Mn + ions which arises from these deparmres is negligibly small. The non-stoichiometry then varies as in this region. When the departure from non-stoichio-... 

This handbook deals only with systems involving metallic materials and electrolytes. Both partners to the reaction are conductors. In corrosion reactions a partial electrochemical step occurs that is influenced by electrical variables. These include the electric current I flowing through the metal/electrolyte phase boundary, and the potential difference A( = 0, - arising at the interface. and represent the electric potentials of the partners to the reaction immediately at the interface. The potential difference A0 is not directly measurable. Therefore, instead the voltage U of the cell Me /metal/electrolyte/reference electrode/Me is measured as the conventional electrode potential of the metal. The connection to the voltmeter is made of the same conductor metal Me. The potential difference - 0 is negligibly small then since A0g = 0b - 0ei ... 

Equation (2-38) is valid for every region of the surface. In this case only weight loss corrosion is possible and not localized corrosion. Figure 2-5 shows total and partial current densities of a mixed electrode. In free corrosion 7 = 0. The free corrosion potential lies between the equilibrium potentials of the partial reactions and U Q, and corresponds in this case to the rest potential. Deviations from the rest potential are called polarization voltage or polarization. At the rest potential = ly l, which is the corrosion rate in free corrosion. With anodic polarization resulting from positive total current densities, the potential becomes more positive and the corrosion rate greater. This effect is known as anodic enhancement of corrosion. For a quantitative view, it is unfortunately often overlooked that neither the corrosion rate nor its increase corresponds to anodic total current density unless the cathodic partial current is negligibly small. Quantitative forecasts are possible only if the Jq U) curve is known. 

A steel surface can be wetted and corroded by permeation of corrosive agents (see Section 5.2.2) and by cathodic disbonding (see Section 5.2.1.5). In all cases the corrosion rates are negligibly small (see Table 5-2). In the case of cathodic... 

The lines of an ac railway produce changes in the potential of the soil surface at right angles to the surface of the soil [8]. Since the potential differences on the soil surface are, however, much lower than the voltage between the rails and the reference ground, which, for contact protection, must not exceed 65 V, the potential changes are negligibly small. 

Using the relation between the Froude number and the Archimedes number, Atq = 1/F, the length of the linear jet zone, x, where the buoyancy forces are negligibly small can be calculated as follows ... 

The model prediets that due to negligibly small nueleation rates in the main body of liquid, the number of small erystals is redueed eompared with the ideal MSMPR model. 

FIG. 1 The mean force potential acting between colloidal species, /3fV (r), in adsorbed colloidal dispersion. In parts (a) and (b) the matrix density is taken as negligibly small, = 10 and = 0.193, respectively. In both parts, the evolution of the mean force potential with solvent density is shown p = 0.2, 0.3 and 0.4 (solid, dashed, and dotted lines, respectively). In part (c) the evolution of the PMF on matrix density is presented. The solvent density is held constant, p =0.3 the matrix density is Pmcr = 0.193, 0.386, and 0.772 (dotted, dashed, and solid lines, respectively). The diameter of the matrix species is = 7.055. The density of colloids is Pcg] = 10 , with Uc = 5, in all the cases in question. 

It was observed that while the ester (3) and ketone (4) derivatives of p-/erf-butyl calix[4]arene extracted negligibly small amounts of Cu " and Cr " ions, its oxime derivative efficiently extracted these ions. Furthermore, 5 was found to be more effective than 6 in extracting Cr ion. 

At extreme dilution the difference between Kx and Ka becomes negligibly small and so does the difference between Km and K. 

The same remarks can be made about each part of the c.m.f., separately. The unitary part of the e.m.f., expressed in volts, is numerically equal to the unitary change in the free energy, expressed in electron-volts per ion pair. At the same time, the cratic term in the e.m.f., expressed in volts, is numerically equal to the cratic change in the free energy, expressed in electron-volts per ion pair. A similar statement can be made about the interionic part but we are usually interested in the value of the e.m.f., extrapolated to extreme dilution, where this part is negligibly small. 

We shall be interested in pairs of cells, in which the mole fraction of the solute in one solvent is equal to its mole fraction in the other solvent. Suppose then that a series of such pairs of cells is made up, with the solute at progressively greater dilutions. When the members of these pairs of cells are placed back to back, the resultant e.m.f. s will contain progressively smaller contributions from the intcrionic forces and, on extrapolation to extreme dilution, this contribution will be negligibly small. Since the mole fraction on each side is the same, the difference between the eratic terms will be zero. In any such scries of cells, the measured e.m.f. s when extrapolated to extreme dilution thus yield the unitary part of the change in free energy. 

This is a quadratic equation in [H + ] and may be solved in the usual manner. It can, however, be simplified by introducing the following further approximations. In a mixture of a weak acid and its salt, the dissociation of the acid is repressed by the common ion effect, and [H + ] may be taken as negligibly small by... 

With 0.1M solutions, the ideal pH range for an indicator is limited to 45-9.5. Methyl orange will exist chiefly in the alkaline form when 99.8 mL of alkali have been added, and the titration error will be 0.2 per cent, which is negligibly small for most practical purposes it is therefore advisable to add sodium hydroxide solution until the indicator is present completely in the alkaline form. The titration error is also negligibly small with phenolphthalein. 

M cerium(IV) solution, and the equivalence point is at 1.10 volts. Ferroin changes from deep red to pale blue at a redox potential of 1.12 volts the indicator will therefore be present in the red form. After the addition of, say, a 0.1 per cent excess of cerium(IV) sulphate solution the potential rises to 1.27 volts, and the indicator is oxidised to the pale blue form. It is evident that the titration error is negligibly small. 

Only freshly prepared starch solution should be used. Two millilitres of a 1 per cent solution per 100 mL of the solution to be titrated is a satisfactory amount the same volume of starch solution should always be added in a titration. In the titration of iodine, starch must not be added until just before the end point is reached. Apart from the fact that the fading of the iodine colour is a good indication of the approach at the end point, if the starch solution is added when the iodine concentration is high, some iodine may remain adsorbed even at the end point. The indicator blank is negligibly small in iodimetric and iodometric titrations of 0.05M solutions with more dilute solutions, it must be determined in a liquid having the same composition as the solution titrated has at the end point. 

Coulson, C. A., Jacobs, J., and Craig, D. P., Proc. Roy. Soc. London) A206, 297, Electronic levels in simple conjugated systems. III. The significance of configuration interaction." It has been concluded that the effect of configuration interactions are not negligibly small. 

P. phosphoreum. In the case of A. fischeri, the total amount of aldehydes was only 15% of that from P. phosphoreum, which consisted of dodecanal (36%), tetradecanal (32%) and hexadecanal (20%). The contents of aldehydes having the carbon atoms of 10, 11, 13, 15, 17 and 18 were negligibly small in both bacterial species. 

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