Spectral and temporal features of multiple spontaneous NMR-maser emissions

When a system composed of dissolved laser-polarized xenon with negative spin temperature is put inside a high field NMR magnet, a series of spontaneous maser emissions can be observed. We report here their spectral and temporal features using a processing model derived from the solution of the Bloch equations in the presence of radiation damping. We show, in particular, that by combining Fourier transformation and squared modulus, a parameter allowing the characterization of the burst of transverse magnetization can be determined. This parameter is shown to be correlated with the radiated energy. Moreover, this processing clearly reveals features which can probably be assigned to effects resulting from distant dipolar fields. Finally, the analysis of the experimental data reveals an unexpected behavior of the ¹²⁹Xe transverse self-relaxation.     

How accurately can the diffusion profiles indicate multiple fiber orientations? A study on general fiber crossings in diffusion MRI

The q-space imaging techniques and high angular resolution diffusion (HARD) imaging have shown promise to identify intravoxel multiple fibers. The measured orientation distribution function (ODF) and apparent diffusion coefficient (ADC) profiles can be used to identify the orientations of the actual intravoxel fibers. The present study aims to examine the accuracy of these profile-based orientation methods by comparing the angular deviations between the estimated local maxima of the profiles and the real fiber orientation for a fiber crossing simulated with various intersection angles under different b values in diffusion-weighted MRI experiments. Both noisy and noise-free environments were investigated. The diffusion spectrum imaging (DSI), q-ball imaging (QBI), and HARD techniques were used to generate ODF and ADC profiles. To provide a better comparison between ODF and ADC techniques, the phase-corrected angular deviations were also presented for the ADC method based on a circular spectrum mapping method. The results indicate that systematic angular deviations exist between the actual fiber orientations and the corresponding local maxima of either the ADC or ODF profiles. All methods are apt to underestimation of acute intersection and overestimation of obtuse intersection angle. For a typical slow-exchange fiber crossing, the ODF methods have a non-deviation zone around the 90 degrees intersection. Before the phase-correction, the deviation of ADC profiles approaches a peak at the 90 degrees intersection, while after the correction the ADC deviations are significantly reduced. When the b factor is larger than 1000 s/mm2, the ODF methods have smaller angular deviations than the ADC methods for the intersections close to 90 degrees . QBI method demonstrates a slight yet consistent advantage over the DSI method under the same conditions. In the noisy environment, the mean value of the deviation angles shows a high consistency with the corresponding deviation in the nose-free condition.     

BIFURCATION ANALYSIS OF A CLASS OF PLANAR PIECEWISE SMOOTH LINEAR-QUADRATIC SYSTEM

In this paper,we consider a planar piecewise smooth differential system consisting of a linear system and a quadratic Hamiltonian system.The quadratic system ha...     

The distribution of values of trigonometric sums with linearly independent frequencies: Kac's problem revisited

The average frequency with which a trigonometric sum having linearly independent frequencies achieves a given value in a specified time interval was solved by Kac in the form of a double integral. In the present paper, Kac's solution is generalized by allowing the amplitudes of the sinusoidal terms to be statistically independent random variables possessing compact probability density functions. The average frequency is expressed as a Fourier cosine series. Representative numerical calculations are shown. The asymptotic form of the average frequency is also discussed.