In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existe...In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.展开更多
The kagome system has attracted great interest in condensed matter physics due to its unique structure that canhost various exotic states such as superconductivity(SC),charge density waves(CDWs)and nontrivial topologi...The kagome system has attracted great interest in condensed matter physics due to its unique structure that canhost various exotic states such as superconductivity(SC),charge density waves(CDWs)and nontrivial topological states.The topological semimetal RbTi_(3)Bi_(5)consisting of a Ti kagome layer shares a similar crystal structure to the topologicalcorrelated materials AV_(3)Sb_(5)(A=K,Rb,Cs)but without the absence of CDW and SC.Systematic de Haas-van Alphenoscillation measurements are performed on single crystals of RbTi_(3)Bi_(5)to pursue nontrivial topological physics and exoticstates.Combining this with theoretical calculations,the detailed Fermi surface topology and band structure are investigated.A two-dimensional Fermi pocket b is revealed with a light effective mass,consistent with the semimetal predictions.TheLandau fan diagram of RbTi_(3)Bi_(5)reveals a zero Berry phase for the b oscillation in contrast to that of CsTi_(3)Bi_(5).Theseresults suggest that kagome RbTi_(3)Bi_(5)is a good candidate for exploring nontrivial topological exotic states and topologicalcorrelated physics.展开更多
The low-frequency oscillation(LFO)has occurred in the train-network system due to the introduction of the power electronics of the trains.The modeling and analyzing method in current researches based on electrified ra...The low-frequency oscillation(LFO)has occurred in the train-network system due to the introduction of the power electronics of the trains.The modeling and analyzing method in current researches based on electrified railway unilateral power supply system are not suitable for the LFO analysis in a bilateral power supply system,where the trains are supplied by two traction substations.In this work,based on the single-input and single-output impedance model of China CRH5 trains,the node admittance matrices of the train-network system both in unilateral and bilateral power supply modes are established,including three-phase power grid,traction transformers and traction network.Then the modal analysis is used to study the oscillation modes and propagation characteristics of the unilateral and bilateral power supply systems.Moreover,the influence of the equivalent inductance of the power grid,the length of the transmission line,and the length of the traction network are analyzed on the critical oscillation mode of the bilateral power supply system.Finally,the theoretical analysis results are verified by the time-domain simulation model in MATLAB/Simulink.展开更多
The penetration of new energy sources such as wind power is increasing,which consequently increases the occurrence rate of subsynchronous oscillation events.However,existing subsynchronous oscillation source-identific...The penetration of new energy sources such as wind power is increasing,which consequently increases the occurrence rate of subsynchronous oscillation events.However,existing subsynchronous oscillation source-identification methods primarily analyze fixed-mode oscillations and rarely consider time-varying features,such as frequency drift,caused by the random volatility of wind farms when oscillations occur.This paper proposes a subsynchronous oscillation sourcelocalization method that involves an enhanced short-time Fourier transform and a convolutional neural network(CNN).First,an enhanced STFT is performed to secure high-resolution time-frequency distribution(TFD)images from the measured data of the generation unit ports.Next,these TFD images are amalgamated to form a subsynchronous oscillation feature map that serves as input to the CNN to train the localization model.Ultimately,the trained CNN model realizes the online localization of subsynchronous oscillation sources.The effectiveness and accuracy of the proposed method are validated via multimachine system models simulating forced and natural oscillation events using the Power Systems Computer Aided Design platform.Test results show that the proposed method can localize subsynchronous oscillation sources online while considering unpredictable fluctuations in wind farms,thus providing a foundation for oscillation suppression in practical engineering scenarios.展开更多
The REAgSb_(2)(RE = rare earth and Y) family has drawn considerable research interest because the two-dimensional Sb net in their crystal structures hosts topological fermions and hence rich topological properties. We...The REAgSb_(2)(RE = rare earth and Y) family has drawn considerable research interest because the two-dimensional Sb net in their crystal structures hosts topological fermions and hence rich topological properties. We report herein the magnetization and magnetotransport measurements of SmAgSb_(2) single crystal, which unveil very large magnetoresistance and high carrier mobility up to 6.2 × 10^(3)% and 5.58 × 10^(3)cm^(2)·V^(-1)·s^(-1), respectively. The analysis of both Shubnikov–de Haas and de Haas–van Alphen quantum oscillations indicates nontrivial Berry phases in the paramagnetic state while trivial Berry curvature in the antiferromagnetic state, indicating a topological phase transition induced by the antiferromagnetic order. It is also supported by the first-principles calculations. The results not only provide a new interesting topological material but also offer valuable insights into the correlation between magnetism and nontrivial topological states.展开更多
In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are establishe...In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delay.展开更多
To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem...To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.展开更多
This paper is concerned with the oscillation of second order linear functional equations of the form x(g(t)) = p(t)x(t) + Q(t)X(g(2)(t)), Where p, Q, g : [t(0), infinity) --> R+ = [0, infinity) are given real value...This paper is concerned with the oscillation of second order linear functional equations of the form x(g(t)) = p(t)x(t) + Q(t)X(g(2)(t)), Where p, Q, g : [t(0), infinity) --> R+ = [0, infinity) are given real valued functions such that g(t) not equivalent to t, lim(t-->infinity) g(t) = infinity. It is proved here that when 0 less than or equal to m := lim inf(t-->infinity) Q(t)P(g(t)) less than or equal to 1/4 all solutions of this equation oscillate if the condition lim(t-->infinity) sup Q(t)P(g(t)) > (1 + root1 -4m/2)(2) (*) is satisfied. It should be emphasized that the condition (*) can not be improved in some sense.展开更多
Some sufficient conditions are obtained for the oscillation of first order neutral differential_difference equations with positive and negative periodic coefficients.
This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtai...This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtained.展开更多
Dynamic states in mutual-coupled mid-infrared quantum cascade lasers(QCLs) were numerically investigated in the parameter space of injection strength and detuning frequency based on the Lang-Kobayashi equations model....Dynamic states in mutual-coupled mid-infrared quantum cascade lasers(QCLs) were numerically investigated in the parameter space of injection strength and detuning frequency based on the Lang-Kobayashi equations model. Three types of period-one states were found, with different periods of injection time delay τ_(inj), 2τ_(inj), and reciprocal of the detuning frequency. Besides, square-wave, quasi-period, pulse-burst and chaotic oscillations were also observed. It is concluded that external-cavity periodic dynamics and optical modes beating are the mainly periodic dynamics. The interaction of the two periodic dynamics and the high-frequency dynamics stimulated by strong injection induces the dynamic states evolution.This work helps to understand the dynamic behaviors in QCLs and shows a new way to mid-infrared wide-band chaotic laser.展开更多
A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO mode...A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.展开更多
The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO...The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.展开更多
The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscilla...The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.展开更多
Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation △（pn（△（Xn ＋ CnXn-τ））^γ） ＋ qnX^Bn-σ = 0, n ：0, 1, 2...wh...Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation △（pn（△（Xn ＋ CnXn-τ））^γ） ＋ qnX^Bn-σ = 0, n ：0, 1, 2...which extend and include several oscillation criteria in [11], and also correct a theorem and its proof in [10].展开更多
Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed ...Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory, which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.展开更多
The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of a...The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z^＋ of positive integers and for differential equations when the time scale is the set IR of real numbers.展开更多
In this paper, a class of second order nonlinear neutral difference equations with variable delays are studied. The criteria for existence of bounded eventually positive solution is obtained by using Banach contractio...In this paper, a class of second order nonlinear neutral difference equations with variable delays are studied. The criteria for existence of bounded eventually positive solution is obtained by using Banach contraction mapping principle and some necessary techniques. Moreover, some sufficient conditions for oscillation of the equations are given. Some results available in documents are extended in this paper. Illustrative examples are given.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 tech...： 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 knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.展开更多
A noninvasive Ionization profile monitor(IPM)consisting of micro-channel plates,a phosphor screen and the optical-signal acquisition has been developed at the cooling storage ring of Heavy Ion Research Facility in Lan...A noninvasive Ionization profile monitor(IPM)consisting of micro-channel plates,a phosphor screen and the optical-signal acquisition has been developed at the cooling storage ring of Heavy Ion Research Facility in Lanzhou(HIRFL-CSR).It makes the real-time profile measurements for the transverse beam cooling and orbit oscillation possible and efficient.This paper firstly describes all the IPM design criterions including the theoretical signal yield calculation,the space charge field and initial momentum evaluation,and the electrostatic field distortion simulation as well.In order to investigate the IPM performance,the beam profile measurements are done with different high voltage settings.Subsequently,some valuable beam experiments about the transverse electron cooling and orbit oscillation study are also presented.In the end,fast turn-by-turn profile measurements for the emittance blow-up research in a synchrotron are discussed.In cooperation with the newly deployed emittance instruments at the HIRFL-CSR injector,the IPM shows great prospects for the injection mismatch study,and potential values for the tune,dispersion and chromaticity measurements as well.展开更多
基金supported by the National Natural Science Foundation of China(12071491,12001113)。
文摘In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.
基金supported by the National Key Research and Development Program of China(Grant No.2023YFA1406500)the National Natural Science Foundation of China(Grant Nos.12174454,U2130101,and 92165204)+2 种基金the Guangdong Basic and Applied Basic Research Funds(Grant Nos.2024B1515020040 and 2022A1515010035)Guangzhou Basic and Applied Basic Research Funds(Grant No.2024A04J6417)Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices(Grant No.2022B1212010008).
文摘The kagome system has attracted great interest in condensed matter physics due to its unique structure that canhost various exotic states such as superconductivity(SC),charge density waves(CDWs)and nontrivial topological states.The topological semimetal RbTi_(3)Bi_(5)consisting of a Ti kagome layer shares a similar crystal structure to the topologicalcorrelated materials AV_(3)Sb_(5)(A=K,Rb,Cs)but without the absence of CDW and SC.Systematic de Haas-van Alphenoscillation measurements are performed on single crystals of RbTi_(3)Bi_(5)to pursue nontrivial topological physics and exoticstates.Combining this with theoretical calculations,the detailed Fermi surface topology and band structure are investigated.A two-dimensional Fermi pocket b is revealed with a light effective mass,consistent with the semimetal predictions.TheLandau fan diagram of RbTi_(3)Bi_(5)reveals a zero Berry phase for the b oscillation in contrast to that of CsTi_(3)Bi_(5).Theseresults suggest that kagome RbTi_(3)Bi_(5)is a good candidate for exploring nontrivial topological exotic states and topologicalcorrelated physics.
基金This work was supported by the Applied Basic Research Program of Science and Technology Plan Project of Sichuan Province of China(No.2020YJ0252).
文摘The low-frequency oscillation(LFO)has occurred in the train-network system due to the introduction of the power electronics of the trains.The modeling and analyzing method in current researches based on electrified railway unilateral power supply system are not suitable for the LFO analysis in a bilateral power supply system,where the trains are supplied by two traction substations.In this work,based on the single-input and single-output impedance model of China CRH5 trains,the node admittance matrices of the train-network system both in unilateral and bilateral power supply modes are established,including three-phase power grid,traction transformers and traction network.Then the modal analysis is used to study the oscillation modes and propagation characteristics of the unilateral and bilateral power supply systems.Moreover,the influence of the equivalent inductance of the power grid,the length of the transmission line,and the length of the traction network are analyzed on the critical oscillation mode of the bilateral power supply system.Finally,the theoretical analysis results are verified by the time-domain simulation model in MATLAB/Simulink.
基金supported by the Science and Technology Project of State Grid Corporation of China(5100202199536A-0-5-ZN)。
文摘The penetration of new energy sources such as wind power is increasing,which consequently increases the occurrence rate of subsynchronous oscillation events.However,existing subsynchronous oscillation source-identification methods primarily analyze fixed-mode oscillations and rarely consider time-varying features,such as frequency drift,caused by the random volatility of wind farms when oscillations occur.This paper proposes a subsynchronous oscillation sourcelocalization method that involves an enhanced short-time Fourier transform and a convolutional neural network(CNN).First,an enhanced STFT is performed to secure high-resolution time-frequency distribution(TFD)images from the measured data of the generation unit ports.Next,these TFD images are amalgamated to form a subsynchronous oscillation feature map that serves as input to the CNN to train the localization model.Ultimately,the trained CNN model realizes the online localization of subsynchronous oscillation sources.The effectiveness and accuracy of the proposed method are validated via multimachine system models simulating forced and natural oscillation events using the Power Systems Computer Aided Design platform.Test results show that the proposed method can localize subsynchronous oscillation sources online while considering unpredictable fluctuations in wind farms,thus providing a foundation for oscillation suppression in practical engineering scenarios.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12004405,12334008,and 12374148)the Double First-Class Initiative Fund of Shanghai Tech University+2 种基金the Analytical Instrumentation Center of Shanghai Tech University(Grant No.SPST-AIC10112914)the research fund from the Shanghai Sailing Program(Grant No.23YF1426900)the fund from the National Key R&D Program of China(Grant Nos.2022YFA1402702 and 2021YFA1401600)。
文摘The REAgSb_(2)(RE = rare earth and Y) family has drawn considerable research interest because the two-dimensional Sb net in their crystal structures hosts topological fermions and hence rich topological properties. We report herein the magnetization and magnetotransport measurements of SmAgSb_(2) single crystal, which unveil very large magnetoresistance and high carrier mobility up to 6.2 × 10^(3)% and 5.58 × 10^(3)cm^(2)·V^(-1)·s^(-1), respectively. The analysis of both Shubnikov–de Haas and de Haas–van Alphen quantum oscillations indicates nontrivial Berry phases in the paramagnetic state while trivial Berry curvature in the antiferromagnetic state, indicating a topological phase transition induced by the antiferromagnetic order. It is also supported by the first-principles calculations. The results not only provide a new interesting topological material but also offer valuable insights into the correlation between magnetism and nontrivial topological states.
文摘In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delay.
文摘To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.
文摘This paper is concerned with the oscillation of second order linear functional equations of the form x(g(t)) = p(t)x(t) + Q(t)X(g(2)(t)), Where p, Q, g : [t(0), infinity) --> R+ = [0, infinity) are given real valued functions such that g(t) not equivalent to t, lim(t-->infinity) g(t) = infinity. It is proved here that when 0 less than or equal to m := lim inf(t-->infinity) Q(t)P(g(t)) less than or equal to 1/4 all solutions of this equation oscillate if the condition lim(t-->infinity) sup Q(t)P(g(t)) > (1 + root1 -4m/2)(2) (*) is satisfied. It should be emphasized that the condition (*) can not be improved in some sense.
文摘Some sufficient conditions are obtained for the oscillation of first order neutral differential_difference equations with positive and negative periodic coefficients.
文摘This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtained.
基金Project supported by the National Key Research and Development Program of China (Grant No. 2019YFB1803500)the National Natural Science Foundation of China (Grant No. 61805168)+4 种基金the Natural Science Foundation of Shanxi Province, China (Grant Nos. 201801D221183 and 20210302123185)International Cooperation of Key Research and Development Program of Shanxi Province (Grant No. 201903D421012)Research Project Supported by Shanxi Scholarship Council of China (Grant No. 2021-032)Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (Grant No. 2019L0133)Fund for Shanxi “1331 Project” Key Innovative Research Team。
文摘Dynamic states in mutual-coupled mid-infrared quantum cascade lasers(QCLs) were numerically investigated in the parameter space of injection strength and detuning frequency based on the Lang-Kobayashi equations model. Three types of period-one states were found, with different periods of injection time delay τ_(inj), 2τ_(inj), and reciprocal of the detuning frequency. Besides, square-wave, quasi-period, pulse-burst and chaotic oscillations were also observed. It is concluded that external-cavity periodic dynamics and optical modes beating are the mainly periodic dynamics. The interaction of the two periodic dynamics and the high-frequency dynamics stimulated by strong injection induces the dynamic states evolution.This work helps to understand the dynamic behaviors in QCLs and shows a new way to mid-infrared wide-band chaotic laser.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 90111011 and 10471039）, the National Key Basic Research Special Foundation of China （Grant Nos 2003CB415101-03 and 2004CB418304）, the Key Basic Research Foundation of the Chinese Academy of Sciences （Grant No KZCX3-SW-221） and in part by E-Institutes of Shanghai Municipal Education Commission （Grant No N.E03004）.
文摘A class of coupled system for the E1 Nifio-Southern Oscillation （ENSO） mechanism is studied. Using the method of variational iteration for perturbation theory, the asymptotic expansions of the solution for ENSO model are obtained and the asymptotic behaviour of solution for corresponding problem is considered.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 40676016 and 10471039)the State KeyProgram for Basic Research of China (Grant Nos 2003CB415101-03 and 2004CB418304)+2 种基金the Key Project of the Chinese Academy of Sciences (Grant No KZCX3-SW-221)in partly by E-Institutes of Shanghai Municipal Education Commission (Grant NoN.E03004)the Natural Science Foundation of Zhejiang Province,China (Grant No Y606268)
文摘The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.
文摘The oscillatory behavior of neutral differential equation with positive and negative coefficients is investigated by mathematics analysis technique and the fixed point principle. Some sufficient conditions for oscillation of neutral differential equation with positive and negative coefficients are obtained.
基金revised September 27,2005.Research support by Natural Science Foundation of China(10271043)
文摘Some oscillation criteria are established by Raccati transformation techniques for the following second-order nonlinear neutral difference equation △（pn（△（Xn ＋ CnXn-τ））^γ） ＋ qnX^Bn-σ = 0, n ：0, 1, 2...which extend and include several oscillation criteria in [11], and also correct a theorem and its proof in [10].
基金Project supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(Grant No.51521065)
文摘Chattering phenomenon and singularity are still the main problems that hinder the practical application of sliding mode control. In this paper, a fixed time integral sliding mode controller is designed based on fixed time stability theory, which ensures precise convergence of the state variables of controlled system, and overcomes the drawback of convergence time growing unboundedly as the initial value increases in finite time controller. It makes the controlled system converge to the control objective within a fixed time bounded by a constant as the initial value grows, and convergence time can be changed by adjusting parameters of controllers properly. Compared with other fixed time controllers, the fixed time integral sliding mode controller proposed in this paper achieves chattering-free control, and integral expression is used to avoid singularity generated by derivation. Finally, the controller is used to stabilize four-order chaotic power system. The results demonstrate that the controller realizes the non-singular chattering-free control of chaotic oscillation in the power system and guarantees the fixed time convergence of state variables, which shows its higher superiority than other finite time controllers.
基金Project supported by the National Education Committee Doctoral Foundation of China (20020558092)
文摘The article is concerned with oscillation of nonautonomous neutral dynamic delay equations on time scales. Sufficient conditions are established for the existence of bounded positive solutions and for oscillation of all solutions of this equation. Some results extend known results for difference equations when the time scale is the set Z^＋ of positive integers and for differential equations when the time scale is the set IR of real numbers.
基金Supported by the Scientific Research Fund of Education Department of Hunan Province(07C680)
文摘In this paper, a class of second order nonlinear neutral difference equations with variable delays are studied. The criteria for existence of bounded eventually positive solution is obtained by using Banach contraction mapping principle and some necessary techniques. Moreover, some sufficient conditions for oscillation of the equations are given. Some results available in documents are extended in this paper. Illustrative examples are given.
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 knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.
基金This work was supported by the National Natural Science Foundation of China(No.11805250).
文摘A noninvasive Ionization profile monitor(IPM)consisting of micro-channel plates,a phosphor screen and the optical-signal acquisition has been developed at the cooling storage ring of Heavy Ion Research Facility in Lanzhou(HIRFL-CSR).It makes the real-time profile measurements for the transverse beam cooling and orbit oscillation possible and efficient.This paper firstly describes all the IPM design criterions including the theoretical signal yield calculation,the space charge field and initial momentum evaluation,and the electrostatic field distortion simulation as well.In order to investigate the IPM performance,the beam profile measurements are done with different high voltage settings.Subsequently,some valuable beam experiments about the transverse electron cooling and orbit oscillation study are also presented.In the end,fast turn-by-turn profile measurements for the emittance blow-up research in a synchrotron are discussed.In cooperation with the newly deployed emittance instruments at the HIRFL-CSR injector,the IPM shows great prospects for the injection mismatch study,and potential values for the tune,dispersion and chromaticity measurements as well.
