Statistical factors

Statistical Factors for the Upper Warning Limit and Upper Control Limit... 

Concrete nuclear reactor vessels, of the order of magnitude of 15-m (50-ft) inside diameter and length, have inner linings of steel which confine the pressure. After fabrication of the liner, the tubes for the cables or wires are put in place and the concrete is poured. High-strength reinforcing steel is used. Because there are thousands of reinforcing tendons in the concrete vessel, there is a statistical factor of safety. The failure of 1 or even 10 tendons would have little effec t on the overall structure. 

Estimations based on statistics can be made for total accuracy, precision, and reproducibility of results related to the sampling procedure being applied. Statistical error is expressed in terms of variance. Total samphng error is the sum of error variance from each step of the process. However, discussions herein will take into consideration only step (I)—mechanical extraction of samples. Mechanical-extracdion accuracy is dependent on design reflecding mechanical and statistical factors in carrying out efficient and practical collection of representative samples S from a bulk quantity B,... 

Deviations from this generalization may have several sources, including charge repulsion, steric effects, statistical factors, intramolecular hydrogen bonding, and other structural effects that alter electron density at the reaction site. Hague - ° P has discussed these effects. 

Ground roughness, building size and height above ground factors S3 Statistical factor S4 Directional factor... 

Br0nsted s correlation was developed some years before Hammett s. Here we present a formulation that shows how both LFERs are related for general acid catalysts. For the sake of simplicity, we ignore the statistical factors of p and q. The Hammett equation applied to the values of bh is... 

In order to assess the analysis given in Figures 1 and 2 in terms of the components 1 and 2, the theoretically predicted abundances of the two components were calculated at 30 K, using the ZPVE values from Table 3. Including the statistical factors, the ratio obtained from the ZPVE s is 0.31 0.69, implying that substitution at the H2 position is slightly favoured compared to the purely statistical probability, as expected from the difference in bond strengths bewtween Cj—H and C2—H2. In a comparision with the... 

Includes a statistical factor of 1/2. Includes a statistical factor of 2. 

Table 2. Least-squares statistical factors R, Rw and GoF of the refinement strategies. 

In the case of R = C6H5, the P/C phenyl shift dominates over the C/C shift to the extent of 2 1, the statistical factor already having been accounted for1U. 

At this point, it is instructive to emphasize that smax is a statistical factor associated with the maximum interaction energy u(tt)max and consistent with the quadratic dependence of... 

The steric factor P is high enough for the bimolecular reaction to occur when two radicals met in the cage. This reaction is limited only by translational diffusion of the reacting radicals and depends on the viscosity of the solvent. The rate constant of such reaction is close to the frequency of encounters of radicals, namely, k = a, kn = 0.25 x 47rrABZ)AB = RT 100007] where spin-statistical factor, rAB is the sum of radii of reactants A and B, and DAB is the sum of their diffusion coefficients. 

Neglect of the statistical factor of2for L L is irrelevant to the present discussion. 

Symmetry corrections for rate or equilibrium constant are usually expressed in a formally different but perfectly equivalent way by means of statistical factors (Leffler and Grunwald, 1963). If the two reagents of (33) have pA and ph equivalent reactive sites, then the rate constant for the forward reaction must be divided by a statistical factor of pA-pB- Since similar considerations apply to the back reaction as well, the equilibrium constant must be divided by a statistical factor ofpApJpc Pv> as n (35). The assign-... 

The relative magnitude of the two concentrations evidently depends on the magnitude of the equilibrium constants and of the concentrations of M and X. Two further points need to be made, (i) It is likely that the formation of 3 from 2 will be favoured, i.e., the equilibrium constant will be enhanced, by a statistical factor akin to an entropy of mixing, (ii) For the species 2 there is no front and back , the MP+BM is symmetrical, and therefore the probability of the propagation, i.e., the, is twice as great as it would be for XP+BM, even if the free energy of complexing is the same for X and M. 

However, the behaviour near m = raB needs some other explanation. My proposal involves the specific solvation of the backside of the carbenium ion by the strong dipole of the solvent this displaces the monomer molecule which is located there in the absence of the solvent, so that the 7t-bond to the monomer at the front is weakened and the unimolecular isomerization-propagation becomes accelerated, despite the statistical factor which, alone, would produce a deceleration, as explained at the end of Section 3a. As the dilution proceeds from m = raB downwards, the polymerization goes through a dieidic phase, in... 

Statistical factor (to permit random orientation), g = Probability of the electronic transition... 

Basilevsky, A. Statistical Factor Analysis and Related Methods. Theory and Applications. Wiley, New York, 1994. 

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