Frequency continued ratio

The theorem can be exemplified by considering the effect of the perturbation on the phase-space tori. Tori of the unperturbed Hamiltonian with incommensurate frequencies continue to exist, being only slightly distorted by the perturbation. On the other hand, the tori with commensurate frequencies, or with incommensurate frequencies whose ratio is well approximated by a ratio of small integers are grossly deformed. The KAM... 

Flowever, it also necessitates a strictly constant ratio of field to frequency, over the duration of the experiment. Although the master frequency source can be held very constant by a thennostatted source, the field is always vulnerable to local movements of metal, and to any non-persistence of the magnet current. Therefore the field is locked to the frequency tlirough a feedback loop that uses continuous, background... 

Figure 4.7 Changes in intraceiiuiar calcium in cultured rat ventricular myocytes exposed to oxidant stress. Calcium was measured using the fluorescent probe Fura>2. The ratio of the Fura-2 fluorescence measured at 340 and 380 nm excitation is shown and this is proportional to the intracellular calcium concentration. The fast-speed traces shown (note the 3.5 s time-scale) were recorded after various durations of oxidant stress. Myocytes under control conditions (before t = 0) show spontaneous calcium transients. These transients decreased in frequency with oxidant stress until cells failed to show spontaneous activity but continued to maintain a low intracellular calcium.

Fisher s exact test should be used to compare two sets of discontinuous, quantal (all or none) data. Small sets of such data can be checked by contingency data tables, such as those of Finney et al. (1963). Larger sets, however, require computation. These include frequency data such as incidences of mortality or certain histopatho-logical findings, and so on. Thus, the data can be expressed as ratios. These data do not fit on a continuous scale of measurement but usually involve numbers of responses classified as either negative or positive that is, contingency table situation (Sokal and Rohlf, 1994). 

Crystals lack some of the dynamic complexity of solutions, but are still a challenging subject for theoretical modeling. Long-range order and forces in crystals cause their spectrum of vibrational frequencies to appear more like a continuum than a series of discrete modes. Reduced partition function ratios for a continuous vibrational spectrum can be calculated using an integral, rather than the hnite product used in Equation (3) (Kieffer 1982),... 

Quadrupole mass analyzers consist of four rods that produce a radio frequency quadrupole field. Only a single mass-to-charge ratio has a stable trajectory through the mass analyzer, but the electric potentials can be swept rapidly, either continuously or in discrete steps to measure a variety of masses. Quadrupole mass spectrometers are used in a wide variety of applications, but are not widely used in cosmochemistry. 

One of the main advantages of FT spectrometers is that, since the FID is in digital form, we can repeat the excitation/detection process a number of times and all the resulting scans can be added and the FT performed on the resultant FID. In this way, we can improve the signal-to-noise ratio and can detect nuclei which are not very abundant (e.g. C) or have low sensitivity to NMR (see Section 4.2). These nuclei could not have been detected on the older continuous wave instruments, as the spectrum was the result of a single scan, obtained as one of the frequency or magnetic held were varied while keeping the other constant. 

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