Pseudo definition

In this figure the next definitions are used A - projection operator, B - pseudo-inverse operator for the image parameters a,( ), C - empirical posterior restoration of the FDD function w(a, ), E - optimal estimator. The projection operator A is non-observable due to the Kalman criteria [10] which is the main singularity for this problem. This leads to use the two step estimation procedure. First, the pseudo-inverse operator B has to be found among the regularization techniques in the class of linear filters. In the second step the optimal estimation d (n) for the pseudo-inverse image parameters d,(n) has to be done in the presence of transformed noise j(n). 

Most distillation systems ia commercial columns have Murphree plate efficiencies of 70% or higher. Lower efficiencies are found under system conditions of a high slope of the equiHbrium curve (Fig. lb), of high Hquid viscosity, and of large molecules having characteristically low diffusion coefficients. FiaaHy, most experimental efficiencies have been for biaary systems where by definition the efficiency of one component is equal to that of the other component. For multicomponent systems it is possible for each component to have a different efficiency. Practice has been to use a pseudo-biaary approach involving the two key components. However, a theory for multicomponent efficiency prediction has been developed (66,67) and is amenable to computational analysis. 

The slope of the operating line is F7S, just as in Eqs. (15-11) and (15-12), but only stages 2 through / — 1 will fall directly on the operating line. And one knows that X will be on the equihbrium line in equilibrium with by definition (see Fig. 15-12). One can calculate a pseudo feed concentration Ay that will fall on the operating line [Eq. 05-11)] at = Y, [Eq. (15-19)]. 

A definitive determination of the waste sludge production and the oxygen requirement can be obtained using the pseudo constants referred to previously. The ultimate BOD in the waste will be accounted for by the sum of the oxidation and sludge synthesis (Eq. 25-20). 

To illustrate the relationship between the microscopic structure and experimentally accessible information, we compute pseudo-experimental solvation-force curves F h)/R [see Eq. (22)] as they would be determined in SEA experiments from computer-simulation data for T z [see Eqs. (93), (94), (97)]. Numerical values indicated by an asterisk are given in the customary dimensionless (i.e., reduced) units (see [33,75,78] for definitions in various model systems). Results are correlated with the microscopic structure of a thin film confined between plane parallel substrates separated by a distance = h. Here the focus is specifically on a simple fluid in which the interaction between a pair of film molecules is governed by the Lennard-Jones (12,6) potential [33,58,59,77,79-84]. A confined simple fluid serves as a suitable model for approximately spherical OMCTS molecules confined... 

Symbols used are defined at the end of this paper. The definitions of other pseudo-kinetic rate constants can be found in earlier papers (6,7). 

In order to exemplify the potential of micro-channel reactors for thermal control, consider the oxidation of citraconic anhydride, which, for a specific catalyst material, has a pseudo-homogeneous reaction rate of 1.62 s at a temperature of 300 °C, corresponding to a reaction time-scale of 0.61 s. In a micro channel of 300 pm diameter filled with a mixture composed of N2/02/anhydride (79.9 20 0.1), the characteristic time-scale for heat exchange is 1.4 lO" s. In spite of an adiabatic temperature rise of 60 K related to such a reaction, the temperature increases by less than 0.5 K in the micro channel. Examples such as this show that micro reactors allow one to define temperature conditions very precisely due to fast removal and, in the case of endothermic reactions, addition of heat. On the one hand, this results in an increase in process safety, as discussed above. On the other hand, it allows a better definition of reaction conditions than with macroscopic equipment, thus allowing for a higher selectivity in chemical processes. 

The first pseudo force, Fi, is called the Coriolis force, and its magnitude is directly proportional to the angular velocity of the rotating frame of reference and the linear velocity of the particle in this frame. By definition, this force is perpendicular to the plane where vectors Vi and o are located, Fig. 2.3a, and depends on the mutual position of these vectors. The second fictitious force, F2, is called the centrifugal force. Its magnitude is directly proportional to the square of the angular velocity and the distance from the particle to the center of rotation. It is directed outward from the center and this explains the name of the force. It is obvious that with an increase of the angular velocity the relative contribution of this force... 

For a linear plan the pseudo-overall yield as defined above is numerically close to the multiplicative product of the reaction yields. The difference between the two values diminishes as the reaction yields approach 1 as would be expected. However, for complex plans with several converging branches this alternative definition becomes less useful. For the triclosan branch equation (4.16) yields 0.405 (40.5%) for the pseudo-overall yield. 

Comparing the potentials across each row, we can test the idea of additivity of ortAo-substituent effects for 2-fluoro, 6-chloro, and then 2-fluoro-6-chloro substitution. The definition of a = 0 changes across each row to permit easy visual addition of the potentials in the physically appropriate manner to assess the degree of additivity of ort/io-chlorine and ort/io-fluorine substituent effects. For o-fluorotoluene and 2-fluoro-6-chlorotoluene, a = 0 denotes the (minimum-energy) pseudo-trans conformation for o-chlorotoluene, a=0 denotes the pseudo-cis conformation. The notion of additivity has considerable merit in all three electronic states. 

In transition metal-catalyzed domino reactions, more than one catalyst is often employed. In Tietze s definition and the classification of domino reactions, no distinction has been made between transformations where only one or more transition metal catalyst is used for the different steps, provided that they take place in a chronologically distinct order. Poli and coworkers [13] differentiated between these processes by calling them pure-domino reactions (which consisted of a single catalytic cycle driven by a single catalytic system) or pseudo-domino reactions . The latter type was subdivided into ... 

The coverage of the survey has though been deliberately restricted to those sandwich systems in which the pseudo-axial structure is definitely established or is strongly indicated by the available evidence, and species in which extensive distortion from this geometry is likely have thus been excluded. Consequently this has had the effect of largely limiting the coverage to the metallocenes and bisarene compounds of the 3d series since in the 4c and... 

Kinetic theory indicates that equation (32) should apply to this mechanism. Since the extent of protonation as well as the rate constant will vary with the acidity, the sum of protonated and unprotonated substrate concentrations, (Cs + Csh+), must be used. The observed reaction rate will be pseudo-first-order, rate constant k, since the acid medium is in vast excess compared to the substrate. The medium-independent rate constant is k(), and the activity coefficient of the transition state, /, has to be included to allow equation of concentrations and activities.145 We can use the antilogarithmic definition of h0 in equation (33) and the definition of Ksh+ in equation (34) ... 

In the same way, the parameters kij and hij are joined to form a unique parameter matrix H. With these definitions a linear problem may be written like that of equation 5. The matrix H can then be estimated either by direct pseudo-inversion or by PLS. It is worth noting... 

Brown (1959) has presented a charge transfer model of the transition state for electrophilic reactions which differs appreciably from that proposed by Fukui and his collaborators and leads to the definition of a new reactivity index termed the Z value . The model is based on a more conventional formulation of the charge transfer mechanism, which avoids the complete transfer of electrons associated with v = 0,1,2 in Fukui s model. There is no dependence on the formation of a pseudo tt orbital in the transition state, nor is hyperconjugation invoked. A wave function for a charge transfer complex is written as a linear combination of a wave function < o describing the unperturbed ground state of the molecule under attack, and a function which differs from (Pq in the replacement... 

Mulliken s model is entirely compatible with the descriptions given previously in this Section, since charge shifts that result from polarization are already taken into account in forming the cr-complex by subsequent changes in hybridization. Fukui s model, upon which the definition of the superdelocalizability is based, resembles Mulliken s only in the use of a pseudo-TT orbital , and the formulation of the hyperconjugation problem is quite different, since )3 is taken by Fukui to be small, so that 8f can be defined by perturbation formulae. In particular, the bonding of the pseudo-TT orbital in Fukui s model primarily involves the least bound, or frontier orbitals, whereas in Mulliken s model the most bound MO is involved. 

Small differences in light sources have definite effects on photochemical processes. Some irradiation systems match the solar spectrum poorly, thus affecting the relative importance of the various photodissociation processes occurring in the atmosphere. Ambient variations in the nitrogen dioxide photolysis pseudo-first-order rate constant,... 

Thus we see that the pseudo-steady-state approximation gives orders of the reaction as the thermodynamic equilibrium approximation, the only difference being the definition of the rate constant... 

Pseudo-ChE (also known as butyryl-, plasma, and nonspecific cholinesterase) has a widespread distribution, with enzyme especially abundant in the liver, where it is synthesized, and in the plasma. In spite of the abundance of pseudo-ChE, its physiological function has not been definitively identified. It does, however, play an important role in the metabolism of such clinically important compounds as succinylcholine, procaine, and numerous other esters. 

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