Linear line

Topological indices are used to describe some components of connectivity. A more complete description is afforded by unidimensional codes (linear line notations) such as SMILES. Connectivity plus explicit attention to valence electrons is afforded by the electrotopological indices... 

Figure 13 shows the Guinier plots of Ix d(q, t) at after quenching up to a little higher t than ri(SAXS). Linear lines are obtained and the slope does not change with an increase in time. From the slope, we estimated... 

Side length of a square electrode Specific resistivity of the electrolyte Reduced species Slope of the linear line... 

The actual Hill plot for Hb is far from a linear line with constant slope. The actual curve has a varying slope between one to three. Thermodynamically, Eq. (6.8.2) implies that all n ligands bind simultaneously to Hb. There is no provision in this model for intermediary occupancy states. Therefore, this model is thermodynamically unacceptable. This is true a fortiori when n, obtained by fitting the experimental data, turns out to be a nonintegral number. 

The combustion process in internal combustion engines as an isobaric or isometric heat-addition process is oversimplistic and not realistic. A real cycle p-v diagram of the Otto or Diesel cycle looks like a curve (combination of isobaric and isometric) rather than a linear line. Are the combustion processes in the dual cycle more realistic ... 

Instead, optical measurement was applied to clarify the formation mechanism of Agl nanoparticles in diluted suspensions. Figure 4.4.10A shows the absorption spectra of the 1-day aged suspension containing 3.33 X 10-4 M Ag+ and 6.67 X 10-4 M I- as a function of RSH concentration. When the content of RSH increased from 0 to 6.67 X I0-3 M (curves a-d), the absorption spectra of Agl particles blue-shifted, suggesting the quantum size effect. The relationship between the particle diameter, d (A), and the concentration of RSH, c (A/), was plotted in the inset, which shows the double-logarithmic linear line of d versus c. The aggregation number is found to be proportional to the cube of the size. The same relationship was reported on the formation of CdS nanoparticles (37). These correlations indicate that Agl and CdS have the same ionic nature and have the same reaction modules of thiols. 

Figure 12.2 (A) Cross section of a hemispherical or hemicylindrical electrode and the linear lines of flux to the electrode surface. (B) Cross section of a disk or band electrode and the nonlinear lines of flux.

The half lives of (E)- and (Z)-14 obtained from the decay profiles at 415 nm are 800 and 710 ns, respectively. These half-lives are almost the same, but both are slightly larger than that of 15. The logarithms of decay profiles of the transient absorptions versus time also show very good linear lines, indicating a first-order kinetics for decay. 

In figure 5.34 the retention lines have been approximated by a series of linear line segments, rather than by a smooth curve. The alternative is to fit a mathematical equation to the data, for example a quadratic function for In k vs. the mixing ratio x. If more than... 

Equation (6.173) implies that the release rate is governed by the porosity of the membrane, which influences the permeability the polymer material, which influences the semipermeability of the membrane the thickness and surface area of the membrane the solubility and osmotic pressure and the amount of drug in the core. Figure 6.41 shows the effect of osmotic pressure on the release of KC1 from MPOPS. By extrapolating the linear line to zero osmotic pressure, the release rate of drug by diffusion through the microporous membrane structure can be obtained. 

The propagation steps of the zipper -mode cascade cydization are by definition all-intramolecular processes. Some prototypical examples of the zip-per -mode cascade cyclic carbopalladation producing two to five fused rings in one step are summarized in Scheme 40 [11,113-116,122], One of the major attractive features of this synthetic methodology is the ease of retrosynthetic analysis, which involves finding a linear line of dissection indicated in bro-... 

Besides, the hybrid silicones synthesized nsing the method in Scheme 3 produced scattered linear lines, whereas those obtained from precursor M mostly overlap on a single line, with a y intercept lower than 0.2 units compared to the PDMS one. This difference is typical of the theoretical lower hydrodynamic volumes for cyclic structures, compared to linear ones [21, 22]. From this analysis, it is reasonable to conclude that the formation of macrocycles prevents high molar masses to be reached, since the hybrid silicones are not capable of ring scission through redistribution reactions within the macromolecular chains, unless PDMS chains. 

Each polymer plate is positioned perpendicular to the water s surface before every Wilhelmy experiment so that each point on the bottom edge of the plate contacts the water s surface at the same time. However, this is not a mandatory requirement, and adding a small weight that is attached to the bottom of the sample allows use of a nonrectangular sample. If two edges are not parallel and irregular, no linear line for buoyancy is obtained, and the simple extrapolation method cannot be used to calculate the interfacial tension. The slope of immersion or emersion line is determined by the geometrical factor of sample as seen in Eq. (26.3). 

Where W is the equilibrium adsorption capacity. Wo is the total volume of the micropores aecessible to the given adsorbate, k is a characteristic constant related to the pore structure of the adsorbent, P is an affinity coefficient, Csai is the saturation concentration in the gas phase of liquid adsorbate at the adsorption temperature T, and C is the eoncentration of adsorbate vapor in equilibrium. Plotting ln(W) versus [RTln(Csai/C)] the parameters K/p and Wo in the DR equation were determined by the slope and the intercept of the linear lines respeetively. The obtained results and correlation coefficients are eompiled in Table 2. This Table shows the DR equation parameters and the... 

The iteration process (5.14) together with the linear line search described by formula (5.21) gives us a numerical scheme for the steepest descent method for misfit functional minimization. Thus, this algorithm for the steepest descent method can be summarized as follows ... 

Applying a linear line search to the last problem, we obtain the optimum length of the step equal to... 

The algorithm of the Newton rnotliod wiUi the linear line search can be sum-... 

A linear line search in the conjugate gradient method... 

In particular, applying the linear line search, we find that the minimum of the parametric functional is reached if is determined by the following formula ... 

Solution of this minimization problem gives the following best estimation for the length of the step using a linear line search ... 

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