In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients....In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.展开更多
Controller area network(CAN) is a widely used fieldbus protocol in various industrial applications.To understand the network behavior under errors for the optimal design of networked control systems, the message respo...Controller area network(CAN) is a widely used fieldbus protocol in various industrial applications.To understand the network behavior under errors for the optimal design of networked control systems, the message response time of the CAN network needs to be analyzed. In this study, a novel delay time distribution analysis method for the response messages is proposed when considering errors. In this method the complex message queues are decomposed into typical message patterns and cases. First, a stochastic fault model is developed, and the probability factor is defined to calculate the error distribution. Then the message delay time distribution for the single slave node configuration is analyzed based on the error distribution. Next, based on the delay time distribution analysis of typical patterns and cases, an analysis framework of message delay time distribution for the master/slave configuration is developed. The testbed is constructed and case studies are conducted to demonstrate the proposed methodology under different network configurations. Experimental results show that the delay time distributions calculated by the proposed method agree well with the actual observations.展开更多
Let Ω CR^d,1≤d≤3, be a bounded d-polytope. Consider the parabolic equation on Q with the Dirac delta function on the right hand side. We study the well-posedness, regularity, and the interior error estimate of semi...Let Ω CR^d,1≤d≤3, be a bounded d-polytope. Consider the parabolic equation on Q with the Dirac delta function on the right hand side. We study the well-posedness, regularity, and the interior error estimate of semidiscrete finite element approximations of the equation. In particular, we derive that the interior error is bounded by the best local approximation error, the negative norms of the error, and the negative norms of the time derivative of the error. This result implies different convergence rates for the numerical solution in different interior regions, especially when the region is close to the singular point. Numerical test results are reported to support the theoretical prediction.展开更多
基金supported by the National Natural Science Foundation of China(11371225)National Natural Science Foundation of Guangdong Province(2016A030313686)
文摘In this article, we consider the non-linear difference equation(f(z + 1)f(z)-1)(f(z)f(z-1)-1) =P(z, f(z))/Q(z, f(z)),where P(z, f(z)) and Q(z, f(z)) are relatively prime polynomials in f(z) with rational coefficients. For the above equation, the order of growth, the exponents of convergence of zeros and poles of its transcendental meromorphic solution f(z), and the exponents of convergence of poles of difference △f(z) and divided difference △f(z)/f(z)are estimated. Furthermore, we study the forms of rational solutions of the above equation.
基金the National Natural Science Foundation of China (Nos. 51475422 and 51521064).
文摘Controller area network(CAN) is a widely used fieldbus protocol in various industrial applications.To understand the network behavior under errors for the optimal design of networked control systems, the message response time of the CAN network needs to be analyzed. In this study, a novel delay time distribution analysis method for the response messages is proposed when considering errors. In this method the complex message queues are decomposed into typical message patterns and cases. First, a stochastic fault model is developed, and the probability factor is defined to calculate the error distribution. Then the message delay time distribution for the single slave node configuration is analyzed based on the error distribution. Next, based on the delay time distribution analysis of typical patterns and cases, an analysis framework of message delay time distribution for the master/slave configuration is developed. The testbed is constructed and case studies are conducted to demonstrate the proposed methodology under different network configurations. Experimental results show that the delay time distributions calculated by the proposed method agree well with the actual observations.
基金Li Guo was supported in part by the National Natural Science Foundation of China under the grant 11601536.Hengguang Li was supported in part by the National Science Foundation Grant DMS-1418853,by the Natural Science Foundation of China Grant 11628104,and by the Wayne State University Grants Plus Program.Yang Yang was supported in part by the National Natural Science Foundation of China under the grants 11571367&11601536 and the Fundamental Research Funds for the Central Universities 18CX05003A.
文摘Let Ω CR^d,1≤d≤3, be a bounded d-polytope. Consider the parabolic equation on Q with the Dirac delta function on the right hand side. We study the well-posedness, regularity, and the interior error estimate of semidiscrete finite element approximations of the equation. In particular, we derive that the interior error is bounded by the best local approximation error, the negative norms of the error, and the negative norms of the time derivative of the error. This result implies different convergence rates for the numerical solution in different interior regions, especially when the region is close to the singular point. Numerical test results are reported to support the theoretical prediction.
