This paper investigates an improved SIR model for COVID-19 based on the Caputo fractional derivative. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system...This paper investigates an improved SIR model for COVID-19 based on the Caputo fractional derivative. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system. Numerical simulations were conducted using MATLAB, and the results indicate that our model is valuable for studying virus transmission.展开更多
We propose a restoration strategy using microgrids for restoring power supply to critical loads after an extreme event and thereby enhancing the resilience of the distribution power grid. The limited capacities of dis...We propose a restoration strategy using microgrids for restoring power supply to critical loads after an extreme event and thereby enhancing the resilience of the distribution power grid. The limited capacities of distributed generators(DGs) within the microgrids and those of intermittent energy sources such as wind and photovoltaic power are considered. An enhanced strategy model of the distribution network is established for maximizing the power supply to critical loads. Firstly, the importance of the load is quantified by using the analytic hierarchy process(AHP) and the model of the microgrid output is further improved. In the demand response mechanism, an interruptible load is used to suppress the fluctuation in the distributed power output. Secondly, piecewise linearization method is applied to address the power flow constraints. Then, the resilience enhancement model of the distribution network is transformed into a mixed integer quadratic programming problem. The CPLEX solver is adopted to solve the above problem on the MATLAB platform. Finally, the proposed method is verified by applying it to practical scenarios.展开更多
In this paper an introduction of the moving least squares approach is presented in the context of data approximation and interpolation problems in Geodesy.An application of this method is presented for geoid height ap...In this paper an introduction of the moving least squares approach is presented in the context of data approximation and interpolation problems in Geodesy.An application of this method is presented for geoid height approximation and interpolation using different polynomial basis functions for the approximant and interpolant,respectively,in a regular grid of geoid height data in the region 16.0417°≤φ≤47.9583°and 36.0417°≤λ≤69.9582°,with increment 0.0833°in both latitudal and longitudal directions.The results of approximation and interpolation are then compared with the geoid height data from GPS-Levelling approach.Using the standard deviation of the difference of the results,it is shown that the planar interpolant,with reciprocal of distance as weight function,is the best choice in this local approximation and interpolation problem.展开更多
Dynamic data replication is a technique used in data grid environments that helps to reduce access latency and network bandwidth utilization. Replication also increases data availability thereby enhancing system relia...Dynamic data replication is a technique used in data grid environments that helps to reduce access latency and network bandwidth utilization. Replication also increases data availability thereby enhancing system reliability. In this paper we discuss the issues with single-location strategies in large-scale data integration applications, and examine potential multiple-location schemes. Dynamic multiple-location replication is NP-complete in nature. We therefore transform the multiple-location problem into several classical mathematical problems with different parameter settings, to which efficient approximation algorithms apply experimental results indicate that unlike single-location strategies our multiple-location schemes are efficient with respect to access latency and bandwidth consumption, especially when the requesters of a data set are distributed over a large scale of locations.展开更多
It has been evident that the theory and methods of dynamic derivatives are playing an increasingly important role in hybrid modeling and computations. Being constructed on various kinds of hybrid grids, that is, tim...It has been evident that the theory and methods of dynamic derivatives are playing an increasingly important role in hybrid modeling and computations. Being constructed on various kinds of hybrid grids, that is, time scales, dynamic derivatives offer superior accuracy and flexibility in approximating mathematically important natural processes with hard-to-predict singularities, such as the epidemic growth with unpredictable jump sizes and option market changes with high uncertainties, as compared with conventional derivatives. In this article, we shall review the novel new concepts, explore delicate relations between the most frequently used second-order dynamic derivatives and conventional derivatives. We shall investigate necessary conditions for guaranteeing the consistency between the two derivatives. We will show that such a consistency may never exist in general. This implies that the dynamic derivatives provide entirely different new tools for sensitive modeling and approximations on hybrid grids. Rigorous error analysis will be given via asymptotic expansions for further modeling and computational applications. Numerical experiments will also be given.展开更多
文摘This paper investigates an improved SIR model for COVID-19 based on the Caputo fractional derivative. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system. Numerical simulations were conducted using MATLAB, and the results indicate that our model is valuable for studying virus transmission.
基金supported by the State Grid Science & Technology Project (Grant No.17H300000437)
文摘We propose a restoration strategy using microgrids for restoring power supply to critical loads after an extreme event and thereby enhancing the resilience of the distribution power grid. The limited capacities of distributed generators(DGs) within the microgrids and those of intermittent energy sources such as wind and photovoltaic power are considered. An enhanced strategy model of the distribution network is established for maximizing the power supply to critical loads. Firstly, the importance of the load is quantified by using the analytic hierarchy process(AHP) and the model of the microgrid output is further improved. In the demand response mechanism, an interruptible load is used to suppress the fluctuation in the distributed power output. Secondly, piecewise linearization method is applied to address the power flow constraints. Then, the resilience enhancement model of the distribution network is transformed into a mixed integer quadratic programming problem. The CPLEX solver is adopted to solve the above problem on the MATLAB platform. Finally, the proposed method is verified by applying it to practical scenarios.
文摘In this paper an introduction of the moving least squares approach is presented in the context of data approximation and interpolation problems in Geodesy.An application of this method is presented for geoid height approximation and interpolation using different polynomial basis functions for the approximant and interpolant,respectively,in a regular grid of geoid height data in the region 16.0417°≤φ≤47.9583°and 36.0417°≤λ≤69.9582°,with increment 0.0833°in both latitudal and longitudal directions.The results of approximation and interpolation are then compared with the geoid height data from GPS-Levelling approach.Using the standard deviation of the difference of the results,it is shown that the planar interpolant,with reciprocal of distance as weight function,is the best choice in this local approximation and interpolation problem.
基金the National Natural Science Foundation of China (70671011)the National High-Technology Research and Development Program of China (863 Program) (2007AA04Z1B1)the Social Science Youth Foundation of Chongqing University ( CDSK2007-37)
文摘Dynamic data replication is a technique used in data grid environments that helps to reduce access latency and network bandwidth utilization. Replication also increases data availability thereby enhancing system reliability. In this paper we discuss the issues with single-location strategies in large-scale data integration applications, and examine potential multiple-location schemes. Dynamic multiple-location replication is NP-complete in nature. We therefore transform the multiple-location problem into several classical mathematical problems with different parameter settings, to which efficient approximation algorithms apply experimental results indicate that unlike single-location strategies our multiple-location schemes are efficient with respect to access latency and bandwidth consumption, especially when the requesters of a data set are distributed over a large scale of locations.
文摘It has been evident that the theory and methods of dynamic derivatives are playing an increasingly important role in hybrid modeling and computations. Being constructed on various kinds of hybrid grids, that is, time scales, dynamic derivatives offer superior accuracy and flexibility in approximating mathematically important natural processes with hard-to-predict singularities, such as the epidemic growth with unpredictable jump sizes and option market changes with high uncertainties, as compared with conventional derivatives. In this article, we shall review the novel new concepts, explore delicate relations between the most frequently used second-order dynamic derivatives and conventional derivatives. We shall investigate necessary conditions for guaranteeing the consistency between the two derivatives. We will show that such a consistency may never exist in general. This implies that the dynamic derivatives provide entirely different new tools for sensitive modeling and approximations on hybrid grids. Rigorous error analysis will be given via asymptotic expansions for further modeling and computational applications. Numerical experiments will also be given.
