INDEX M

From now on, the index M will be omitted and it will be understood that any subject to be treated will refer to a finite sub-Hilbert space of dimension M. 

The index m drops out of the last summation we compensate for this by multiplying the final result by n - 1 in recognition of the fact that the summation adds up n - 1 identical terms. Accordingly, the desired result is obtained ... 

We introduce, for the sake of convenience, species indices 5 and c for the components of the fluid mixture mimicking solvent species and colloids, and species index m for the matrix component. The matrix and both fluid species are at densities p cr, Pccl, and p cr, respectively. The diameter of matrix and fluid species is denoted by cr, cr, and cr, respectively. We choose the diameter of solvent particles as a length unit, = 1. The diameter of matrix species is chosen similar to a simplified model of silica xerogel [39], cr = 7.055. On the other hand, as in previous theoretical works on bulk colloidal dispersions, see e.g.. Ref. 48 and references therein, we choose the diameter of large fluid particles mimicking colloids, cr = 5. As usual for these dispersions, the concentration of large particles, c, must be taken much smaller than that of the solvent. For all the cases in question we assume = 1.25 x 10 . The model for interparticle interactions is... 

Brechungs-ebene, /. (Optica) plane of refraction. -exponent, m. refractive index, -ge-setz, n. law of refraction. -Index, m. refractive index, -k effizient, m. coefficient of refraction. -kraft, /. refractive power, -messer, m. refractometer. -verhaltnis, n. refractive index, -vermfigen, n. refractive power, -winkel, m, angle of refraction, Brech-walzwerk, n. crushing rolls (or rollers), crushing mill. >weln, m. (Pharm.) wine of antimony, antimonial wine, -weiustein, m. tartar emetic, -werk, n. crusher, -wurzel, -wurz,/. ipecacuanha, ipecac. 

Sach-index, m. subject index, -kenner, m. expert, -kenntnis, -kimde, /. expert or special knowledge experience, sachfcundig, a. experienced, expert. Sachkundiger, m. expert, specialist. 

Zahlen-angabfen, /. pi. numericardata. -folge, /, -zHuherical ord. . -grbsse, /. numerical quantity. -Index, m. numerical Index or suffix. 

The subscripts 1,2,3 refer to the main solvent, the polymer, and the solvent added, respectively. The meanings of the other symbols are n refractive index m molarity of respective component in solvent 1 C the concentration in g cm"3 of the solution V the partial specific volume p the chemical potential M molecular weight (for the polymer per residue). The surscript ° indicates infinite dilution of the polymer. 

The only difference is that a(0) is now an operator acting in jm) space of angular momentum eigenfunctions. This space consists of an infinite number of states, unlike those discussed above which had only four. This complication may be partly avoided if one takes into account that the scalar product in Eq. (4.55) does not depend on the projection index m. From spherical isotropy of space, Eq. (4.55) may be expressed via reduced matrix elements (/ a(0 /) as follows... 

The index n is the radial degree and the index m is the azimuthal frequency. The function R r) is a radial function given by... 

Provided that the m variances Vj - sj are roughly equal (Bartlett s test, see Section 1.7.3), the m means are ordered (cf. subroutine SORT, Table 5.17). The smallest mean has index 1, the largest has index m. A triangular matrix (see Tables 4.9, 4.10) is then printed that gives the m (m- l)/2 differences AXmean.wi = Xmean.M Xmean.i for all possible pairings. Every element of the... 

A composite index for the United States process plant industry is published monthly in the journal Chemical Engineering, the CPE plant cost index. This journal also publishes the Marshall and Swift index (M and S equipment cost index), base year 1926. The CPE index over a ten-year period is shown in Figure 6.1 b. 

The polydispersity index, M /M, values of comparable samples 78-C24 (V, plus ETCA) and 78-Elln(V0CL, no ETCA) in Figure 7C were 3.95 and 4.79, respectively. Another set of comparable... 

Figure 7. Modulation index (m), as a function of filter centre wavelength, assuming the reference and measurement cells contain 100% C02 gas at 1 Bar, 20 °C and are of lm length. An optical filter with 2 nm FWHM bandwidth is assumed. This shows that, with this filter bandwidth, the maximum modulation index occurs at a filter centre wavelength of 2.004 pm.

Figure 9. C02 Detection variation of modulation Index (m), with optical filter centre wavelength and bandwidth. The broad range of absorption lines causes a very complex variation of modulation indices when using narrow filters (not all peaks at narrow filter bandwidths are shown, as this would obscure the behaviour with wider filter bandwidths). Reference and measurement cells are assumed to he of 1 m length and contain 100% C02 gas at 1 Bar/20 °C.

Figure 10. Predicted modulation index (m), as a function of C02 gas concentration (%v/v) in the measurement cell. Reference and measurement cells were of lm length and the reference cell contained 100% C02 gas at lBar/20 °C. A choice of optical filter, having a bandwidth of 100 nm and a centre wavelength of 2.004 pm, was assumed.

As in energy representation the fundamental thermodynamic equation in entropy representation (3) may also be subjected to Legendre transformation to generate a series of characteristic functions designated as Massieu-Planck (MP) functions, m. The index m denotes the number of intensive parameters introduced as independent variables, i.e. 

Take the electron from just outside the solution across to a position just outside the metal the work required is — e0( m — ips) the index m denotes the metal, s the solution. 

The interface is in contact with two bulk phases, the metal electrode (index m ) and the solution (index s). Formally, we consider the metal to be composed of metal atoms M, metal ions Mz+, and electrons e " these particles are present both in the electrode and the interface, but not in the solution. On the other hand, certain cations and anions and neutral species occur both in the solution and the interface. Since the electrode is ideally polarizable, no charged species can pass through the interface. 

Figures also display an index m (see, for example, l(n) in Figure 6) and this serves to indicate the number of repeating units of the bridge. For l(n), n = 2m + 2...

Power law depentanizer f(c/c ) = const(c/c )m is postulated for the semi-diluted solution (c/c 1), in which the unknown index m accordingly to the second position of the Scaling method is from independence n on the length of a chain. This leads to the value m = 1/(3 v— l), that is m = 4/5 for d= 3-dimensional space. That is why the expression (6) is as follow... 

Here the film coefficients are in kW/m2 K and the fluidising velocity uc is in m/s. As equation 6.54 is not in dimensionally consistent units (because some of the relevant properties were not varied), the coefficient, 24.4, is valid only for the units stated. The value of the index m is given by ... 

The photoinduced absorbance anisotropy in a TPD experiment relaxes according to the same correlation function as in Eq. (4.16).(29) Effects of spatial variations in the excitation and probe beams, and chromophore concentration, have been treated and shown not to alter the final result.(29) NMR dipolar relaxation rates are expressed in terms of Fourier transforms of the correlation functions, 4ji< T2m[fi(0)] T2m[i2(f)]>> where fl(f) denotes the orientation of a particular internuclear vector. In view of Eq. (4.7), these correlation functions are independent of the index m, hence formally the same as in Eq. (4.16). For the analysis of NMR relaxation data, it is necessary also to evaluate Fourier transforms of the correlation functions. Methods to accomplish this in the case of deformable DNAs have been developed and applied to analyze a variety of data.(81 83)... 

Figure 8.4. The ratio of the volume-averaged local field to the square of the incident field El, for a particle S /an in diameter and having a refractive index m = 1.47 + 10 6 i.

GPT = glutamic pyruvic transaminase GSH = glutathione Hemato = hematological hr = hour(s) LCso= lethal concentration. 50% kill LOAEL = lowest-observed-adverse-effect level LI = labeling index M = male min = mlnute(s) mo = moth(s) musc/skel = musculoskeletal NOAEL = no-observed-adverse-effect level NS = not specified Resp = respiratory ... 

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