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Global weak solutions for the relativistic Vlasov-Klein-Gordon system in two dimensions
Meixia Xiao,Xianwen Zhang 대한수학회 2018 대한수학회보 Vol.55 No.2
This paper is concerned with global existence of weak solutions to the relativistic Vlasov-Klein-Gordon system. The energy of this system is conserved, but the interaction term $\int_{\mathbb{R}^{n}}\rho\varphi dx$ in it need not be positive. So far existence of global weak solutions has been established only for small initial data \cite{Kunzinger0001,Wei0001}. In two dimensions, this paper shows that the interaction term can be estimated by the kinetic energy to the power of $\frac{4q-4}{3q-2}$ for $1<q<2$. As a consequence, global existence of weak solutions for general initial data is obtained.
Mild solutions for the relativistic Vlasov-Klein-Gordon system
Meixia Xiao,Xianwen Zhang 대한수학회 2019 대한수학회보 Vol.56 No.6
In this paper, the relativistic Vlasov-Klein-Gordon system in one dimension is investigated. This non-linear dynamics system consists of a transport equation for the distribution function combined with Klein-Gordon equation. Without any assumption of continuity or compact support of any initial particle density $f_{0}$, we prove the existence and uniqueness of the mild solution via the iteration method.
Spectrum Leasing and Cooperative Resource Allocation in Cognitive OFDMA Networks
Meixia Tao,Yuan Liu 한국통신학회 2013 Journal of communications and networks Vol.15 No.1
This paper considers a cooperative orthogonal frequency division multiple access (OFDMA)-based cognitive radio network where the primary system leases some of its subchannels to the secondary system for a fraction of time in exchange for the secondary users (SUs) assisting the transmission of primary users (PUs) as relays. Our aim is to determine the cooperation strategies among the primary and secondary systems so as to maximize the sum-rate of SUs while maintaining quality-of-service (QoS) requirements of PUs. We formulate a joint optimization problem of PU transmission mode selection, SU (or relay) selection, subcarrier assignment,power control, and time allocation. By applying dual method, this mixed integer programming problem is decomposed into parallel per-subcarrier subproblems, with each determining the cooperation strategy between one PU and one SU. We show that, on each leased subcarrier, the optimal strategy is to let a SU exclusively act as a relay or transmit for itself. This result is fundamentally different from the conventional spectrum leasing in single-channel systems where a SU must transmit a fraction of time for itself if it helps the PU’s transmission. We then propose a subgradient-based algorithm to find the asymptotically optimal solution to the primal problem in polynomial time. Simulation results demonstrate that the proposed algorithm can significantly enhance the network performance.
Wang Meixia,Wang Huiping 한국기상학회 2021 Asia-Pacific Journal of Atmospheric Sciences Vol.57 No.1
Based on the PM2.5 concentration and economic and social data in the Yangtze River Delta during 2006–2016, the spatial distribution characteristics of PM2.5 pollution and the spatial heterogeneity of its influencing factors are analyzed using exploratory spatial data analysis and a geographically weighted regression model. The results show the following . The PM2.5 pollution situation is serious and presents a remarkable feature of spatial agglomeration in the Yangtze River Delta. Highly polluted areas are mainly concentrated in the northern cities of the Yangtze River Delta, while the air quality of the southern cities of the Yangtze River Delta is better. There is a significant positive spatial spillover effect of PM2.5 pollution in the Yangtze River Delta, which is to say that the air quality will be worsened by the PM2.5 pollution of surrounding cities . The influence coefficients of the population density, industrial proportion, car ownership and FDI on PM2.5 have spatial heterogeneity; that is, there are significant differences in their degrees of influence between different periods and cities.
GLOBAL WEAK SOLUTIONS FOR THE RELATIVISTIC VLASOV-KLEIN-GORDON SYSTEM IN TWO DIMENSIONS
Xiao, Meixia,Zhang, Xianwen Korean Mathematical Society 2018 대한수학회보 Vol.55 No.2
This paper is concerned with global existence of weak solutions to the relativistic Vlasov-Klein-Gordon system. The energy of this system is conserved, but the interaction term ${\int}_{{\mathbb{R}}^n}\;{\rho}{\varphi}dx$ in it need not be positive. So far existence of global weak solutions has been established only for small initial data [9, 14]. In two dimensions, this paper shows that the interaction term can be estimated by the kinetic energy to the power of ${\frac{4q-4}{3q-2}}$ for 1 < q < 2. As a consequence, global existence of weak solutions for general initial data is obtained.
MILD SOLUTIONS FOR THE RELATIVISTIC VLASOV-KLEIN-GORDON SYSTEM
Xiao, Meixia,Zhang, Xianwen Korean Mathematical Society 2019 대한수학회보 Vol.56 No.6
In this paper, the relativistic Vlasov-Klein-Gordon system in one dimension is investigated. This non-linear dynamics system consists of a transport equation for the distribution function combined with Klein-Gordon equation. Without any assumption of continuity or compact support of any initial particle density $f_0$, we prove the existence and uniqueness of the mild solution via the iteration method.
Spectrum Leasing and Cooperative Resource Allocation in Cognitive OFDMA Networks
Tao, Meixia,Liu, Yuan The Korea Institute of Information and Commucation 2013 Journal of communications and networks Vol.15 No.1
This paper considers a cooperative orthogonal frequency division multiple access (OFDMA)-based cognitive radio network where the primary system leases some of its subchannels to the secondary system for a fraction of time in exchange for the secondary users (SUs) assisting the transmission of primary users (PUs) as relays. Our aim is to determine the cooperation strategies among the primary and secondary systems so as to maximize the sum-rate of SUs while maintaining quality-of-service (QoS) requirements of PUs. We formulate a joint optimization problem of PU transmission mode selection, SU (or relay) selection, subcarrier assignment, power control, and time allocation. By applying dual method, this mixed integer programming problem is decomposed into parallel per-subcarrier subproblems, with each determining the cooperation strategy between one PU and one SU. We show that, on each leased subcarrier, the optimal strategy is to let a SU exclusively act as a relay or transmit for itself. This result is fundamentally different from the conventional spectrum leasing in single-channel systems where a SU must transmit a fraction of time for itself if it helps the PU's transmission. We then propose a subgradient-based algorithm to find the asymptotically optimal solution to the primal problem in polynomial time. Simulation results demonstrate that the proposed algorithm can significantly enhance the network performance.
Multiple Constrained Dynamic Path Optimization based on Improved Ant Colony Algorithm
Seng Dewen,Tang Meixia,Wu Hao,Fang Xujian,Xu Haitao 보안공학연구지원센터 2014 International Journal of u- and e- Service, Scienc Vol.7 No.6
Vehicle navigation system can effectively alleviate traffic congestion, reduce pollution, and reduce travel cost and other problems. As is known to all, the traditional ones are all just static path planning with problems of not only weak effectiveness but also lack of standard optimal path options. They usually provide only one path which represents the shortest time or shortest distance, and ignore the actual demands of the dirivers. Based on traffic data of the past, the upcoming traffic flows can be estimated. With the help of the improved ant colony algorithm, the dynamic optimal path planning results will meet the need of the travelers according with multiple actual constraints.
New Terminal Sliding Mode Consensus Algorithm for Disturbed Second-order Multi-agent Systems
Yan Ren,Huimin Wang,Meixia Yue,Kai Weng,Wei Gao,Ning Liu,Dong Xie 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.8
A finite-time adaptive tracking control algorithm based on non-singular terminal sliding mode (NTSM) is proposed to solve the consensus problem of second-order multi-agent system (MAS) with disturbance. Firstly, a finite-time disturbance observer based on NTSM is introduced to estimate and compensate the disturbance. Then, a NTSM adaptive controller is designed to enhance the robustness of the system, and improve the response speed and tracking accuracy. A proof of the finite-time convergence of the method is given by using Lyapunov theory. Finally, simulation experiments are carried out to demonstrate the effectiveness of the proposed method.