Resonance contour

When simple electrical RC filters are treated, the truncated exponential e, x,H(x) is indispensable. Its transform is given by (2n) 1/2(1 — jco)/( 1 + co2). If the truncated exponential is reflected about the origin, eliminating H(x) and leaving e x, the imaginary part of the transform disappears. We obtain the transform (2/7c)1/2/(l + co2). This is the resonance contour, Cauchy distribution, or Lorentzian shape encountered previously in Section III.B. 

The experimental set-up is presented in Fig. 6. In the inductive coil of the resonance contour of LC-generator it is placed cylindrical tipped ferrite rod used as probe. The investigated rectangular shape magnetic polymer composite film is displaced relatively the immovable ferrite tips. The scaiming of the film surface is realized along the previously marked net contour (Fig. 6). 

The change of magnetic particle concentration causes the change of inductance 6L of the resonance contour of LC-generator resulting in the frequency displacement of LC-generator 6f related with 6L by relation 6f/f =1/26L/L. This frequency displacement could be precision measured what stipulates the high sensitivity of the mefiiod. 

D. C. Raskazov et al. [2.13] used a modified Rankine viscometer with a closed-contour capillary. The distinctive feature of this viscometer was the removal of mercury, which creates the pressure in the capillary, to the region of room temperature and fixing the falling time of the mercury droplets by the noncontact method using high-quality resonance contour. The maximum relative error of experimental data, according to the author s evaluation did not exceed 2-2.3%. The content of impurities in Freon-21 amounted to 0.13%. 

The contour lines represent points of relative density 1.0, 0.9, 0.8,..0.1 for a hydrogen atom. This figure, with the added proton 1.06 A from the atom, gives the electron distribution the hydrogen molecule-ion would have (in the zeroth approximation) if the resonance phenomenon did not occur it is to be compared with figure 6 to show the effect of resonance. 

Figure 8.7 Diborane, BaH. (a) Contour map of pb in the plane of the terminal hydrogens, (b) Contour map of pb in the plane of the bridging hydrogens, (c) Calculated geometry, (d) Experimental geometry. (e) Interatomic H-H distances, (f) Ionic model, (g) Resonance structures, (h) Protonated doublebond model, (i) VSEPR domain model showing the two three-center, two-electron bridging domains, (j) Hybrid orbital model.

Figure 31 Superposition of the 10-ppm HMBC spectrum (filled black peaks) with the 9.9-ppm HMBC spectrum (dotted grey contours) of Cyclosporine A. In the 9.9-ppm spectrum, the chemical shifts are shifted in a quantized manner relative to the signals in the 10-ppm spectrum according to the first two digits of the high-order chemical shift. The two insets show the actual difference A<5 between the cross-peaks in the two spectra for the H-C(e) and the CH3N resonances of MeBmt 1.

Using strychnine (1) as a model compound, a pair of HSQC spectra are shown in Fig. 10.16. The top panel shows the HSQC spectrum of strychnine without multiplicity editing. All resonances have positive phase. The pulse sequence used is that shown in Fig. 10.15 with the pulse sequence operator enclosed in the box eliminated. In contrast, the multiplicity-edited variant of the experiment is shown in the bottom panel. The pulse sequence operator is comprised of a pair of 180° pulses simultaneously applied to both H and 13C. These pulses are flanked by the delays, A = l/2(xJcii), which invert the magnetization for the methylene signals (red contours in Fig. 10.16B), while leaving methine and methyl resonances (positive phase, black contours) unaffected. Other less commonly used direct heteronuclear shift correlation experiments have been described in the literature [47]. 

Fig. 10.16. (A) GHSQC spectrum of strychnine (1) using the pulse sequence shown in Fig. 10.15 without multiplicity editing. (B) Multiplicity-edited GHSQC spectrum of strychinine showing methylene resonances (red contours) inverted with methine resonances (black contours) with positive phase. (Strychnine has no methyl resonances.) Multiplicity-editing does have some cost in sensitivity, estimated to be 20% by the authors. For this reason, when severely sample limited, it is preferable to record an HSQC spectrum without multiplicity editing. Likewise, there is a sensitivity cost associated with the use of gradient based pulse sequences. For extremely small quantities of sample, non-gradient experiments are preferable.

Fig. 11.13 An N(CO)CA spectrum of the decapep- these two spectra in a stepwise fashion as inditide antamanide (contours) together with the cated by the arrows, all 15N and 13C resonances...

LOo is the resonance frequency in rad/s. Figure 1 shows a contour plot of the cross-relaxation rates versus correlation time and interproton distance, according to eqs. (1) and (2). For wqTc > V /2, c" is negative, directly... 

Such a small crystal behaves like an infinitely expanded crystal. However, if the crystal vibrations remain restricted to the center, one can clamp the outer edge to a crystal holder, without engendering undesired side effects. Moreover, contouring reduces the resonance intensity of undesired anharmonics. This limits the capacity of the resonator to maintain these oscillations considerably. 

Second, the resonance frequency of the cantilever must be high enough to follow the contour of the surface. In a typical application, the frequency of the corrugation signal during a scan is up to a few kHz. Therefore, the natural frequency of the cantilever must be greater than 10 kHz. 

IVCT). The second e value corresponds to the abundance of 28 Mo centers (see Ref. 5). Using an excitation line within the contour of the 1070-nm band gives rise to a resonance-Raman spectrum showing hve bands in the region between 900 and 200 cm very characteristic for all molybdenum blue species [802 (s), 535 (m), 462 (s), 326 (s), 215 (s) cm ]. 

Figures 13.7 and 13.8 are two examples of two-dimensional NMR spectroscopy applied to polymers. Figure 13.7 is the proton homonuclear correlated spectroscopy (COSY) contour plot of Allied 8207A poly(amide) 6 [29]. In this experiment, the normal NMR spectrum is along the diagonal. Whenever a cross peak occurs, it is indicative of protons that are three bonds apart. Consequently, the backbone methylenes of this particular polymer can be traced through their J-coupling. Figure 13.8 is the proton-carbon correlated (HETCOR) contour plot of Nylon 6 [29]. This experiment permits the mapping of the proton resonances into the carbon-13 resonances.

Fig. 2.54 presents a two-dimensional carbon-proton shift correlation of D-lactose after mutarotational equilibration (40% a-, 60% / -D-lactose in deuterium oxide), demonstrating the good resolution of overlapping proton resonances between 3.6 and 4 ppm by means of the larger frequency dispersion of carbon-13 shifts in the second dimension. The assignment known for one nucleus - carbon-13 in this case - can be used to analyze the crowded resonances of the other nucleus. This is the significance of the two-dimensional CH shift correlation, in addition to the identification of CH bonds. For practical evaluation, the contour plot shown in Fig. 2.54(b) proves to be more useful than the stacked representation (Fig. 2.54(a)). In the case of D-lactose, selective proton decoupling between 3.6 and 4 ppm would not afford results of similiar quality. 

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