Mutually independent products

In common with all multidimensional separations, two-dimensional GC has a requirement that target analytes are subjected to two or more mutually independent separation steps and that the components remain separated until completion of the overall procedure. Essentially, the effluent from a primary column is reanalysed by a second column of differing stationary phase selectivity. Since often enhancing the peak capacity of the analytical system is the main goal of the coupling, it is the relationship between the peak capacities of the individual dimensions that is crucial. Giddings (2) outlined the concepts of peak capacity product and it is this function that results in such powerful two-dimensional GC separations. 

The spin part rspin and the orbital part rorblt (which are mutually independent within the group G) form members of the direct product... 

Figure 1 shows schematically a closed system used for the production and the deposition of UFPs. Raw powders of Ti (average diameter = 27 pm) and AI2O3 (10 pm) are fed into the plasma flame with two mutually independent dispersion feeders, where Ar gas is used as carrier. By adjusting the feeding rates of the two feeders the ratio r of the raw powders can be adjusted at any value between 0 and 1. The total feeding rate is kept at 2 g/min. As for the details of UFP production, see refs. [6-8]. 

In Raman scattering it is usually assumed that the vibration and rotation of a molecule are mutually independent so that the Ivh spectrum in Eqs. (15.3.2) factors into a product of independent terms, one depending solely on rotation and the other on vibration. This assumption has not yet been justified by experiment. When this assumption is made it may be seen (cf. Appendix 7. B) that for vibrations of cylindrically symmetric molecules that preserve the molecular symmetry, Ivh is proportional to <7 2(11 (0)-u ( ))> where u is a unit vector along the molecular symmetry axis. 

The r.v. s Xj, X2,..., X. are said to be mutually independent if and only if their joint distribution factors into the product of their marginal distributions, that is,... 

Modular design combines both, the benefits of standardization and the benefits of customization. The advantages of modularity result from the reuse of parts and the repetition of operations. Hence, higher quality, lower cost of production, lower delivery time and easier spare parts procurement are expected [10]. Modularity facilitates collaboration and thereby helps to increase flexibility and to minimize economic risk. Since many modules already exist and can be purchased from an external vendor, the best module available (outsourcing) can be selected. Because of mutual independency a module is easier to design, produce, test, maintain and repair than a single more complex system [11]. As a result, a large product variance can be covered with a minimum quantity of modules. 

Sequential moulding is based on mutually independent opening and closing of the nozzles in the mould cavity in such a way as to allow the weld lines to be shifted until they reach an optimum position. This technique is used for products of large area and with numerous apertures which cause weld lines to appear. The use of simulation clearly provides a good starting point for optimisation of nozzle control. 

When the occurrence Likelihood (L) of a hazard and its consequence Severity (S) are assumed to be mutually independent, their combination is equal to the product of the two. Hence, under the same assumption, the product of the two triangular fuzzy numbers denoted by TFN = b, Cj) and TFN =... 

Even more important is to see the properties of the first function,, which is liable for an appropriate match of temperature progression of reaction mechanism under study. The long-lasting practice accredited the routine in which the function fa fo ,Tj is divided into the two mutually independent functions k(T) and ffaj. This implies that the rafe of change, or, is assumed to be proportional to the product of two separate functions, i.e., the rate constant k(T), dependent solely on the temperature, and the mathematical portrayal of the reaction mechanism, ffa), reliant on the variation of the degree of conversion, only. 

The matrix A in Eq. (7-21) is comprised of orthogonal vectors. Orthogonal vectors have a dot product of zero. The mutually perpendicular (and independent) Cartesian coordinates of 3-space are orthogonal. An orthogonal n x n such as matr ix A may be thought of as n columns of n-element vectors that are mutually perpendicular in an n-dimensional vector space. 

The time approach relies entirely on independent diffusion-reaction time without reference to distances. The reaction product inherits the time sequence of one of the parents chosen at random however, its residual time to react with another species is scaled inversely relative to its mutual diffusion confident. A heuristic correction is also made for the change of reaction radius (Clifford et al, 1986). 

An especially important result from these studies is that a,j is remarkably independent of the complexity of the reacting ions (in marked contrast to electron dissociative recombination), only varying over the limited range (4-10) x 10 8 cm3 s-1 at 300 K, even for ions as different as those involved in reactions (67) and (71). This coupled with the relatively weak temperature dependence of ari in practice allows a single value for ari ( 6 x 10-8 cm3 s 1) to be used for all mutual neutralization reactions in ionospheric de-ionization calculations without introducing serious errors. This value is in close accordance with estimates of ionic recombination coefficients obtained by Ulwick211 from observations of ionization production and loss rates in the atmosphere in the altitude region 50-75 km. 

Four routes are available for obtaining a marketing authorization (MA) for a human medicinal product in the European Economic Area independent national procedure, mutual recognition procedure (MRP), decentralized procedure (DCP), and centralized procedure (CP) [5-7],... 

If the oppositely charged carriers are generated independently far away of each other (e.g. injected from electrodes) volume-controlled recombination (VR) takes place, the carriers are statistically independent of each other, the recombination process is kinetically bimolecular. It naturally proceeds through a Coulombically correlated electron-hole pair (e h) leading to various emitting states in the ultimate recombination step (mutual carrier capture) (Fig. 3 for more details, see Figs. 11 and 27 in Sec. 2.3). As a result, the overall recombination probability becomes a product of the probability of the pair formation, Pr(1) = (1 + Tm/Tt) , and the capture probability, PR(2) = (1 + tc/t(1)... 

Until recently, knowledge about absolute and relative rates of reaction of alkenes with carbocations was very limited and came almost exclusively from studies of carbocationic polymerizations [119-125]. The situation changed, when it became obvious that reactions of carbocations with alkenes do not necessarily yield polymers, but terminate at the 1 1 product stage under appropriately selected conditions (see Section III.A). Three main sources for kinetic data are now available Relative alkene and carbo-cation reactivities from competition experiments, absolute rates for reactions of stable carbocation salts with alkenes, and absolute rates for the reactions of Laser-photolytically generated carbocations with alkenes. All three sets of data are in perfect mutual agreement, i.e., each of these sets of data is supported by two independent data sets. 

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