Quasi-linearization

The indium molybdate InnMo4o062, prepared by heating the appropriate mixture of In, Mo and M0O2 at 1100°C, features novel quasi-linear chain cations. Ins + and Ing + in channels... 

Other ideas are connected with two types of purely implicit difference schemes (the forward ones with cr = 1) available for the simplest quasi-linear heat conduction equation... 

Finally, a group from General Motors has explored the mechanistic importance of the N20 + CO reaction as an intermediate step during the reduction of NO by CO on noble metal exhaust catalysts [87,88]. Quasi-linearization of the non-linear NO + CO reaction system by identifying a critical kinetic parameter revealed that, indeed, the rate of the N20 + CO conversion as an intermediate step in the overall NO + CO conversion can be two to three orders of magnitude faster than the isolated N20 + CO reaction. This suggests that the observed suppression of N20 production at higher temperatures may be due to its fast reaction with adsorbed CO once produced, and that, contrary to the accepted wisdom, the formation of N20 and its subsequent reaction with CO can make a major contribution to the kinetics of the reduction of NO by CO in three-way catalytic converters. The validity of the theoretical results was verified by both... 

Regression analysis by means of linear or quasi-linear models (Parczewski [1981], Singer and Danzer [1984], Parczewski et al. [1986]). 

Figure 4b shows a quasi linear relation between the activity in alcohol dehydration and the quantity of Bronsted acid sites obtained by DMP adsorption. However a low amount of sites is active in dehydration (on theta alumina) but practically no Bronsted acid sites are detected by DMP adsorption because of their low number and strength. 

Rhee, Aris, and Amundson, First-Order Partial Differential Equations Volume 1. Theory and Application of Single Equations Volume 2. Theory and Application of Hyperbolic Systems of Quasi-Linear Equations, Prentice Hall, Englewood Cliffs, New Jersey, 1986,1989. 

Fig. 13.4 Profiles of the intensities l J2, Ey 2, and EZ 2 of the Cartesian coordinate components of the electric field in a fundamental mode with quasi linear polarization. The insets show the inner parts of the profiles, which correspond to the field inside the fiber. The parameters used a 200 nm, X 1,300 nm, 1.4469, n2 1. Reprinted from Ref. 61 with permission. 2008 Elsevier...

The charge control equation related to this device in the quasi-linear region is approximately given by ... 

Iachello, F., Manini, N., and Oss, S. (1992), Quasi-linear Four-Atomic Molecules in the Vibron Model, 7. Mol. Spectrosc. 156, 190. 

The Schulz-Zimm distribution would be found for/end-to-end coupled linear chains which obey the most probable distribution, as well as for/of such chains which are coupled onto a star center. This behavior demonstrates once more the quasi-linear behavior of star branched macromolecules. In fact, to be sure of branching, other structural quantities have to be measured in addition to the molar mass distribution. 

The nonlinear part of the susceptibility was introduced into the quasi-linear finite-difference scheme via iterations, so that at any longitudinal point, the magnitude of E calculated at the previous longitudinal point was used as a zero approximation. This approach is better than the split-step method since it allows one to jointly simulate both the mode field diffraction on irregular sections of the waveguide and the self-action effect by introducing the nonlinear permittivity into the implicit finite-difference scheme which describes the propagation of the total field. 

Carbon suboxide (C(CO)2) can be prepared according to the method of dehydrating malonic acid with P2O5 [96]. The molecule has a linear geometry but the bending potential is remarkably shallow and it was therefore suggested that carbon suboxide is a quasi-linear molecule [16-19]. Calculations on the DFT level on [(CO)5W(C CO 2)], [(CO)3Ni(C CO 2)], and [(CO)2Ni(C CO 2)] with coordination have been presented [97] however, as yet only compounds with r (C,C) coordination could be synthesized with platinum [98, 99] and nickel [100]. 

The quasi-linear relationship between the logarithm of the retention factor and volume fraction organic cosolvent in the mobile lase seems to be the general rule in RPC. However, special effects can ur to cause this rule to be violated. Marked deviation from linearity was observed by Melander et al. (158) with retention data o poiy(ethylene glycol) derive-... 

The phosphorescence spectra of chlorinated 1,4-dibenzodioxins, in hexane solutions at 77 and 4.2 K, have a well-resolved vibronic structure with distinctions in quasi-linear phosphorescence spectra even for closely related isomers of polychlorinated dioxins <1998MI129>. 

A distinctive feature of the O2 and S2 luminescence spectra in minerals is a quasi-linear vibrational structure of the broad luminescence band (Tarash-chan 1978). The O2 and S2 molecular ions are isoelectronic. From the molecular orbital diagram describing their electron structure the emission transition Eg- n l2 is determined. When observing luminescence spectra at 77 K, a fine structure associated with the frequency of intra-molecular vibrations of O2 and S2 is detected. This frequency depends on the type of the molecular ion, on inter-nuclear distance and upon the particular position of the molecular ion in the structures. For S2 the maximum of the emission band lies within the range of 600-700 nm with a mean vibration frequency of 500-600 cm , while for O2 the respective maximum is 450-550 nm with a frequency in the 800-1,200 cm range. 

For linear and quasi-linear, such as a 3-site model for acetonitrile, molecules, only two angles instead of three hsted above are needed to specify the molecular orientation. Eq. (21) gives... 

If we further assume that the solute motion can be neglected and that the solvent velocity autocorrelations are independent of the presence of the solute, we get in the case of (quasi)linear solvent molecules... 

The system of hyperbolic and parabolic partial differential equations representing the ID or 2D model of monolith channel is solved by the finite differences method with adaptive time-step control. An effective numerical solution is based on (i) discretization of continuous coordinates z, r and t, (ii) application of difference approximations of the derivatives, (iii) decomposition of the set of equations for Ts, T, c and cs, (iv) quasi-linearization of... 

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