Symmetrical lines

A diagonal matrix has nonzero elements only on the principal diagonal and zeros elsewhere. The unit matrix is a diagonal matrix. Large matrices with small matrices symmetrically lined up along the principal diagonal are sometimes encountered in computational chemistry. 

In radial lines this is determined for the entire length of line while for symmetrical lines, it is calculated up to the mid-point, i.e. it refers to 0/2. 

In the first case, if we had considered a safe line length of 250 km, this would become 500 km for a symmetrical line. Figure 24.18 illustrates such a condition. Depending upon the length and type of line, a line length compensation may be required. Most transmission lines are seen to be within permissible lengths and only a few may require such a compensation. Nevertheless, it may be worth reducing the phase displacement between E, and to less than 15° electrical, to further iinprove the quality and stability level of power transmission. 

Figure 24.18 Voltage profile of a 400 kV/400 km symmetrical line on a no-load illustrating the Ferranti effect...

Line length effect or Ferranti effect, sin 6, that will determine the optimum line length which will also depend upon whether it is a radial or a symmetrical line. 

A line can be theoretically loaded up to these levels. But at these levels, during a load variation, the far-end voltage may swing far beyond the desirable limits of 5% and the system may not remain stable. With the use of reactive control it is possible to transfer power at the optimum level (Pnias) hd yet maintain the far-end (or midpoint in symmetrical lines) voltage near to and also to have a near-flat voltage profile. 

It will be useful to outline the basic features of solid state 2H NMR spectra. Deuteron is a spin 7= 1 nucleus possessing an electric quadrupole moment. The EFG interacts with the electric quadrupole moment to produce a frequency shift. Frequencies of the symmetric line shape centred around the Larmor frequency >0, which depend on the relative orientation of an external magnetic field B0 and the EFG tensor, are given by1 7... 

In these formulae, Gd is the desymmetrized profile, Gc is the classical (symmetric) line profile c and T are angular frequency and temperature. In all cases, the desymmetrized function Go(ft>) obeys Eq. 5.73 exactly. We note that at low frequencies, h(o < kT, the four expressions are practically equivalent. However, at high frequencies the results of these desymmetrizations differ strikingly. One needs only to compare the magnitude of the factors of Gc of the upper three defining equations, for ft) — +oo, to realize enormous differences among these. Hence, the question arises as to which one (if any) of these procedures approximates the exact quantum profile, G(co). We note that in EgelstafFs procedure the desymmetrization is accomplished in the time domain rather than the frequency domain. The classical correlation function, Cci(t), and spectral function, Gci (co), are related by Fourier transform. 

The striking feature of the compartmental lines on the wing disc is their clear twofold symmetry. Anterior, posterior, ventral, and dorsal quan-drants look fundamentally similar. Good evidence suggests that these compartmental lines arise in situ in the growing disc, and do not reflect movement of cells relative to one another. Therefore, the question arises of how such symmetrical lines might arise. 

The 31P spectra consist of two lines at -24 and -26 ppm with equal intensity (Figure 8). Dense aluminium phosphates and AlPO-n materials generally show a single symmetrical line in the range from -19 till -30 ppm, consistent with the presence of tetrahedral phosphorus (14). A1P04-H, is actually the first aluminum phosphate for which a 1P spectrum with two tetrahedral lines is... 

Note Added in Proof Doniach and Sunjic [J. Phys. C3, 285 (1970)] have presented a theory for core level line shape assymetry associated with the excitation of low-energy electron-hole pairs in a metal. This skews the otherwise symmetric line towards higher binding energy and such shapes have been observed experimentally [e.g. P. H. Citrin, Phys. Rev. B 8, 5545 (1973) ... 

Sodium-23 MASNMR measurements have been used to examine the extent to which this method can be used to determine the cation distribution in hydrated and dehydrated Y-zeolites. Results have been obtained on Na-Y and series of partially exchanged (NH, Na)-Y, (Ca,Na)-Y and (La,Na)-Y zeolites which demonstrate that the sodium cations in the supercages can be distinguished from those in the smaller sodalite cages and hexagonal prisms. For the hydrated Y zeolites, spectral simulation with symmetric lines allows the cation distribution to be determined quantitatively. 

Spectrum is presented by a narrow symmetric line. If all lithium ions occupy octahedral sites, the broadening of line shonld appear owing to electric field gradient. 

This approach is similar to the use of the field variation of the centre of gravity of the MAS centreband, but has the advantage that the narrower, more symmetric line makes determination of the correct position of the centre of gravity more precise. For experiments carried out at two magnetic fields where the Larmor frequencies are voi and vo2 for the measured DOR peak positions (in ppm) at the two magnetic fields of 8dori,2 then... 

The groundwater flow into a well also can be analyzed by using a flow net. Because the well is symmetrical, lines of constant drawdown (isopotentials) are circles centered at the center of the well (Fig. 3-11). Streamlines are arranged radially around the well if there is no regional flow in the aquifer. 

Also in the photoemission case the signature of the multilayer spectrum is essentially conserved at the interface, but in this case minor changes occur. The peak at 286.2 eV in the multilayer spectram, which is due to a shake up excitation, is almost completely quenched for the monolayer data. Moreover, the symmetric line shape of the multilayer C Is line is slightly changed in the monolayer it becomes more asymmetric with additional spectral weight on the low energy side. At the same time the line width is slightly reduced from 0.7 eV to about 0.6 eV. While the latter observation could be explained by a... 

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