Steep function

Fig. 2. Left Dissociation yield U for a positive chirp ( + ), no chirp ( 0 ), and negative chirp experiment (gray, left scale) and theory (light gray, right scale). Right The dissociation yield U is a steep function of negative chirp experiment (bars, left scale) and theory (open circles, right scale).

The rate enhancement of the polymer over that of simple pyridoxamine was a steep function of the length of the alkyl chains added, in polymers with roughly the same percentage of alkylation and of pyridoxamine attachment. At pH 7.0 and 30 °C, the acceleration over the rate with pyridoxamine was 160 for C-l chains, 180 for C-3, 500 for C-6, 1000 for C-9, 2300 for C-12, and 2500 for the C-15 and C-18 normal alkyl chains. This chain effect seems unlikely to involve hydrophobic binding of a substrate as hydrophilic as pyruvic acid. Instead the hydrophobic chains modify the pK,s of the amino groups in the polymer and also create a cavity in which the transamination can take place in a less than fully aqueous environment. 

There is one major feature that appears to be of much greater importance with gold than with other metals its catalytic ability in carbon monoxide oxidation and some other reactions is a steep function of the size of particle responsible. We shall therefore need to examine closely how the properties of gold depend on the size of the assembly of atoms. Fortunately, there is much relevant information to consider and to bear in mind when thinking about catalysis by gold this is surveyed in the following chapter. 

Voltage-dependent channels, such as the classical sodium or potassium channels in nerve tissue, change their conductance with membrane potential. The changes in conductance are a very steep function of membrane voltage conductance values can increase as much as 150 times for an increment of 10 mV in membrane potential (Hodgkin and Huxley, 1952). 

It is noted that the original Reynolds axioms are not applicable to discontinuous functions as normally occur across the interfaces in multiphase flow. As a remedy. Drew [54] extended these functions making them continuous by use of the generalized function concept coimecting the functions of the continuous phases on each side of the interface across the interface. Hence the discontinuous functions are modified to be continuous but locally very steep functions across the interface. Formally the averaging axioms can then be extended to include the interfaces, giving rise to the modified formulations of the axioms. 

It is evident from the form of this equation that a should be strongly dependent on H and H which are steep functions of the charge distribution. Now, the charge distribution (and hence the values of H and H ) cannot be the same in, say, CuCll , as in Cuds " yet we assume that a given value of internuclear distances concerned) can fit the d d spectra of both compounds. It is of interest to note that in the well-documented cubic systems it is readily apparent that the ligand field splitting indeed depends only... 

It will be noted that the B value for Mg2+ is proportional to the square of the Na+ concentration. In the case of a cation with many charges, for example, a protein or polypeptide cation, the B value will be an extremely steep function of the Na+ concentration. 

The scalar interaction is assumed here to be a function of the distance between the I and 5 spins. As in the dipolar case, the variation of r with time is responsible for the time dependence of the interaction. Thus, unlike the sticking model, the unpaired electron density produced at the nucleus is not at one instant finite and then zero (i.e., switched on and then off), but it approaches its maximum value as the radical and solvent molecules collide and then decays to zero again as the molecules recede. Since scalar interaction could arise from the electron—orbital overlap with the nucleus, the interaction is assumed to be of very short range and thus a steep function of the intemuclear... 

Two effects are observed in homogeneous nucleation experiments for all substances. First, the nucleation rate is always a steep function of saturation ratio S. The second feature common to all systems is that the critical saturation ratio Sc decreases as T increases, and J increases as T increases at constant S. Also, critical nuclei become smaller as 5 increases and as T increases. 

In the Fresnel type, the intensity of the refracted beam is measured. The optical conditions are such that this intensity is a steep function of the refractive index of the liquid. Therefore, the beam is sent from glass into the liquid at an angle of incidence that approximates to the critical angle. Instruments based on this principle have provisions for changing the angle of incidence of the beam in order to fulfill this requirement. 

In order for fog to form, a nuclei must first be formed. Homogeneous nucleation is difficult because of the energy barrier associated with the creation of an interface. The rate of nucleation is a very steep function of the supersaturation ratio. Generally, below a certain critical supersaturation ratio nucleation is slow enough to be ignored, and above this, it will be substantial. The critical supersaturation ratio can be predicted from Amelin s equation (78, 242, 380). Procedures for fog formation prediction are outlined in the cited references. 

Since the linewidth of the spectra is a steep function of the interspin distance, empirical or semiempirical parameters such as spectral amplitude ratios or spectral second moment values were used to extract distances semiquantitatively and to answer structural questions in the past. In the following, the software available to extract distances and the caveats hidden in the analysis are presented. 

Since the retention factor is a steep function of the salt concentration, hydrophobic interaction chromatography is normally carried out using gradient elution from a high salt concentration to a low salt concentration. The selectivity of the separation can be influenced by the stationary phase, the type of salt, the temperature, the pH, and other additives to the mobile phase. 

Though dry cellulose is to be considered as an extremely hygroscopic substance, the velocity with which equilibrium is attained at low vapour pressures is very small. It is, however, an extremely steep function of the vapour pressure. 

In an attempt to obtain a semiquantitative estimate of relative surface coverage (RSC), we propose to use the ratio of overlayer/substrate related intensities as defined in eq 1. RSC is expected to be a steep function of surface coverage and may be of value for (future) correlations between PLL-PEG surface coverage and protein resistance. 

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