Positivity and geometric function theory constraints on pion scattering

This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with O(N) global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion relation in the z-variable, rather than the fixed channel dispersion relation. We have written down fully crossing symmetric dispersion relation for O(N) model in z-variable for three independent combinations of isospin amplitudes. We have presented three independent sum rules or locality constraints for the O(N) model arising from the fully crossing symmetric dispersion relations. We have derived three sets of positivity conditions. We have obtained two-sided bounds on Taylor coefficients of physical Pion amplitudes around the crossing symmetric point (for example, π+π−→ π0π0) applying the positivity conditions and the Bieberbach-Rogosinski inequalities from geometric function theory.

Single Versus Multi-channel Dispersion Analysis of Ultrasonic Guided Waves Propagating in Long Bones

Ultrasonic guided wave techniques have been applied to characterize cortical bone for osteoporosis assessment. Compared with the current gold-standard X-ray-based diagnostic methods, ultrasound-based techniques pose some advantages such as compactness, low cost, lack of ionizing radiation, and their ability to detect the mechanical properties of the cortex. Axial transmission technique with a source-receiver offset is employed to acquire the ultrasound data. The dispersion characteristics of the guided waves in bones are normally analyzed in the transformed domains using the dispersion curves. The transformed domain can be time-frequency map using a single channel or wavenumber-frequency (or phase velocity-frequency) map with multi-channels. In terms of acquisition effort, the first method is more cost- and time-effective than the latter. However, it remains unclear whether single-channel dispersion analysis can provide as much quantitative guided-wave information as the multi-channel analysis. The objective of this study is to compare the two methods using numerically simulated and ex vivo data of a simple bovine bone plate and explore their advantages and disadvantages. Both single- and multi-channel signal processing approaches are implemented using sparsity-constrained optimization algorithms to reinforce the focusing power. While the single-channel data acquisition and processing are much faster than those of the multi-channel, modal identification and analysis of the multi-channel data are straightforward and more convincing.

Estimation of Overspread Underwater Acoustic Channel Based on Low-Rank Matrix Recovery

In this paper, the estimation of overspread, i.e., doubly spread underwater acoustic (UWA) channels of strong dispersion is considered. We show that although the UWA channel dispersion causes the degeneration of channel sparsity, it leads to a low-rank structure especially when the channel delay-Doppler-spread function is separable in delay and Doppler domain. Therefore, we introduce the low-rank criterion to estimate the UWA channels, which can help to improve the estimation performance in the case of strong dispersion. The estimator is based on the discrete delay-Doppler-spread function representation of channel, and is formulated as a low-rank matrix recovery problem which can be solved by the singular value projection technique. Simulation examples are carried out to demonstrate the effectiveness of the proposed low-rank-based channel estimator.

Efficient T-OOFDM System to Mitigate the Dispersion of Long-Haul Optical Fiber Channel at Wans

Due to its attractive features, the utilization of fiber optics as a transmission medium with various applications is increased rapidly. In despite, when signals are transmitted with high data rates through ultra-long haul distances of single-mode fiber (SMF), which is usually used at wide area networks (WANs), the nonlinear dispersion of signals is raised. This phenomenon leads digital pulses to interfere with the adjacent pulses. In this paper, an optical orthogonal frequency division multiplexing based T-transform (T-OOFDM) system is proposed to mitigate the effect of fiber dispersion significantly and reduce the peak-to-average power ratio (PAPR) of the transmitted signal when compared with conventional optical OFDM (OOFDM) system. Simulations results confirmed by the analytical analysis demonstrated that the detrimental effects arising from fiber channel dispersion on the subcarrier orthogonality of the transmitted signals can be efficiently minimized by using T-OOFDM system. Moreover, the peak of the transmitted signal will be considerably reduced whilst preserving the average power of signals.