To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid sear...To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, thus its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an appropriate grid spacing adaptively, and is able to yield approximate maximum likelihood estimate （MLE） with a computational complexity of O（n2）. Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing methods. Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate similarly by grid search.展开更多
An accurate period is important to recover the pulse profile from a recorded photon event series of an X-ray pulsar and to estimate the pulse time of arrival,which is the measurement of X-ray pulsar navigation.Epoch f...An accurate period is important to recover the pulse profile from a recorded photon event series of an X-ray pulsar and to estimate the pulse time of arrival,which is the measurement of X-ray pulsar navigation.Epoch folding is a classical period estimation method in the time domain;however,its computational complexity grows as the number of trail periods increases.In order to reduce the computational complexity,this paper improves the fast folding algorithm through segment correlation and amplitude accumulation,which is based on the post-order traversal of a binary tree.Compared with epoch folding,the improved fast folding algorithm can achieve a similar accuracy at the cost of a lower computational burden.Compared with the original fast folding algorithm,the improved algorithm can be applied to detectors with a much smaller effective area.The performance of the method is investigated by simulation data and observation data from the Neutron star Interior Composition Explorer(NICER).展开更多
In this paper,we explore how to estimate the phase damping parameter γ and the tunneling amplitude parameter ？from a spin-boson dephasing quantum model by periodical projective measurements.The preparation of initia...In this paper,we explore how to estimate the phase damping parameter γ and the tunneling amplitude parameter ？from a spin-boson dephasing quantum model by periodical projective measurements.The preparation of initial states is accomplished by performing the period measurements in our scheme.The parameter γ can be always estimated when projective measurement bases are chosen as θ = π/2 and φ = 0.Based on the estimated value of γ and the interval information of ？,we can select another measurement bases（θ = π/4 and φ = π/2） to obtain the estimated value of ？.A coherent control is indispensable to estimate ？ if γ is in the interval of ？;whereas the control is not necessary if γ is out of the known interval of ？.We establish the relation between the optimal period time and the parameter γ or ？ in terms of Fisher information.Although the optimal measurement period cannot be selected beforehand,the aforementioned relation can be utilized to adjust the measurement period to approach the optimal one.展开更多
In view of the complexity of existing linear frequency modulation(LFM)signal parameter estimation methods and the poor antinoise performance and estimation accuracy under a low signal-to-noise ratio(SNR),a parameter e...In view of the complexity of existing linear frequency modulation(LFM)signal parameter estimation methods and the poor antinoise performance and estimation accuracy under a low signal-to-noise ratio(SNR),a parameter estimation method for LFM signals with a Duffing oscillator based on frequency periodicity is proposed in this paper.This method utilizes the characteristic that the output signal of the Duffing oscillator excited by the LFM signal changes periodically with frequency,and the modulation period of the LFM signal is estimated by autocorrelation processing of the output signal of the Duffing oscillator.On this basis,the corresponding relationship between the reference frequency of the frequencyaligned Duffing oscillator and the frequency range of the LFM signal is analyzed by the periodic power spectrum method,and the frequency information of the LFM signal is determined.Simulation results show that this method can achieve high-accuracy parameter estimation for LFM signals at an SNR of-25 dB.展开更多
The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0...The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0 is considered. Formulas that determine the greatest value of mean square error and the minimax estimation for the functional are proposed for the given class of admissible processes. It is shown that one-sided moving average stationary sequence gives the greatest value of the mean square error.展开更多
A conservative system performing a small oscillation near every equilibrium position is analysed in classical way. The paper tries to answer the following question: How many types of the periodic small oscillation in ...A conservative system performing a small oscillation near every equilibrium position is analysed in classical way. The paper tries to answer the following question: How many types of the periodic small oscillation in the whole configuration space of the system are there? Making some hypotheses, it expresses the lower bounds of the number of the types for two cases where critical points of the potential function are nondegenerate and degenerate respectively by the Betti numbers and dimension of the constraint manifold only.展开更多
Analyzed the relation between time delay difference and time delay estimation errors, based on the principles of three-point locating, a reformed threshold method for time delay difference estimation of impulse signal...Analyzed the relation between time delay difference and time delay estimation errors, based on the principles of three-point locating, a reformed threshold method for time delay difference estimation of impulse signals, called as amendment estimation for short, is developed by introducing channel equalization technique to its conventional version, named as direct estimation in this paper, to improve the estimation stability. After inherent relationship between time delay and phase shift of signals is analyzed, an integer period error compensation method utilized the diversities of both contribution share and contribution mode of concerned estimates is proposed under the condition of high precision phase lag estimation. Finally, a cooperative multi-threshold estimation method composed of amendment and direct estimations to process impulse signals with three thresholds is established. In sea trials data tests of passive locating, this method improves the estimation precision of time delay difference efficiently. The experiments verify the theoretical predictions.展开更多
The attempt to obtain long-term observed data around some sea areas we concern is usually very hard or even impossible in practical offshore and ocean engineering situations. In this paper, by means of linear mean-squ...The attempt to obtain long-term observed data around some sea areas we concern is usually very hard or even impossible in practical offshore and ocean engineering situations. In this paper, by means of linear mean-square estimation method, a new way to extend short-term data to long-term ones is developed. The long-term data about concerning sea areas can be constructed via a series of long-term data obtained from neighbor oceanographic stations, through relevance analysis of different data series. It is effective to cover the insufficiency of time series prediction method＇s overdependence upon the length of data series, as well as the limitation of variable numbers adopted in multiple linear regression model. The storm surge data collected from three oceanographic stations located in Shandong Peninsula are taken as examples to analyze the number-selection effect of reference oceanographic stations（adjacent to the concerning sea area） and the correlation coefficients between sea sites which are selected for reference and for engineering projects construction respectively. By comparing the N-year return-period values which are calculated from observed raw data and processed data which are extended from finite data series by means of the linear mean-square estimation method, one can draw a conclusion that this method can give considerably good estimation in practical ocean engineering, in spite of different extreme value distributions about raw and processed data.展开更多
A fast parameter estimation algorithm is discussed for a polyphase coded Continuous Waveform(CW) signal in Additive White Gaussian Noise(AWGN).The proposed estimator is based on the sum of the modulus square of the am...A fast parameter estimation algorithm is discussed for a polyphase coded Continuous Waveform(CW) signal in Additive White Gaussian Noise(AWGN).The proposed estimator is based on the sum of the modulus square of the ambiguity function at the different Doppler shifts.An iterative refinement stage is proposed to avoid the effect of the spurious peaks that arise when the summation length of the estimator exceeds the subcode duration.The theoretical variance of the subcode rate estimate is derived.The Monte-Carlo simulation results show that the proposed estimator is highly accurate and effective at moderate Signal-to-Noise Ratio(SNR).展开更多
In this paper, a new scheme that combines Space-Time Block-Coding (STBC) based on an Alamouti-like scheme and the Least Squares (LS) channel estimation using optimal training sequences in Cyclic-Prefix-based (CP)\Sing...In this paper, a new scheme that combines Space-Time Block-Coding (STBC) based on an Alamouti-like scheme and the Least Squares (LS) channel estimation using optimal training sequences in Cyclic-Prefix-based (CP)\Single-Carrier (SC) systems is proposed. With two transmit antennas, based on Cramer-Rao lower bound for channel estimation, it is shown that the Periodic Comple- mentary Set (PCS) is optimal over frequency-selective fading channels. Compared with the normal scheme without STBC, 3dB Mean Square Error (MSE) performance gains and fewer restrictions on the length of channel impulse response are demonstrated.展开更多
It is well known that the periodic performance of spread spectrum sequence heavily affects the correlative and secure characteristics of communication systems. The chaotic binary sequence is paid more and more attenti...It is well known that the periodic performance of spread spectrum sequence heavily affects the correlative and secure characteristics of communication systems. The chaotic binary sequence is paid more and more attention since it is one kind of applicable spread spectrum sequences. However, there are unavoidable short cyclic problems for chaotic binary sequences in finite precision. The chaotic binary sequence generating methods are studied first. Then the short cyclic behavior of the chaotic sequences is analyzed in detail, which are generated by quantification approaches with finite word-length. At the same time, a chaotic similar function is defined for presenting the cyclic characteristics of the sequences. Based on these efforts, an improved method with scrambling control for generating chaotic binary sequences is proposed. To quantitatively describe the improvement of periodic performance of the sequences, an orthogonal estimator is also defined. Some simulating results are provided. From the theoretical deduction and the experimental results, it is concluded that the proposed method can effectively increase the period and raise the complexity of the chaotic sequences to some extent.展开更多
The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2...The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(W1*1。*3/4]′ 2(t)=-b 0x α 2(t)+b 1f 2(x 1(t-τ 3),x 2(t-τ 4)).This approach is based on the continuation theorem of the coincidence degree, and the a priori estimate of periodic solutions.展开更多
The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1...The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions展开更多
To take the seismic zone that includes the great shock with M S8.5 as the statistical unit of estimating b value can often lead to more large variance, because the seismogenic zone of the great shock with M...To take the seismic zone that includes the great shock with M S8.5 as the statistical unit of estimating b value can often lead to more large variance, because the seismogenic zone of the great shock with M S8.5 are larger than that delineated in general seismic zone. Two-level statistical units are considered in this paper. The seismic province is the first level unit that is suitable for group of earthquakes including the great shock of M S8.5. A seismic province can be divided into several seismic zones. They can be taken as the second level unit for group of quakes in which the super magnitude of the greatest shock do not exceed 8. Because of the nonstationarity in time of seismic activity, the unbalancedness of data and differential of seismic temporal series feature in different areas need to be considered when we select the time period for estimating b value. According to local conditions, the time period is selected at one′s discretion in order to reflect seismicity level of this statistical unit in future 100 years.展开更多
The environmental noise can restrict the accuracy of period estimation since the torsion pendulum is sensitive to weak forces. Two typical models for the environmental noise are proposed to make an evaluation. General...The environmental noise can restrict the accuracy of period estimation since the torsion pendulum is sensitive to weak forces. Two typical models for the environmental noise are proposed to make an evaluation. Generally, the stationary environmental noise is modeled as a white noise, and contributes to the period uncertainty as a function of the initial amplitude, the quality factor, the variance of noise and the time length. As to a sudden sharp disturbance acting on the pendulum, a narrow impulse model is constructed. It results in a sharp jump in the phase difference, which can be excluded with the 3σ criterion for a correction. An experimental data analysis for the measurement of the gravitational constant G with the time-of-swing method shows that the period uncertainty due to the environmental noise is about one and a half times the fundamental thermal noise limit. Though this result is dependent on the ambient environment, the analysis is instructive to improve the measurement accuracy of experiments.展开更多
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time peri...The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray_Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.展开更多
Suppose that a continuous 2re-periodic function f on the real axis changes its monotonicity at points Yi In this paper, for each n _ N, a trigonometric polynomial Pn of order cn is found such that： Pn has the same ...Suppose that a continuous 2re-periodic function f on the real axis changes its monotonicity at points Yi In this paper, for each n _ N, a trigonometric polynomial Pn of order cn is found such that： Pn has the same monotonicity as f, everywhere except, perhaps, the small intervals.展开更多
In this paper we investigate the existence and stability of periodic solutions(on a half-line R_(+))and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded ...In this paper we investigate the existence and stability of periodic solutions(on a half-line R_(+))and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded domains of R^(n) in the framework of interpolation spaces.For the linear Boussinesq system we combine the L^(p)—L^(q)-smoothing estimates and interpolation functors to prove the existence of bounded mild solutions.Then,we prove the existence of periodic solutions by invoking Massera’s principle.We also prove the existence of almost periodic solutions.Then we use the results of the linear Boussinesq system to establish the existence,uniqueness and stability of the small periodic and almost periodic solutions to the Boussinesq system using fixed point arguments and interpolation spaces.Our results cover and extend the previous ones obtained in[13,34,38].展开更多
In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, w...In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, we show that the existence, uniqueness and time-asymptotic stability of time periodic solutions when the space dimension n 〉 5. Our proof is based on a combination of the energy method and the contraction mapping theorem.展开更多
By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficien...By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficient conditions to coexistence of periodic system are obtained.展开更多
基金supported by the National Natural Science Foundation of China (No. 61002026)
文摘To estimate the period of a periodic point process from noisy and incomplete observations, the classical periodogram algorithm is modified. The original periodogram algorithm yields an estimate by performing grid search of the peak of a spectrum, which is equivalent to the periodogram of the periodic point process, thus its performance is found to be sensitive to the chosen grid spacing. This paper derives a novel grid spacing formula, after finding a lower bound of the width of the spectral mainlobe. By employing this formula, the proposed new estimator can determine an appropriate grid spacing adaptively, and is able to yield approximate maximum likelihood estimate （MLE） with a computational complexity of O（n2）. Experimental results prove that the proposed estimator can achieve better trade-off between statistical accuracy and complexity, as compared to existing methods. Simulations also show that the derived grid spacing formula is also applicable to other estimators that operate similarly by grid search.
基金the National Natural Science Foundation of China(No.61703413).
文摘An accurate period is important to recover the pulse profile from a recorded photon event series of an X-ray pulsar and to estimate the pulse time of arrival,which is the measurement of X-ray pulsar navigation.Epoch folding is a classical period estimation method in the time domain;however,its computational complexity grows as the number of trail periods increases.In order to reduce the computational complexity,this paper improves the fast folding algorithm through segment correlation and amplitude accumulation,which is based on the post-order traversal of a binary tree.Compared with epoch folding,the improved fast folding algorithm can achieve a similar accuracy at the cost of a lower computational burden.Compared with the original fast folding algorithm,the improved algorithm can be applied to detectors with a much smaller effective area.The performance of the method is investigated by simulation data and observation data from the Neutron star Interior Composition Explorer(NICER).
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61673389,61273202,and 61134008)
文摘In this paper,we explore how to estimate the phase damping parameter γ and the tunneling amplitude parameter ？from a spin-boson dephasing quantum model by periodical projective measurements.The preparation of initial states is accomplished by performing the period measurements in our scheme.The parameter γ can be always estimated when projective measurement bases are chosen as θ = π/2 and φ = 0.Based on the estimated value of γ and the interval information of ？,we can select another measurement bases（θ = π/4 and φ = π/2） to obtain the estimated value of ？.A coherent control is indispensable to estimate ？ if γ is in the interval of ？;whereas the control is not necessary if γ is out of the known interval of ？.We establish the relation between the optimal period time and the parameter γ or ？ in terms of Fisher information.Although the optimal measurement period cannot be selected beforehand,the aforementioned relation can be utilized to adjust the measurement period to approach the optimal one.
基金Project supported by the National Natural Science Foundation of China(Grant No.61973037)。
文摘In view of the complexity of existing linear frequency modulation(LFM)signal parameter estimation methods and the poor antinoise performance and estimation accuracy under a low signal-to-noise ratio(SNR),a parameter estimation method for LFM signals with a Duffing oscillator based on frequency periodicity is proposed in this paper.This method utilizes the characteristic that the output signal of the Duffing oscillator excited by the LFM signal changes periodically with frequency,and the modulation period of the LFM signal is estimated by autocorrelation processing of the output signal of the Duffing oscillator.On this basis,the corresponding relationship between the reference frequency of the frequencyaligned Duffing oscillator and the frequency range of the LFM signal is analyzed by the periodic power spectrum method,and the frequency information of the LFM signal is determined.Simulation results show that this method can achieve high-accuracy parameter estimation for LFM signals at an SNR of-25 dB.
文摘The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0 is considered. Formulas that determine the greatest value of mean square error and the minimax estimation for the functional are proposed for the given class of admissible processes. It is shown that one-sided moving average stationary sequence gives the greatest value of the mean square error.
文摘A conservative system performing a small oscillation near every equilibrium position is analysed in classical way. The paper tries to answer the following question: How many types of the periodic small oscillation in the whole configuration space of the system are there? Making some hypotheses, it expresses the lower bounds of the number of the types for two cases where critical points of the potential function are nondegenerate and degenerate respectively by the Betti numbers and dimension of the constraint manifold only.
文摘Analyzed the relation between time delay difference and time delay estimation errors, based on the principles of three-point locating, a reformed threshold method for time delay difference estimation of impulse signals, called as amendment estimation for short, is developed by introducing channel equalization technique to its conventional version, named as direct estimation in this paper, to improve the estimation stability. After inherent relationship between time delay and phase shift of signals is analyzed, an integer period error compensation method utilized the diversities of both contribution share and contribution mode of concerned estimates is proposed under the condition of high precision phase lag estimation. Finally, a cooperative multi-threshold estimation method composed of amendment and direct estimations to process impulse signals with three thresholds is established. In sea trials data tests of passive locating, this method improves the estimation precision of time delay difference efficiently. The experiments verify the theoretical predictions.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51379195 and 41476078)the Natural Science Foundation of Shandong Province(Grant No.ZR2013EEM034)+2 种基金the Scientific Research Foundation of Science Technology Department of Zhejiang Province(Grant No.2015C34013)the Science Research Program of Zhoushan(Grant No.2014C41003)the Innovation Fund for Graduate Student of Shandong Province(Grant No.SDYY12152)
文摘The attempt to obtain long-term observed data around some sea areas we concern is usually very hard or even impossible in practical offshore and ocean engineering situations. In this paper, by means of linear mean-square estimation method, a new way to extend short-term data to long-term ones is developed. The long-term data about concerning sea areas can be constructed via a series of long-term data obtained from neighbor oceanographic stations, through relevance analysis of different data series. It is effective to cover the insufficiency of time series prediction method＇s overdependence upon the length of data series, as well as the limitation of variable numbers adopted in multiple linear regression model. The storm surge data collected from three oceanographic stations located in Shandong Peninsula are taken as examples to analyze the number-selection effect of reference oceanographic stations（adjacent to the concerning sea area） and the correlation coefficients between sea sites which are selected for reference and for engineering projects construction respectively. By comparing the N-year return-period values which are calculated from observed raw data and processed data which are extended from finite data series by means of the linear mean-square estimation method, one can draw a conclusion that this method can give considerably good estimation in practical ocean engineering, in spite of different extreme value distributions about raw and processed data.
文摘A fast parameter estimation algorithm is discussed for a polyphase coded Continuous Waveform(CW) signal in Additive White Gaussian Noise(AWGN).The proposed estimator is based on the sum of the modulus square of the ambiguity function at the different Doppler shifts.An iterative refinement stage is proposed to avoid the effect of the spurious peaks that arise when the summation length of the estimator exceeds the subcode duration.The theoretical variance of the subcode rate estimate is derived.The Monte-Carlo simulation results show that the proposed estimator is highly accurate and effective at moderate Signal-to-Noise Ratio(SNR).
基金Supported by the National Natural Science Foundation of China (No.60472089, No.90604035).
文摘In this paper, a new scheme that combines Space-Time Block-Coding (STBC) based on an Alamouti-like scheme and the Least Squares (LS) channel estimation using optimal training sequences in Cyclic-Prefix-based (CP)\Single-Carrier (SC) systems is proposed. With two transmit antennas, based on Cramer-Rao lower bound for channel estimation, it is shown that the Periodic Comple- mentary Set (PCS) is optimal over frequency-selective fading channels. Compared with the normal scheme without STBC, 3dB Mean Square Error (MSE) performance gains and fewer restrictions on the length of channel impulse response are demonstrated.
基金the National Natural Science Foundation of China (60572075)the Natural Science Researching Project for Jiangsu Universities (05KJD510177).
文摘It is well known that the periodic performance of spread spectrum sequence heavily affects the correlative and secure characteristics of communication systems. The chaotic binary sequence is paid more and more attention since it is one kind of applicable spread spectrum sequences. However, there are unavoidable short cyclic problems for chaotic binary sequences in finite precision. The chaotic binary sequence generating methods are studied first. Then the short cyclic behavior of the chaotic sequences is analyzed in detail, which are generated by quantification approaches with finite word-length. At the same time, a chaotic similar function is defined for presenting the cyclic characteristics of the sequences. Based on these efforts, an improved method with scrambling control for generating chaotic binary sequences is proposed. To quantitatively describe the improvement of periodic performance of the sequences, an orthogonal estimator is also defined. Some simulating results are provided. From the theoretical deduction and the experimental results, it is concluded that the proposed method can effectively increase the period and raise the complexity of the chaotic sequences to some extent.
文摘The sufficient condition for the existence of non constant periodic solutions of the following planar system with four delays are obtained:x [FK(W1*1。*3/4]′ 1(t)=-a 0x α 1(t)+a 1f 1(x 1(t-τ 1),x 2(t-τ 2)), x [FK(W1*1。*3/4]′ 2(t)=-b 0x α 2(t)+b 1f 2(x 1(t-τ 3),x 2(t-τ 4)).This approach is based on the continuation theorem of the coincidence degree, and the a priori estimate of periodic solutions.
基金Supported by the National Natural Science Foundation of China(1 9971 0 2 6 )
文摘The sufficient condition for the existence of2 π- periodic solutions of the following third- order functional differential equations with variable coefficients a(t) x (t) +bx″2 k- 1(t) +cx′2 k- 1(t) + 2 k- 1 i=1 cixi(t) +g(x(t-τ) ) =p(t) =p(t+2π) is obtained.The approach is based on the abstract continuation theorem from Mawhin and the a- priori estimate of periodic solutions
文摘To take the seismic zone that includes the great shock with M S8.5 as the statistical unit of estimating b value can often lead to more large variance, because the seismogenic zone of the great shock with M S8.5 are larger than that delineated in general seismic zone. Two-level statistical units are considered in this paper. The seismic province is the first level unit that is suitable for group of earthquakes including the great shock of M S8.5. A seismic province can be divided into several seismic zones. They can be taken as the second level unit for group of quakes in which the super magnitude of the greatest shock do not exceed 8. Because of the nonstationarity in time of seismic activity, the unbalancedness of data and differential of seismic temporal series feature in different areas need to be considered when we select the time period for estimating b value. According to local conditions, the time period is selected at one′s discretion in order to reflect seismicity level of this statistical unit in future 100 years.
基金supported by the National Basic Research Program of China(Grant No.2010CB832800)the National Natural Science Foundation of China(Grant Nos.11175160 and 11275075)the Natural Science Foundation of Key Projects of Hubei Province,China(Grant No.2013CFA045)
文摘The environmental noise can restrict the accuracy of period estimation since the torsion pendulum is sensitive to weak forces. Two typical models for the environmental noise are proposed to make an evaluation. Generally, the stationary environmental noise is modeled as a white noise, and contributes to the period uncertainty as a function of the initial amplitude, the quality factor, the variance of noise and the time length. As to a sudden sharp disturbance acting on the pendulum, a narrow impulse model is constructed. It results in a sharp jump in the phase difference, which can be excluded with the 3σ criterion for a correction. An experimental data analysis for the measurement of the gravitational constant G with the time-of-swing method shows that the period uncertainty due to the environmental noise is about one and a half times the fundamental thermal noise limit. Though this result is dependent on the ambient environment, the analysis is instructive to improve the measurement accuracy of experiments.
文摘The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray_Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.
文摘Suppose that a continuous 2re-periodic function f on the real axis changes its monotonicity at points Yi In this paper, for each n _ N, a trigonometric polynomial Pn of order cn is found such that： Pn has the same monotonicity as f, everywhere except, perhaps, the small intervals.
基金financially supported by the Vietnam National Foundation for Science and Technology Development under grant number 101.02-2021.04financially supported by Vietnam Ministry of Education and Training under Project B2022-BKA-06.
文摘In this paper we investigate the existence and stability of periodic solutions(on a half-line R_(+))and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded domains of R^(n) in the framework of interpolation spaces.For the linear Boussinesq system we combine the L^(p)—L^(q)-smoothing estimates and interpolation functors to prove the existence of bounded mild solutions.Then,we prove the existence of periodic solutions by invoking Massera’s principle.We also prove the existence of almost periodic solutions.Then we use the results of the linear Boussinesq system to establish the existence,uniqueness and stability of the small periodic and almost periodic solutions to the Boussinesq system using fixed point arguments and interpolation spaces.Our results cover and extend the previous ones obtained in[13,34,38].
基金Supported by National Natural Science Foundation of China(11271305)
文摘In this paper, we study the non-isentropic compressible magnetohydrodynamic system with a time periodic external force in R^n. Under the condition that the optimal time decay rates are obtained by spectral analysis, we show that the existence, uniqueness and time-asymptotic stability of time periodic solutions when the space dimension n 〉 5. Our proof is based on a combination of the energy method and the contraction mapping theorem.
基金Supported by the Science Foundation of Hangzhou Dianzi University(KYF091504021)Supported by the Science Foundation of China Jiliang University(XZ0442)
文摘By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficient conditions to coexistence of periodic system are obtained.
