Induction factor, defined

Schilow recognized that induced reactions fall into two classes. The first class now is called an induced chain reaction, which can be described in terms of an initiation step, a propagation sequence, and a termination step. The other class is the coupled reaction, which can be distinguished from an induced chain reaction by the behavior of the induction factor defined by the ratio equivalents of induced reaction/ equivalents of primary reaction. In an induced chain reaction the induction factor increases without limit as the propagation chain length is increased. In a coupled reaction the induction factor approaches some definite small value such as 1, 2, or 1/2 as the induction reaction is favored. 

Reaction (1) is called the primary, main, or inducing reaction, which brings about induced reaction (2). Substances A, I and Ac taking part in both reactions (1) and (2) are called actor, inductor, and acceptor, respectively. The extent of the induced change is conventionally expressed by the induction factor F , defined as the ratio of the equivalents of the induced reaction to those of the primary reaction. 

The induction factor is defined as the ratio of the treated batch luminescence to the average luminescence of controls. 

To arrive at this limiting case the reaction (50) must be prevented. This obviously can be done by making the concentration of a zero, while any increase of that concentration will increase s, the velocity of the side reaction. This causes the amount of X5 and therefore also of X2, X3, and X4 to decrease, which means that the velocity of the overall reaction (R) decreases. We may say that the side reaction induces the main reaction and that the induction factor is r/s. If the reaction (50) is completely irreversible, i.e., if the reaction (05) does not occur at all, and if, furthermore, the velocity of the reaction (21) is vanishingly small as compared to that of (50), the induction factor becomes identical with the chain length, defined as the number of overall reactions (R) occurring for every intermediate X2 formed according to reaction (12) (cf. p. 341). 

For such reactions an induction factor IF is defined as the number of equivalents of reductant oxidized per equivalent of inducer (here Fe ) oxidized. In essence reducing agent and inducer compete with each other in the further reduction of the intermediate valence states of oxidizing agent. 

There is another factor defining an upper limit of frequency. It is dictated by the fact that the efficiency of focusing multi-coil induction probes takes place provided that currents in the borehole have to be shifted in phase by 90°. 

Therefore, the main factors defining the value of the geometric factor of the borehole for conventional induction probes are length and diameter of the nonconducting base. 

In As(III)-induced oxidation of carboxylic acid by Mn04 in acidic medium, the Mn +, Mn" +, and Mn + ions were considered to be reactive intermediates in view of the inductor factors determined under different experimental conditions. The induction factor is defined as the ratio of equivalent of oxidant consumed per equivalent of substrate oxidized and the inductor. It is suggested that a trace amount of carboxylate ion influenced the titration of As(III) by Mn04 ion. ... 

Although cTi estimates by different methods or from different data sets may disagree, it is generally held that the inductive effect of a substituent is essentially independent of the nature of the reaction. It is otherwise with the resonance effect, and Ehrenson et al. have defined four different ctr values for a substituent, depending upon the electronic nature of the reaction site. An alternative approach is to add a third term, sometimes interpreted as a polarizability factor, and to estimate the inductive and resonance contribution statistically with the added parameter the resonance effect appears to be substantially independent of reaction site. " " ... 

The ortho effect may consist of several components. The normal electronic effect may receive contributions from inductive and resonance factors, just as with tneta and para substituents. There may also be a proximity or field electronic effect that operates directly between the substituent and the reaction site. In addition there may exist a true steric effect, as a result of the space-filling nature of the substituent (itself ultimately an electronic effect). Finally it is possible that non-covalent interactions, such as hydrogen bonding or charge transfer, may take place. The role of the solvent in both the initial state and the transition state may be different in the presence of ortho substitution. Many attempts have been made to separate these several effects. For example. Farthing and Nam defined an ortho substituent constant in the usual way by = log (K/K ) for the ionization of benzoic acids, postulating that includes both electronic and steric components. They assumed that the electronic portion of the ortho effect is identical to the para effect, writing CTe = o-p, and that the steric component is equal to the difference between the total effect and the electronic effect, or cts = cr — cte- They then used a multiple LFER to correlate data for orrAo-substituted reactants. 

This provides an inductive, and a constructive, proof of the possibility of a triangular factorization of the specified form, provided only certain submatrices are nonsingular. For suppose first, that Au is a scalar, A12 a row vector, and A21 a column vector, and let Ln = 1. Then i u = A1U B12 — A12, and L2l and A22 axe uniquely defined, provided only Au = 0. But Au can be made 0, at least after certain row permutations have been made. Hence the problem of factoring the matrix A of order n, has been reduced to the factorization of the matrix A22 of order n — 1. 

The most clearly defined factors in determining the differentiation of Th responses are the cytokines present during T cell receptor engagement of the peptide MHC complex. IL-12 and IFN-y are important in the development of type 1 responses (Hsieh et al., 1993 Seder et al, 1993), while IL-4 is important in the induction of type 2 responses (Abishira-Amar et al., 1992 Seder et al., 1992). The importance of these cytokines in influencing... 

Takahashi K, Tanabe K, Yamanaka S et al (2007) Induction of pluripotent stem cells from adult human fibroblasts by defined factors. Cell 131 861-872... 

We note that in the definition of moments, we have used frequency v in units of cm-1. Other units of frequency are sometimes chosen instead of the experimentalist s standard use of frequency in wavenumber units (cm-1), angular frequencies co = 2ncv are the most likely choice of theorists, which leads to different dimensions of the moments, and to the appearence of factors like powers of 2nc. We note, moreover, that in the early days of collisional induction studies the zeroth moment yo was defined without the hyperbolic cotangens function, Eqs. 5.6. For the vibrational bands (hco 3> kT), the old and new definitions are practically identical. However, for the ro to translational band substantial differences exist. The old definition of yo was never intended to be used for the far infrared [314] only Eq. 5.6 gives total intensity in that case. 

Time Factor Prior to Occurrence of a Thermal Explosion (Induction Periods). In the study of spontaneous explosions occurring in closed vessels, a well defined induction period frequently elapses prior to the development of an actual explosion. The length of this time interval has been observed to be anywhere from a few seconds to several minutes, depending upon the experimental conditions employed. Such observations are not surprising, in view of the fact that in order for an explosion to occur a build-up either of the internal energy or of chain carriers is first required. The rate of such a nonstationary process would then be expected to determine the duration of these pre-explosion times. For the case of a purely thermal explosion, the over-all rate of heat release, dq/di, prior to explosion is given by... 

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