The authors present the detailed theory and the new results associated with the triple quantum (TQ) nutation and the line narrowing effect of the TQ resonance in the two-level NMR system which we reported previously. The TQ resonance is induced in the spin-locked system by the oscillating field produced by the sinusoidal phase modulation (PM) of the RF field. The theory predicts that the TQ nutation is accompanied by several higher frequency oscillations and we detected them experimentally by improving the detection system. These higher frequency oscillations are due to the fluctuation of the angle between the transverse or effective field causing the TQ nutation and the RF field. We obtain the result that the modulation index 2phim of the PM is the key parameter that essentially controls the conditions of the TQ resonance and the narrowing effect. Under the exact TQ resonance, the ratio of the TQ resonance frequency to the Larmor frequency of the RF field depends only on phim, and the secular part of the magnetic dipole Hamiltonian of a like spin system in the triply rotating frame disappears at a particular value of phim. The condition is different from that of the well-known magic angle condition.
An absolute quantitative analysis method has been recently developed as a third generation polymerase chain reaction method "PCR" for fractionated DNA. The method is designed to determine the number of DNA molecules in target DNA samples by counting the number of PCR products obtained from fractionated DNA. We applied EXCEL Macro to perform the conversion of two dimensional orthogonal coordinate (x, y) fluorescent signal plot data obtained by digital PCR device to two dimensional polar coordinate (r, θ) fluorescent signal plot data, followed by analyzing the angle (θ) histogram of plot data without overlapping of plot data occurring by two dimensional orthogonal coordinate (x, y) histogram. The analysis made it possible to identify gene mutation and count the number of DNA molecules with mutation faster and easier.
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