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In this paper, we investigate a backward problem of 1D multi-term time–space fractional diffusion equation, which is ill-posed. With the help of quasi-reversibility regularization method, we give the regularization solution, based on some properties of Fourier transform and Mittag-Leffler functions. Besides, we establish a-priori and a-posteriori convergence estimates, respectively. Finally, we illustrate two numerical examples to verify the effectiveness and feasibility of our proposed method. • We firstly give the quasi-reversibility method to multi-term fractional equations. • We give the error estimates for the proposed method by a priori and a posteriori parameter choice rules, respectively. • We display two typical numerical examples to show the efficiency and accuracy of the method. [ABSTRACT FROM AUTHOR]

• Four inerter-based suppression mechanisms are designed and used in the vehicle suspension to restrain the vehicle shimmy. • The vehicle shimmy model using inerter-based suppression mechanism is established. • The effect of inerter-based suppression mechanism on the vehicle shimmy performance is analyzed to show its benefit. • The structural parameter optimization of the inerter-based suppression mechanism is investigated. Shimmy may occur in the vehicle normal driving process, which is a harmful motion and should be controlled in practical engineering. In order to improve the vehicle driving and handling stability, four kinds of passive inerter-based suppression mechanisms are proposed and applied in the vehicle suspension to improve its shimmy performance. The configurations S1 and S2 are composed of one inerter and one damper, which are in parallel-connected and series-connected, respectively, furthermore, an auxiliary spring is added to constitute configurations S3 and S4. Combined with the magic nonlinear tire model, the vehicle shimmy model with four inerter-based suppression mechanisms is established using Lagrange theory, its shimmy performance is studied using bifurcation analysis method, the stable area and limit cycle oscillation (LCO) magnitude of the system are obtained and compared with those of the original suspension system. The effect of the structural parameters of the inerter-based suppression mechanisms on the vehicle shimmy performance is analyzed, and the structural parameter optimization of the inerter-based suppression mechanism is investigated. The results show that the only parallel-connected and series-connected configurations S1 and S2 have little improvement effect on the vehicle shimmy performance. As the configurations S3 and S4 are used, the unstable area dominated by left and right steering shimmy reduces, the shimmy occurred vehicle velocity range becomes narrower and the maximum LCO magnitude of the front wheel swing motion becomes smaller, which suppresses the vehicle shimmy effectively and clarifies the benefits of the inerter and the necessity of adding the auxiliary spring. In addition, larger inertance of the inerter and smaller stiffness of the auxiliary spring is beneficial to improve the vehicle shimmy performance. The optimized structural parameters of the configurations S3 and S4 are obtained, which maintain the vehicle shimmy system stable, and further shorten the time for the vehicle shimmy system to reach stability. Therefore, the inerter-based suppression mechanism can effectively restrain the vehicle shimmy motion and give guiding significance for the design of vehicle shimmy suppression mechanism. [ABSTRACT FROM AUTHOR]

The issue of adaptive detection for double subspace (DOS) signals under the Gaussian noise background is investigated in this paper. The DOS signal has the special structure where the rows and columns of the matrix-valued signal lie in known subspaces with unknown coordinates. To deal with the DOS signal detection problem, two kinds of Gradient tests are proposed in homogeneous environments and partially homogeneous environments. Remarkably, the Durbin test, as well as its two-step version, is also used for the detector design, which is consistent with the existing methods. To evaluate the performance of the proposed methods, both simulated data and real data collected by IPIX radar are used. The results indicate that the Gradient tests ensure the constant false alarm rate property. Furthermore, the proposed detectors obtain relatively robust characteristics and achieve superior performance to existing competitors in some scenarios. [ABSTRACT FROM AUTHOR]