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Combination of Parallel Magnetic Resonance Imaging and Compressed Sensing Using L1-SPIRiT
Published in Joseph Suresh Paul, Raji Susan Mathew, Regularized Image Reconstruction in Parallel MRI with MATLAB®, 2019
Joseph Suresh Paul, Raji Susan Mathew
Since the SPIRiT calibration kernel chooses an entire neighborhood compared to GRAPPA, the polynomial mapping is modified before applying to the non-linear calibration of SPIRiT. The polynomial mapping is modified such that all first-order terms and high-order self-terms are kept while truncating all the high-order cross-terms. For a vector =[a1,a2,…,aK]., the modified polynomial mapping is obtained as: () φ(a)=[1,a1,a2,…,aK,a12,…,aK2,a13…,aK3].
Complete stability assessment of LTI systems with multiple constant-coefficient distributed delays using the improved frequency sweeping framework
Published in International Journal of Systems Science, 2023
Qingbin Gao, Jiazhi Cai, Zhenyu Zhang, Zhili Long
We arbitrarily fix and in (36). The maximum feasible solution of is obtained as by the procedures in Section 3.1. Then, the exact lower and upper bounds of the projected imaginary spectra are obtained as 0 and 2.8771 as per Remark 3.1 and Theorem 3.1, respectively. We scan ω within the corresponding range to get the KOH as per Definitions 2.1 and 2.2. Moreover, the SRB is precisely calculated by (32) as a linear equation: Next, a numerical method named Quasi-Polynomial mapping-based Root Finder (QPmR) (Vyhlidal & Zítek, 2009) is employed for the determination of the stability at the point . The QPmR algorithm can approximate the roots of the quasi-polynomial Equation (9) for a given search region in the complex plane. Finally, we utilise the CTCR paradigm to get the complete stability map of the system (35), as shown in Figure 2. Note that the system is significant only when , i.e. only the upper left half of the stability map is tested. As depicted, the SRB is under the line , thus it cannot affect the stability of the actual system.
Interpretation of wake instability at slip line in rotating detonation
Published in International Journal of Computational Fluid Dynamics, 2018
Pengxin Liu, Qin Li, Zhangfeng Huang, Hanxin Zhang
In Li, Liu, and Zhang (2015) new piecewise-polynomial mapping functions were proposed to improve the performance of WENO5, which was fulfilled by invoking a revision on obtained by Equation (8). A fifth-order version of mapping functions is used here as where and . At last, the final nonlinear weights will be acquired by normalising the newly obtained through . The corresponding scheme is called as WENO-PPM5. For more details one can refer Li, Liu, and Zhang (2015). The scheme for the negative part of the flux can be derived according to the symmetry of the algorithm with respect to .
Computation of PI Controllers Ensuring Desired Gain and Phase Margins for Two-Area Load Frequency Control System with Communication Time Delays
Published in Electric Power Components and Systems, 2018
Finally, the accuracy of region boundaries obtained by the proposed method is verified by an independent algorithm, the quasi-polynomial mapping-based root finder (QPmR), which is the third main contribution of this study. The QPmR algorithm is a numerical procedure to computing the spectrum (zeros) of quasi-polynomials over large regions of the complex plane [20] and its effectiveness has been proved by numerous recent studies [21,22]. The accuracy of delay margin results is also validated by time-domain simulations [23]. Simulation results indicate that GPMs as an indication of stability margin should be included in the delay-dependent stability analysis of LFC systems to achieve an improved frequency response in terms of less overshoot, oscillations and shorter settling time.