Convergence Analysis of the Fast Subspace Descent Methods for Convex Optimization Problems

The full approximation storage (FAS) scheme is a widely used multigrid method for nonlinear problems. In this paper, a new framework to design and analyze FAS-like schemes for convex optimization problems is developed. The new method, the Fast Subspace Descent (FASD) scheme, which generalizes classical FAS, can be recast as an inexact version of nonlinear multigrid methods based on space decomposition and subspace correction. The local problem in each subspace can be simplified to be linear and one gradient descent iteration (with an appropriate step size) is enough to ensure a global linear (geometric) convergence of FASD.Comment: 33 page

Double synchronization states of two exciters with horizontal asymmetric structure in a vibrating system

Synchronization of two exciters with asymmetric structure is more widely used in engineering, such as vibrating conveyer, dewatering screen, vibrating screen, however, the synchronization state of two exciters with asymmetric structure in the sub-resonant and super-resonant states is less considered, and it is a valuable research topic. Firstly, we establish a kind of weakly nonlinear vibrating system driven by two exciters with opposite rotation directions and asymmetrical structure. Using Lagrange equations, the differential equations of the vibrating system are obtained. Secondly, we apply Fourier series expansion to obtain the nonlinear elastic force of the nonlinear stiffness. Thirdly, we introduce the modified averaging method of small parameters and Hamilton’s principle to get the criterions of synchronization synchronization stability of two exciters. The theoretical analysis shows that the phase differences are stabilized in the vicinity of Pi phase difference in a super-resonant state when l0 approaches to le, otherwise, in the neighborhood of zero phase difference in a sub-resonant state. Then, the above theory is verified by experiments. The stable phase difference, amplitudes responses and energy consumption are also discussed. This research provides the foundation and guidance for the synchronization of two exciters with horizontal asymmetrical structure and engineering design

Numerical and experimental investigation on self-synchronization of two eccentric rotors in the vibration system

In this paper, we study the coupling dynamic characteristic of a single mass vibration machine driven by two eccentric rotors rotating oppositely. According to the coordinate of rotor flux, we deduce the electromagnetic torque of an induction motor in the steady state operation. From three ways of numerical analysis, model simulation and experiment, we discuss the coupling dynamic characteristic by using the actual parameters of this vibration machine. The results show that when the synchronization condition is satisfied, not only the vibration synchronization transmission can be achieved, but also the synchronization motion of the two motors with different power supply frequencies also can be achieved. The phase of the bigger mass-radius product lags behind that of the smaller one, the phase of the bigger distance between the rotation center of eccentric rotor and the mass center of the vibration rigid body lags behind that of the smaller one, and the phase difference decreases with increasing the synchronization velocity. We present a new method that adjusting the power supply frequencies of the two motors to make the vibration system with different structure parameters carry out the 0 phase difference, and its feasibility is verified by experiment

Cytidine-phosphate-guanosine oligodeoxynucleotides in combination with CD40 ligand decrease periodontal inflammation and alveolar bone loss in a TLR9-independent manner

Local administration of toll-like receptor 9 (TLR9), agonist cytidine-phosphate-guanosine oligodeoxynucleotide (CpG ODNs), and CD40 ligand (CD40L) can decrease ligature-induced periodontal inflammation and bone loss in wild type (WT) mouse. Objective: This study aimed to explore whether such effect is dependent on TLR9 signaling. Material and Methods: Purified spleen B cells isolated from WT C57BL/6J mice and TLR9 knockout (KO) mice were cultured for 48 hours under the following conditions: CD40L, CpG+CD40L, CpG at low, medium and high doses. We determined B cell numbers using a hemocytometer at 24 h and 48 h. Percentages of CD1dhiCD5+ B cells were detected by flow cytometry. Interleukin-10 (IL-10) mRNA expression and protein secretion were measured by quantitative real-time polymerase chain reaction (qRT-PCR) and by ELISA, respectively. The silk ligature was tied around the maxillary second molars for 14 days, during which the CpG+CD40L mixture or PBS was injected into palatal gingiva on days 3, 6, and 9. Results: For both WT and TLR9 KO mice, CpG significantly induced B cell proliferation, increased IL-10 mRNA expression and protein secretion of IL-10 but reduced CD1dhiCD5+ B cells population; local injection of CpG+CD40L mixture significantly decreased alveolar bone loss and the number of TRAP-positive cells adjacent to the alveolar bone surface, and significantly increased the gingival mRNA expression of IL-10 and decreased RANKL and IFN-γ mRNA expression. Conclusions: These results indicated that CpG plus CD40L decreased periodontal inflammation and alveolar bone loss in a TLR9-independent manner in ligature-induced experimental periodontitis

Synchronization and coupling dynamic characteristics of a dual-rotors exciter

In this work, some theoretical analyses, numerical simulations and experimental results on synchronization of a dual-rotors exciter are given. The exciter is made up of two rotors with eccentric masses (REMs) respectively driven by two DC motors with common axis. By adjusting the phase difference between two REMs to change the response amplitude, the decoupling between response amplitude and exciting frequency can be realized. The motion equations of the vibration system are established by using Lagrange equation, and the dimensionless coupling equations of that are obtained by applying the average method of small parameter. According to the existence condition of the zero solution of the dimensionless coupling equations, the synchronization condition of the vibration system is obtained. The stability condition of the vibration system implementing synchronization motion is acquired based on the principle of Hamilton. Through the comparison between numerical simulations and experimental results, the validity of theoretical analyses is proved, which helps the design of the dual-rotors exciter

Numerical and experimental investigation on self-synchronization of two eccentric rotors in the vibration system

In this paper, we study the coupling dynamic characteristic of a single mass vibration machine driven by two eccentric rotors rotating oppositely. According to the coordinate of rotor flux, we deduce the electromagnetic torque of an induction motor in the steady state operation. From three ways of numerical analysis, model simulation and experiment, we discuss the coupling dynamic characteristic by using the actual parameters of this vibration machine. The results show that when the synchronization condition is satisfied, not only the vibration synchronization transmission can be achieved, but also the synchronization motion of the two motors with different power supply frequencies also can be achieved. The phase of the bigger mass-radius product lags behind that of the smaller one, the phase of the bigger distance between the rotation center of eccentric rotor and the mass center of the vibration rigid body lags behind that of the smaller one, and the phase difference decreases with increasing the synchronization velocity. We present a new method that adjusting the power supply frequencies of the two motors to make the vibration system with different structure parameters carry out the 0 phase difference, and its feasibility is verified by experiment