Linear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay.The corresponding convergence results are obtained and successfully confi...Linear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay.The corresponding convergence results are obtained and successfully confirmed by some numerical examples.The results obtained in this work extend the corresponding ones in literature.展开更多
The true-time delay(TTD)units are critical for solving beam squint and frequency selective fading inWideband Large-Scale Antenna Systems(LSASs).In this work,we propose a TTD array architecture for wideband multi-beam ...The true-time delay(TTD)units are critical for solving beam squint and frequency selective fading inWideband Large-Scale Antenna Systems(LSASs).In this work,we propose a TTD array architecture for wideband multi-beam tracking that eliminates the beam squint phenomenon and filters out interference signals by applying a spatial filter and time delay estimations(TDEs).The paper presents a novel approach to spatial filter design by introducing a transformation matrix that can optimize the beam response in a specific direction and at a specific frequency.Using the variable fractional delay(VFD)filters,we propose a TDE algorithm with a Newton-Raphson iteration update process that corrects the arrival time delay difference between sensors.Simulations and examples have demonstrated that the proposed architecture can achieve beam tracking within 10 ms at the low signalto-noise ratio(SNR)and demodulation loss is less than 0.5 dB in wideband multi-beam scenarios.展开更多
In this paper,we aim to derive an averaging principle for stochastic differential equations driven by time-changed Lévy noise with variable delays.Under certain assumptions,we show that the solutions of stochasti...In this paper,we aim to derive an averaging principle for stochastic differential equations driven by time-changed Lévy noise with variable delays.Under certain assumptions,we show that the solutions of stochastic differential equations with time-changed Lévy noise can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence and in convergence in probability,respectively.The convergence order is also estimated in terms of noise intensity.Finally,an example with numerical simulation is given to illustrate the theoretical result.展开更多
This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such a...This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.展开更多
In this paper, we study the convergence of solutions for a class of difference equations with variable delay and give some results about the solutions of the equations converge to a constant. Our results generalize th...In this paper, we study the convergence of solutions for a class of difference equations with variable delay and give some results about the solutions of the equations converge to a constant. Our results generalize the conclusions obtained in .展开更多
The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati techniq...The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many known results for second order dynamic equations. Some examples are given to illustrate the main results of this article.展开更多
This work concerns the stability properties of impulsive solution for a class of variable delay and time-varying measure differential systems. By means of the techniques of constructing broken line function to overcom...This work concerns the stability properties of impulsive solution for a class of variable delay and time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function with discontinuous derivative, some criteria of global exponential asymptotic stability for the system are established. An example is given to illustrate the applicability of results obtained.展开更多
We establish some stability results for delayed Hopfield Neural Network Model with variable coefficients and variable delays, by using the Lyapunov function. These stability criteria are new.
Consider the neutral differential equations with variable coefficients and delays [x(t)-p(t)x(t-r(t))]'+ Qj(t)x(t-σj(t))=0. (1)We establish sufficient conditions for the oscillation of equation (1). Our condition...Consider the neutral differential equations with variable coefficients and delays [x(t)-p(t)x(t-r(t))]'+ Qj(t)x(t-σj(t))=0. (1)We establish sufficient conditions for the oscillation of equation (1). Our condition is 'sharp' in the sense that when all the coefficients and delays of the equation are constants.Our conclusions improve and generalize some known results.展开更多
This article discusses the stability properties of impulsive solution for a class of variable delay and linear time-varying measure differential systems. By means of the techniques of constructing broken line functi...This article discusses the stability properties of impulsive solution for a class of variable delay and linear time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function, some criteria of global exponential asymptotic stability for the impulsive time-delay system are established. An example is given to illustrate the applicability of the obtained results.展开更多
On urban arterials,travel time variability is largely dependent on the variability in the delays vehicles experience at signalized intersections.The interpretation of delay evolvement at intersections will give a comp...On urban arterials,travel time variability is largely dependent on the variability in the delays vehicles experience at signalized intersections.The interpretation of delay evolvement at intersections will give a comprehensive insight into arterial travel time variability and provide more possibilities for travel time estimation.Accordingly,an analytical model is proposed to study delay variability at isolated,fixed-time controlled intersections.Classic cumulative curves are utilized to derive average delay(per cycle) formulas by assuming a deterministic overflow queue.Then,an analogy with the Markov chain process is made to clarify the mechanism of stochastic delays and overflow queues at signalized intersections.It was found that,in undersaturated cases,the shape of the delay distribution changes very little over time,whereas for saturated and oversaturated cases the delay distribution is time-dependent and becomes flatter with an increasing number of cycles.The analysis of arrival distributions,e.g.,Poisson and binomial,produces the conclusion that the variability of arrivals has a significant effect on delay estimates in both undersaturated and oversaturated conditions.A larger variance of arrival flow results in a larger variance of delay distribution.All of these analyses can help road authorities to gain insights into arterial travel time variability.展开更多
基金This work is supported by NSF of China(10971175)Specialized Research Fund for the Doctoral Program of Higher Education of China(20094301110001)+2 种基金Program for Changjiang Scholars and Innovative Research Team in University of China(IRT1179)NSF of Hunan Province(10JJ7001)the Aid Program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province,and Fund Project of Hunan Province Education Office(11C1220).
文摘Linear multistep methods and one-leg methods are applied to a class of index-2 nonlinear differential-algebraic equations with a variable delay.The corresponding convergence results are obtained and successfully confirmed by some numerical examples.The results obtained in this work extend the corresponding ones in literature.
基金supported by the foundation of National Key Laboratory of Electromagnetic Environment(Grant No.202103012).
文摘The true-time delay(TTD)units are critical for solving beam squint and frequency selective fading inWideband Large-Scale Antenna Systems(LSASs).In this work,we propose a TTD array architecture for wideband multi-beam tracking that eliminates the beam squint phenomenon and filters out interference signals by applying a spatial filter and time delay estimations(TDEs).The paper presents a novel approach to spatial filter design by introducing a transformation matrix that can optimize the beam response in a specific direction and at a specific frequency.Using the variable fractional delay(VFD)filters,we propose a TDE algorithm with a Newton-Raphson iteration update process that corrects the arrival time delay difference between sensors.Simulations and examples have demonstrated that the proposed architecture can achieve beam tracking within 10 ms at the low signalto-noise ratio(SNR)and demodulation loss is less than 0.5 dB in wideband multi-beam scenarios.
基金supported by the National NaturalScience Foundation of China(12071003,11901005)the Natural Science Foundation of Anhui Province(2008085QA20)。
文摘In this paper,we aim to derive an averaging principle for stochastic differential equations driven by time-changed Lévy noise with variable delays.Under certain assumptions,we show that the solutions of stochastic differential equations with time-changed Lévy noise can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence and in convergence in probability,respectively.The convergence order is also estimated in terms of noise intensity.Finally,an example with numerical simulation is given to illustrate the theoretical result.
基金The National Natural Science Foundation of China (No.10671078)
文摘This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.
文摘In this paper, we study the convergence of solutions for a class of difference equations with variable delay and give some results about the solutions of the equations converge to a constant. Our results generalize the conclusions obtained in .
基金Supported by the Scientific Research Fund of Hunan Provincial Education Department(09A082)
文摘The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many known results for second order dynamic equations. Some examples are given to illustrate the main results of this article.
文摘This work concerns the stability properties of impulsive solution for a class of variable delay and time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function with discontinuous derivative, some criteria of global exponential asymptotic stability for the system are established. An example is given to illustrate the applicability of results obtained.
文摘We establish some stability results for delayed Hopfield Neural Network Model with variable coefficients and variable delays, by using the Lyapunov function. These stability criteria are new.
文摘Consider the neutral differential equations with variable coefficients and delays [x(t)-p(t)x(t-r(t))]'+ Qj(t)x(t-σj(t))=0. (1)We establish sufficient conditions for the oscillation of equation (1). Our condition is 'sharp' in the sense that when all the coefficients and delays of the equation are constants.Our conclusions improve and generalize some known results.
文摘This article discusses the stability properties of impulsive solution for a class of variable delay and linear time-varying measure differential systems. By means of the techniques of constructing broken line function to overcome the difficulties in employing comparison principle and Lyapunov function, some criteria of global exponential asymptotic stability for the impulsive time-delay system are established. An example is given to illustrate the applicability of the obtained results.
基金supported by the National Natural Science Foundation of China(No.51278455)the National Science Foundation for Post-doctoral Scientists of China(No.2012M521175)the Excellent Post-doctoral Science of Foundation of Zhejiang Province(No.Bsh1202056),China
文摘On urban arterials,travel time variability is largely dependent on the variability in the delays vehicles experience at signalized intersections.The interpretation of delay evolvement at intersections will give a comprehensive insight into arterial travel time variability and provide more possibilities for travel time estimation.Accordingly,an analytical model is proposed to study delay variability at isolated,fixed-time controlled intersections.Classic cumulative curves are utilized to derive average delay(per cycle) formulas by assuming a deterministic overflow queue.Then,an analogy with the Markov chain process is made to clarify the mechanism of stochastic delays and overflow queues at signalized intersections.It was found that,in undersaturated cases,the shape of the delay distribution changes very little over time,whereas for saturated and oversaturated cases the delay distribution is time-dependent and becomes flatter with an increasing number of cycles.The analysis of arrival distributions,e.g.,Poisson and binomial,produces the conclusion that the variability of arrivals has a significant effect on delay estimates in both undersaturated and oversaturated conditions.A larger variance of arrival flow results in a larger variance of delay distribution.All of these analyses can help road authorities to gain insights into arterial travel time variability.