This paper adopts the Riemann-Hilbert method to investigate a variable coefficient nonlocal Gerdjikov-Ivanov (GI) equation. A solvable regular Riemann-Hilbert problem with simple zeros is constructed through spectral analysis. Furthermore, the paper provides the determinant form of N-solutions for the equation.
A novel chaotic system called complex Rikitake system is proposed. Dynamical properties, including symmetry, dissipation, stability of equilibria, Lyapunov exponents and bifurcation, are analyzed on the basis of theoretical analysis and numerical simulation. Further, based on feedback control method, the complex Rikitake system can be controlled to any equilibrium points. Additionally, this paper not only proves the existence of two types of synchronization schemes in the complex Rikitake system but also designs adaptive controllers to realize them. The proposed results are verified by numerical simulations.
Appropriate exercise such as voluntary wheel-running can induce physiological cardiac hypertrophy. Notch1 plays an important role in cardiac hypertrophy; however, the experimental results are inconsistent. In this experiment, we aimed to explore the role of Notch1 in physiological cardiac hypertrophy. Twenty-nine adult male mice were randomly divided into a Notch1 heterozygous deficient control (Notch1+/- CON) group, a Notch1 heterozygous deficient running (Notch1+/- RUN) group, a wild type control (WT CON) group, and a wild type running (WT RUN) group. Mice in the Notch1+/- RUN and WT RUN groups had access to voluntary wheel-running for two weeks. Next, the cardiac function of all of the mice was examined by echocardiography. The H&E staining, Masson trichrome staining, and a Western blot assay were carried out to analyze cardiac hypertrophy, cardiac fibrosis, and the expression of proteins relating to cardiac hypertrophy. After two-weeks of running, the Notch1 receptor expression was decreased in the hearts of the WT RUN group. The degree of cardiac hypertrophy in the Notch1+/- RUN mice was lower than that of their littermate control. Compared to the Notch1+/- CON group, Notch1 heterozygous deficiency could lead to a decrease in Beclin-1 expression and the ratio of LC3II/LC3I in the Notch1+/- RUN group. The results suggest that Notch1 heterozygous deficiency could partly dampen the induction of autophagy. Moreover, Notch1 deficiency may lead to the inactivation of p38 and the reduction of β-catenin expression in the Notch1+/- RUN group. In conclusion, Notch1 plays a critical role in physiologic cardiac hypertrophy through the p38 signaling pathway. Our results will help to understand the underlying mechanism of Notch1 on physiological cardiac hypertrophy.
A series of urban law enforcement events involving city inspectors dispatched by the city management department can reflect some problems in smart city management, such as illegal advertising and unlicensed street operation. In this paper, we propose a model for the allocation of city inspectors and the optimization of patrol paths. The objective is to minimize the average response time and the number of inspectors. We also develop a priority-patrol-and-multiobjective genetic algorithm (DP-MOGA) to classify patrol segments according to the frequency of events and develop an improved genetic algorithm to achieve the aforementioned objective. We conduct numerical experiments using patrol data obtained from city inspectors in Zhengzhou, China, to clearly show that the proposed algorithm generates reasonable routes that reduce the average response time of events and the number of patrol inspectors. Furthermore, we test the algorithm for three different time scenarios (roads with different average numbers of events) and demonstrate the efficiency of the algorithm. The experimental results show that our proposed algorithm is more stable and efficient than other existing algorithms.
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