Inverse proportionalities

GPa) and the relative elongation at break (%). The first of the indices characterizes the resistance of the fiber to deformation under the affect of the acting force and determines the value of the tensile strength causing the formation of the unitary relative elongation (e). The modulus E characterizes the susceptibility of the fiber to deform based on the principle of inverse proportionality. The other parameter, i.e., 6, characterizes the maximum ability of the fiber to deform under the effect of the acting tensile force. 

The quantity Jc3, like k2 and k2, is a constant This is the equation of an inverse proportionality. The fact that volume is inversely proportional to pressure was first established in 1660 by Robert Boyle (1627-1691), an Irish experimental scientist The equation above is one form of Boyle s law. 

Fig. 6.8. The dependence of rj2 on x) by the Ivanov model (I) and friction model (F) in comparison with predictions of the extended. /-diffusion (ED) and Langevin (L) models for linear molecules. The line (H) corresponds to the Hubbard inverse proportionality between xgj and xj at very high densities. Experimental data from [81] are in rectangles around line G with the length of their vertical and horizontal sides being equal, correspondingly, to the experimental errors in x el and rj measurements. Experimental data from [270] (J) are shown both in original position and shifted down by a factor of four (broken line).

Direct and indirect competition formats, illustrated in Figure 1, are widely used for both qualitative and quantitative immunoassays. Direct competition immunoassays employ wells, tubes, beads, or membranes (supports) on to which antibodies have been coated and in which proteins such as bovine semm albumin, fish gelatin, or powdered milk have blocked nonspecific binding sites. Solutions containing analyte (test solution) and an analyte-enzyme conjugate are added, and the analyte and antibody are allowed to compete for the antibody binding sites. The system is washed, and enzyme substrates that are converted to a chromophore or fluorophore by the enzyme-tracer complex are added. Subsequent color or fluorescence development is inversely proportionate to the analyte concentration in the test solution. For this assay format, the proper orientation of the coated antibody is important, and anti-host IgG or protein A or protein G has been utilized to orient the antibody. Immunoassays developed for commercial purposes generally employ direct competition formats because of their simplicity and short assay times. The price for simplicity and short assay time is more complex development needed for a satisfactory incorporation of the label into the antibody or analyte without loss of sensitivity. 

Some important conditions concerning the estimation of error should be pointed out. First, modulus measurements of rectangular bars are made in torsion and the calculations contain assumptions that may depend on geometry. How this influences error, particularly at low torque levels is not known. Second, the strains were kept constant at 0.1% other strains might not yield the same results. On the other hand one would expect an inverse proportionality to exist between the magnitudes of error and strain. Thirdly, these errors were estimated for a frequency of 1Hz. 

There exists a rough proportionality between the surface tension and the hardness as well as an inverse proportionality to the molecular volume of the solid. 

The is the concentration for 50% saturation of the receptors and is inversely proportionate to the affinity of the drug for the receptors. 

In view of this calculation, it is not too surprising that insoluble monolayers do not usually display a simple inverse proportionality between tt and A. At pressures this high, three-dimensional matter is not likely to obey the ideal gas law either. 

These inverse proportionality relationships, which are quite common, are very important in showing that, in some instances at least, adsorption of both reacting substances on the surface of the catalyst itself is necessary. A must not merely strike adsorbed B, but must be adsorbed adjacent to it. Otherwise excess of B could not actually retard the combination. 

In a cc experiment, a thin capillary is lilted with a run bulTcr and a voltage is applied across the capillary. The underlying impetus for separations in ee is. in general, derived front the fact that charged species migrate in response to an applied electric held proportionately to their charge and inversely proportionately to their sire. 

The gaseous diffusion method of isotope separation is based upon the difference in the rate of diffusion of gases that differ in density. Since the rate of diffusion of a gas is inversely proportionate to the square root of its density, die lighter of two gases will diffuse more rapidly than the heavier. Therefore, die result of a partial diffusion process will be an enrichment of the partial product in die lighter component. 

Equation (150) is the well-known equation for adsorption rate found by Zel dovich and Roginskil (45) (sometimes it is erroneously called the Elo-vich equation )- This equation was experimentally confirmed for many cases of chemisorption. It follows from (135) and (146) that on a surface where the Freundlich isotherm is valid, the adsorption rate is proportional to P/6m. Inverse proportionality between r+ and a fractional power of 6 was found by Bangham (46). 

According to Kramers treatment, the proportionality of the Kramers rate to tj in the low viscosity limit turns over to the inverse proportionality in the high viscosity. The interpolating behavior for arbitrary rj was studied by Mel nikov and Meshkov [104]. 

The rates of dissociation of Gd3+ chelates used or proposed as CAs are generally low at pH = 7.4. The complexes dissociate much faster in acidic solutions, when the proton-assisted dissociation predominates. In order to compare the kinetic stabilities of complexes, some authors suggest use of the first-order rate constants (kobs) obtained in 0.1 M HCl or HC104 solution. Wedeking et al. compared the acid-assisted dissociation rates (kobs) of several acyclic and cyclic Gd3+ complexes with the long term (14 days) deposition of Gd in the whole body of mice [ 15]. They found an inverse proportionality between the dissociation rates (kobs) and the total residual Gd, i.e. the lower the dissociation rate, the less the residual Gd found in the bodies of the mice [15]. The (kobs) values determined by Wedeking et al. and other authors for several Gd3+ and Y3+ complexes are shown in Table 1. 

The inverse proportionality of Acp with Tg constitutes a general experimental observation for thermosetting polymers, and leads to X < 1, which is a necessary condition to obtain an upward curvature in the Tg vs x function defined by Eq. (4.10). Low values of X are typical of large (Tgoo-Tg0) values. 

Because of the inverse proportionality between wavelength and energy, the relationship may be written as... 

The results are very revealing and instructive. The rate of melting increases with the total force Fn, but only to the one fourth power. The physical explanation for this is that with increasing force, the film thickness is reduced, thus increasing the rate of melting. However, the thinner the film, the larger the pressure drops that are needed to squeeze out the melt. The dependence on the plate temperature is almost linear. The inverse proportionality with R is perhaps the most important result from a design point of view. If viscous dissipation were included, some of these results would have to be modified. 

The molecular weight of the elastomer depends on the amount of the catalyst since the molecular weight is inversely proportionate to the concentration of the catalyst, the molecular weight of the polymer can be reduced by increasing the concentration, and vice versa. 

The data available on the molecular diffusion coefficient of organic vapors in air are meager, but they indicate (in accordance with approximate theory) an inverse proportionality to the square root of molecular weight. The rate of mass transfer by molecular diffusion will be proportional to the diffusion coefficient and to the SVC, itself proportional to vapor pressure times molecular weight (M). We should expect, therefore, under standard conditions of ventilation, that the rate of loss will be proportional to vapor pressure X The ratio of observed rate to... 

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