Harmonic first

The protection current produced by the usual full-wave rectifier has a 100-Hz alternating component of 48%. There are receivers with selective transmission filters for 100 Hz, which corresponds to the first harmonic of the cathodic protection currents [45]. With such a low-frequency test current, an inductive coupling with neighboring pipelines and cables is avoided, which leads to more exact defect location. 

The potential F(Fourier series, and usually the first harmonic suffices. 

Many electrical problems, or problems associated with the quality of the incoming power and internal to the motor, can be isolated by monitoring the line frequency. Line frequency refers to the frequency of the alternating current being supplied to the motor. In the case of 60-cycle power, monitoring of the fundamental or first harmonic (60 Hertz), second harmonic (120 Hz), and third harmonic (180 Hz) should be performed. 

Clearly, it is possible only in the case when the first harmonic dominates, that is, max is attained for k = 1, so that... 

Acoustic structure functions for pressure coupling in an open-closed tube, for the fundamental and first harmonic. 

Fig. 3.42 represents the symmetric bell shape curve of 7, i.e., the genuine fundamental harmonic ac polarogram, which means the curve of only 7F discriminated for 7C, e.g., by means of phase-selective ac polarography. The term "fundamental is related to the character of the polarographic cell as a non-linearized network whose response is not purely sinusoidal but consists of the sum of a series of sinusoidal signals at ) response, besides that of the second harmonic (2a>), the third harmonic (3a>), etc. 

In most cases, you will use the first harmonic and the normal first-derivative of the absorption spectrum will be presented. If your spectrum has very good S/N and has some regions where you would like better resolution, a second-derivative presentation may help. However, second derivatives from second harmonic detection are very costly in terms of S/N ratio and so you really do have to have a strong signal ... 

Specimen Potential (SCE) Fundamental (First harmonic (mV) Second Harmonic (mV) Third Harmonic (mV) i corr ( A) b a b c... 

Dimensional scaling theory [109] provides a natural means to examine electron-electron correlation, quantum phase transitions [110], and entanglement. The primary effect of electron correlation in the D 00 limit is to open up the dihedral angles from their Hartree-Fock values [109] of exactly 90°. Angles in the correlated solution are determined by the balance between centrifugal effects, which always favor 90°, and interelectron repulsions, which always favor 180°. Since the electrons are localized at the D 00 limit, one might need to add the first harmonic correction in the 1/D expansion to obtain... 

It is important to select the best laser source. For practical applications the first harmonic of Nd-YAG (1,064 nm) is preferential, because such a laser is powerful and exists in ruggedized industrial versions. It was foimd that the spectra are principally the same as under Aex = 355 nm (Fig. 8.15), but the characteristic line of F is much weaker and clearly seen only after a delay time of several microseconds when the overall intensity is already low. The characteristic Une of P at 254 nm is very weak and the strongest Unes in the spectra belong to Ca ions. 

For large j the first harmonic yi ps a1pi Xi dominates in the solution... 

Figure 3. Coherence, induced between two states (lowest and first-harmonic wave functions) and the nature of the hybrid superposition, which evolves with time.

Figure 7.10 shows a simplified emission spectrum of anthracene as it would be observed on a grating fluorimeter over a wide wavelength range. The real emission at around 400-500 nm is reproduced with lower intensity in the 800-1000 nm region which corresponds to the first harmonic. Higher order harmonics are not observed because of the limitations of the sensitivity... 

Figure 7.16 Outline of a frequency multiplier for laser light. Cj, C2, second harmonic generators WS, wavelength separator. The frequencies of light are shown as V (fundamental), y first harmonic and y3 second harmonic...

Now consider a contribution of the following terms to the series of Eq. (2). Prom the conditions at the channel wall and axis it follows that kn = nk1. Consequently, neither of the harmonics, excluding the first one, can be realized singly. For instance, for n = 2 the value of velocities u = (u + u2)1/2 at the extreme point of the flame front at the wall, turns out to be less than un, that is inadmissible. However, to the first harmonic one can add the others separately with a small weight / , in order to fulfill the conditions at all frontal points. 

Here, the effective temperature , r = S l(q), and denotes the amplitude of the first harmonic order parameter.The free energy is minimized with respect to A, at a given temperature and compared for the ordered and disordered phases. 

Fig. 10.18 Experimental coherence spectrum obtained with two anharmonic modulation frequencies I ] = 2.0 and I 2 = 2.7. Additional major peaks in the spectrum correspond to beat frequency (0.7 Hz), first harmonic of I ) (4.0 Hz), frequency sum (4.7 Hz), and first harmonic of / 2 (5.4 Hz). The red line represents the same experiment but with 10% of white noise added (Kikas et al., 2001b)...

Fig. 10.19 (a) Experimental dependence of coherence spectra on distance (10-120 cm) between the modulation source and the sensing array, (b) Ratios of intensities ao/ai at fundamental frequency and at its first harmonic, plotted as the function of distance. The breaks indicate disappearance of the higher harmonics with distance. They indicate softening of plume edges with distance due to diffusion... 

It would be premature, however, to state that the battle has been won, for several reasons. First, harmonized regulations on paper are only a first step. A second and more important one is the interpretation by those who enforce them. All those who have witnessed inspections know how much they depend on the individual doing the assessment. There are differences within one country, but even more between countries. Even when the rules on paper have been modified, the mindset is much slower to adapt to the changes. Reaping the benefits of harmonization in practice will lag behind the formal achievements. 

For a current source ( Rac>>dV/dI ) we set I-Ig=Iucos(a)t). By matching Fourier components we find that the first harmonic signal Vu is proportional to the dynamic resistance of the junction ... 

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