Mean-square value

We have assumed that there are M values of x, aird i/ iir the data sets. This correiatior function can be normalised to a value between —1 and +1 by dividing by the root-mean-square values of z and y ... 

If the magnitude of the fluctuating velocity component is the same in each of the three principal directions, the flow is termed isotropic. If they are different the flow is said to be anisotropic. Thus, if the root mean square values of the random velocity components... 

Table IV lists comparative SD and / values for fittings of all of the reactions of Table II and III with each of the gr scales derived in this paper. The comparison includes figures for fittings with F and R values of Swain and Lupton (S L) and fitting with the Hammett equation. We believe the results given in Table IV provide a clear confirmation of the uniqueness and limited generality of the o/2(ba) scale. Very consistently, the fit achieved by the or (BA) scale is shown in Table IV to be superior by significant factors to that achieved by any of the other scales or by the simple op treatment. This fact is clearly reflected in the overall / values and the similarly weighted root-mean-square / values, F = y/lfnif lN, sum taken over all reactions. The value of F is. 067 for the basis sets of Table II (compare with overall / of. 058). The comparable F values are. 140 for Or, . 088 for S L, and. 155 for 0(p) with the data differences as explained in Table IV. For all sets of Table IV, the corresponding figures are. 073 for o (ba). -143 for a%, . 097 for S L, and. 209 for 0(py...

The statistical distribution of r values for long polymer chains and the influence of chain structure and hindrance to rotation about chain bonds on its root-mean-square value will be the topics of primary concern in the present chapter. We thus enter upon the second major application of statistical methods to polymer problems, the first of these having been discussed in the two chapters preceding. Quite apart from whatever intrinsic interest may be attached to the polymer chain configuration problem, its analysis is essential for the interpretation of rubberlike elasticity and of dilute solution properties, both hydrodynamic and thermodynamic, of polymers. These problems will be dealt with in following chapters. The content of the present... 

Thus the root-mean-square value of the projection is given by... 

On the other hand, the correction factor by which W r) is altered through this refined treatment, namely, exp[ —(9n/20)(r/r, ) ] from Eq. (16), depends both on n and on r/Vm If the distance of separation of the ends of the chain lies in the vicinity of its root-mean-square value, i.e., if r / then... 

The mean and mean square values of the LA coordinate s represent the principal anharmonic and harmonic vibrational contributions, respectively [3]. 

Let (V2) be the mean square value of the fluctuating force, and (Q2) the mean square value of Q. Suppose that the system is known to be in the nth eigenstate. Since Hq is hermitian the expectation value of Q, (En Q En) vanishes and the mean square fluctuation of Q is given by the expectation value of Q2, i.e. 

Resolution can only be determined after noise evaluation of the sensor, keeping in mind that noise is related to the operating point. In practical situations different kinds of noises can be encountered Thermal, Flicker, Generation-Recombination, Shot, and others that are seen in special cases but are not so frequent. The most important parameter used for the characterization of noise devices is the Noise Spectral Density by which, through integration, it is possible to estimate the mean square value of the output voltage ... 

Ratio of the mean-square end-to-end distance, r ), of a linear macromolecular chain in a theta state to NLY, where N is the number of rigid sections in the main chain, each of length L if all of the rigid sections are not of equal length, the mean-square value of L is used, i.e.,... 

Secondly come methods depending on W asastjema s Criterion (36) that the distance D should be split into structural radii in the ratio of the Electron Cloud radii y at approximately their root-mean-square values yrms-... 

The root-mean-square value of the radial velocity fluctuation [ C y] /C varies only slightly with fraction voids and appears to be independent of particle density. 

The damping factors take into account 1) the mean free path k(k) of the photoelectron the exponential factor selects the contributions due to those photoelectron waves which make the round trip from the central atom to the scatterer and back without energy losses 2) the mean square value of the relative displacements of the central atom and of the scatterer. This is called Debye-Waller like term since it is not referred to the laboratory frame, but it is a relative value, and it is temperature dependent, of course It is important to remember the peculiar way of probing the matter that EXAFS does the source of the probe is the excited atom which sends off a photoelectron spherical wave, the detector of the distribution of the scattering centres in the environment is again the same central atom that receives the back-diffused photoelectron amplitude. This is a unique feature since all other crystallographic probes are totally (source and detector) or partially (source or detector) external probes , i.e. the measured quantities are referred to the laboratory reference system. 

A typical freely jointed chain will therefore be quite compact since the root-mean-square value of its end-to-end length, J(ft2) = f N b, will be small compared with its length if it were stretched out (i.e., Nb, when N is large). Figure 10.9 shows a simulated molecule of polyethylene, (-CH2-CH2-)/v, which approximates a freely jointed configuration. 

VAR (var). A unit of reactive power. The. reactive power at the por t of entry of a single-phase two-wire circuit when the product of (a) the rms (root mean square) value in amperes of the sinusoidal current, (b) the rms value in volts of the voltage, and (c) the sine of the angular phase difference by which the voltage leads the current is equal to J. (The SI llnil of reacLive power.)... 

Integration over a time interval long enough compared to the period of the wave, that is, where cos2 x approaches to 1/2, gives the mean square value E(z, t)2 (Equation 6.7) ... 

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