In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above ...In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above function,are obtained.Especially,we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions.Meanwhile,some interesting integral operators and derivative operators of this function,are also discussed.展开更多
Multi-parameter quantum estimation has attracted considerable attention due to its broad applications.Due to the complexity of quantum dynamics,existing research places significant emphasis on estimating parameters in...Multi-parameter quantum estimation has attracted considerable attention due to its broad applications.Due to the complexity of quantum dynamics,existing research places significant emphasis on estimating parameters in time-independent Hamiltonians.Here,our work makes an effort to explore multi-parameter estimation with time-dependent Hamiltonians.In particular,we focus on the discrimination of two close frequencies of a magnetic field by using a single qubit.We optimize the quantum controls by employing both traditional optimization methods and reinforcement learning to improve the precision for estimating the frequencies of the two magnetic fields.In addition to the estimation precision,we also evaluate the robustness of the optimization schemes against the shift of the control parameters.The results demonstrate that the hybrid reinforcement learning approach achieves the highest estimation precision,and exhibits superior robustness.Moreover,a fundamental challenge in multi-parameter quantum estimation stems from the incompatibility of the optimal control strategies for different parameters.We demonstrate that the hybrid control strategies derived through numerical optimization remain effective in enhancing the precision of multi-parameter estimation in spite of the incompatibilities,thereby mitigating incompatibilities between control strategies on the estimation precision.Finally,we investigate the trade-offs in estimation precision among different parameters for different scenarios,revealing the inherent challenges in balancing the optimization of multiple parameters simultaneously and providing insights into the fundamental distinction between quantum single-parameter estimation and multi-parameter estimation.展开更多
Based on waveform fitting,full waveform inversion(FWI)is an important inversion method with the ability to reconstruct multi-parameter models in high precision.However,the strong nonlinear equation used in FWI present...Based on waveform fitting,full waveform inversion(FWI)is an important inversion method with the ability to reconstruct multi-parameter models in high precision.However,the strong nonlinear equation used in FWI presents the following challenges,such as low convergence efficiency,high dependence on the initial model,and the energy imbalance in deep region of the inverted model.To solve these inherent problems,we develop a timedomain elastic FWI method based on gradient preconditioning with the following details:(1)the limited memory Broyden Fletcher Goldfarb Shanno method with faster convergence is adopted to im-prove the inversion stability;(2)a multi-scaled inversion strategy is used to alleviate the nonlinear inversion instead of falling into the local minimum;(3)in addition,the pseudo-Hessian preconditioned illumination operator is involved for preconditioning the parameter gradients to improve the illumination equilibrium degree of deep structures.Based on the programming implementation of the new method,a deep depression model with five diffractors is used for testing.Compared with the conventional elastic FWI method,the technique proposed by this study has better effectiveness and accuracy on the inversion effect and con-vergence,respectively.展开更多
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
In this paper, the progress and development on remote sensing technology applied in earthquake monitoring research are summarized, such as differential interference synthetic aperture radar （D-InSAR）, infrared remot...In this paper, the progress and development on remote sensing technology applied in earthquake monitoring research are summarized, such as differential interference synthetic aperture radar （D-InSAR）, infrared remote sensing, and seismo-ionospheric detecting. Many new monitoring data in this domain have been used, and new data processing methods have been developed to obtain high-precision images about crustal deformation, outgoing longwave radiation （OLR）, surface latent heat flux （SLHF）, and ionospheric parameters. The development in monitoring technology and data processing technique largely enriches earthquake research information and provides new tools for earthquake stereoscope monitoring system, especially on the space part. Finally, new developing trend in this area was introduced, and some key problems in future work were pointed out.展开更多
The level of deformation development of surrounding rocks is a vital predictor to evaluate impending coal mine disasters and it is important to establish accurate measurements of the deformed status to ensure coal min...The level of deformation development of surrounding rocks is a vital predictor to evaluate impending coal mine disasters and it is important to establish accurate measurements of the deformed status to ensure coal mine safety. Traditional deformation monitoring methods are mostly based on single parameter, in this paper, multiple approaches are integrated: firstly, both electric and elastic models are established,from which electric field distribution and seismic wave recording are calculated and finally, the resistivity profiles and source position information are determined using inversion methods, from which then the deformation and failure of mine floor are evaluated. According to the inversion results of both electric and seismic field signals, multiple-parameter dynamic monitoring of surrounding rock deformation in deep mine can be performed. The methodology is validated using numerical simulation results which shows that the multi-parameter dynamic monitoring methods have better results for surrounding rock deformation in deep mine monitoring than single parameter methods.展开更多
The atmospheric corrosion monitoring(ACM)technique has been widely employed to track the real-time corrosion behavior of metal materials.However,limited studies have applied ACM to the corrosion protection properties ...The atmospheric corrosion monitoring(ACM)technique has been widely employed to track the real-time corrosion behavior of metal materials.However,limited studies have applied ACM to the corrosion protection properties of organic coatings.This study compared a bare epoxy coating with one containing zinc phosphate corrosion inhibitors,both applied on ACM sensors,to observe their corrosion protection properties over time.Coatings with artificial damage via scratches were exposed to immersion and alternating dry and wet environments,which allowed for monitoring galvanic corrosion currents in real-time.Throughout the corrosion tests,the ACM currents of the zinc phosphate/epoxy coating were considerably lower than those of the blank epoxy coating.The trend in ACM current variations closely matched the results obtained from regular electrochemical tests and surface analysis.This alignment highlights the potential of the ACM technique in evaluating the corrosion protection capabilities of organic coatings.Compared with the blank epoxy coating,the zinc phosphate/epoxy coating showed much-decreased ACM current values that confirmed the effective inhibition of zinc phosphate against steel corrosion beneath the damaged coating.展开更多
Global efforts for environmental cleanliness through the control of gaseous emissions from vehicles are gaining momentum and attracting increasing attention. Calibration plays a crucial role in these efforts by ensuri...Global efforts for environmental cleanliness through the control of gaseous emissions from vehicles are gaining momentum and attracting increasing attention. Calibration plays a crucial role in these efforts by ensuring the quantitative assessment of emissions for informed decisions on environmental treatments. This paper describes a method for the calibration of CO/CO<sub>2</sub> monitors used for periodic inspections of vehicles in cites. The calibration was performed in the selected ranges: 900 - 12,000 µmol/mol for CO and 2000 - 20,000 µmol/mol for CO<sub>2</sub>. The traceability of the measurement results to the SI units was ensured by using certified reference materials from CO/N<sub>2</sub> and CO<sub>2</sub>/N<sub>2</sub> primary gas mixtures. The method performance was evaluated by assessing its linearity, accuracy, precision, bias, and uncertainty of the calibration results. The calibration data exhibited a strong linear trend with R² values close to 1, indicating an excellent fit between the measured values and the calibration lines. Precision, expressed as relative standard deviation (%RSD), ranged from 0.48 to 4.56% for CO and from 0.97 to 3.53% for CO<sub>2</sub>, staying well below the 5% threshold for reporting results at a 95% confidence level. Accuracy measured as percent recovery, was consistently high (≥ 99.1%) for CO and ranged from 84.90% to 101.54% across the calibration range for CO<sub>2</sub>. In addition, the method exhibited minimal bias for both CO and CO<sub>2</sub> calibrations and thus provided a reliable and accurate approach for calibrating CO/CO<sub>2</sub> monitors used in vehicle inspections. Thus, it ensures the effectiveness of exhaust emission control for better environment.展开更多
In recent years, the increasing frequency of debris flow demands enhanced effectiveness and efficiency of warning systems. Effective warning systems are essential not only from an economic point of view but are also c...In recent years, the increasing frequency of debris flow demands enhanced effectiveness and efficiency of warning systems. Effective warning systems are essential not only from an economic point of view but are also considered as a frontline approach to alleviate hazards. Currently, the key issues are the imbalance between the limited lifespan of equipment, the relatively long period between the recurrences of such hazards, and the wide range of critical rainfall that trigger these disasters. This paper attempts to provide a stepwise multi-parameter debris flow warning system after taking into account the shortcomings observed in other warning systems. The whole system is divided into five stages. Differentwarning levels can be issued based on the critical rainfall thresholds. Monitoring starts when early warning is issued and it continues with debris flow near warning, triggering warning, movement warning and hazard warning stages. For early warning, historical archives of earthquake and drought are used to choose a debris flow-susceptible site for further monitoring. Secondly, weather forecasts provide an alert of possible near warning. Hazardous precipitation, model calculation and debris flow initiation tests, pore pressure sensors and water content sensors are combined to check the critical rainfall and to publically announce a triggering warning. In the final two stages, equipment such as rainfall gauges, flow stage sensors, vibration sensors, low sound sensors and infrasound meters are used to assess movement processes and issue hazardwarnings. In addition to these warnings, communitybased knowledge and information is also obtained and discussed in detail. The proposed stepwise, multiparameter debris flow monitoring and warning system has been applied in Aizi valley China which continuously monitors the debris flow activities.展开更多
Environmentalmonitoring systems based on remote sensing technology have a wider monitoringrange and longer timeliness, which makes them widely used in the detection andmanagement of pollution sources. However, haze we...Environmentalmonitoring systems based on remote sensing technology have a wider monitoringrange and longer timeliness, which makes them widely used in the detection andmanagement of pollution sources. However, haze weather conditions degrade image qualityand reduce the precision of environmental monitoring systems. To address this problem,this research proposes a remote sensing image dehazingmethod based on the atmosphericscattering model and a dark channel prior constrained network. The method consists ofa dehazing network, a dark channel information injection network (DCIIN), and a transmissionmap network. Within the dehazing network, the branch fusion module optimizesfeature weights to enhance the dehazing effect. By leveraging dark channel information,the DCIIN enables high-quality estimation of the atmospheric veil. To ensure the outputof the deep learning model aligns with physical laws, we reconstruct the haze image usingthe prediction results from the three networks. Subsequently, we apply the traditionalloss function and dark channel loss function between the reconstructed haze image and theoriginal haze image. This approach enhances interpretability and reliabilitywhile maintainingadherence to physical principles. Furthermore, the network is trained on a synthesizednon-homogeneous haze remote sensing dataset using dark channel information from cloudmaps. The experimental results show that the proposed network can achieve better imagedehazing on both synthetic and real remote sensing images with non-homogeneous hazedistribution. This research provides a new idea for solving the problem of decreased accuracyof environmental monitoring systems under haze weather conditions and has strongpracticability.展开更多
Wearable sensing systems have been designed to monitor health conditions in real-time by detecting analytes in human biofluids.Wound diagnosis remains challenging,necessitating suitable materials for high-performance ...Wearable sensing systems have been designed to monitor health conditions in real-time by detecting analytes in human biofluids.Wound diagnosis remains challenging,necessitating suitable materials for high-performance wearable sensors to offer prompt feedback.Existing devices have limitations in measuring pH and the concentration of pH-dependent electroactive species simultaneously,which is crucial for obtaining a comprehensive understanding of wound status and optimizing biosensors.Therefore,improving materials and analysis system accuracy is essential.This article introduces the first example of a flexible array capable of detecting pyocyanin,a bacterial virulence factor,while correcting dynamic pH fluctuations.We demonstrate that this combined sensor enhances accuracy by mitigating the impact of pH variability on pyocyanin sensor response.Customized screen-printable inks were developed to enhance analytical performance.The analytical performances of two sensitive sensor systems(i.e.,fully-printed porous graphene/multiwalled carbon nanotube(CNT)and polyaniline/CNT composites for pyocyanin and pH sensors)are evaluated.Partial least square regression is employed to analyze nonzero-order data arrays from square wave voltammetric and potentiometric measurements of pyocyanin and pH sensors to establish a predictive model for pyocyanin concentration in complex fluids.This sensitive and effective strategy shows potential for personalized applications due to its affordability,ease of use,and ability to adjust for dynamic pH changes.展开更多
BACKGROUND At present,the conventional methods for diagnosing cerebral edema in clinical practice are computed tomography(CT)and magnetic resonance imaging(MRI),which can evaluate the location and degree of peripheral...BACKGROUND At present,the conventional methods for diagnosing cerebral edema in clinical practice are computed tomography(CT)and magnetic resonance imaging(MRI),which can evaluate the location and degree of peripheral cerebral edema,but cannot realize quantification.When patients have symptoms of diffuse cerebral edema or high cranial pressure,CT or MRI often suggests that cerebral edema is lagging and cannot be dynamically monitored in real time.Intracranial pressure monitoring is the gold standard,but it is an invasive operation with high cost and complications.For clinical purposes,the ideal cerebral edema monitoring should be non-invasive,real-time,bedside,and continuous dynamic monitoring.The dis-turbance coefficient(DC)was used in this study to dynamically monitor the occu-rrence,development,and evolution of cerebral edema in patients with cerebral hemorrhage in real time,and review head CT or MRI to evaluate the development of the disease and guide further treatment,so as to improve the prognosis of patients with cerebral hemorrhage.AIM To offer a promising new approach for non-invasive adjuvant therapy in cerebral edema treatment.METHODS A total of 160 patients with hypertensive cerebral hemorrhage admitted to the Department of Neurosurgery,Second Affiliated Hospital of Xi’an Medical University from September 2018 to September 2019 were recruited.The patients were randomly divided into a control group(n=80)and an experimental group(n=80).Patients in the control group received conventional empirical treatment,while those in the experimental group were treated with mannitol dehydration under the guidance of DC.Subsequently,we compared the two groups with regards to the total dosage of mannitol,the total course of treatment,the incidence of complications,and prognosis.RESULTS The mean daily consumption of mannitol,the total course of treatment,and the mean hospitalization days were 362.7±117.7 mL,14.8±5.2 days,and 29.4±7.9 in the control group and 283.1±93.6 mL,11.8±4.2 days,and 23.9±8.3 in the experimental group(P<0.05).In the control group,there were 20 patients with pulmonary infection(25%),30 with electrolyte disturbance(37.5%),20 with renal impairment(25%),and 16 with stress ulcer(20%).In the experimental group,pulmonary infection occurred in 18 patients(22.5%),electrolyte disturbance in 6(7.5%),renal impairment in 2(2.5%),and stress ulcers in 15(18.8%)(P<0.05).According to the Glasgow coma scale score 6 months after discharge,the prognosis of the control group was good in 20 patients(25%),fair in 26(32.5%),and poor in 34(42.5%);the prognosis of the experimental group was good in 32(40%),fair in 36(45%),and poor in 12(15%)(P<0.05).CONCLUSION Using DC for non-invasive dynamic monitoring of cerebral edema demonstrates considerable clinical potential.It reduces mannitol dosage,treatment duration,complication rates,and hospital stays,ultimately lowering hospital-ization costs.Additionally,it improves overall patient prognosis,offering a promising new approach for non-invasive adjuvant therapy in cerebral edema treatment.展开更多
Flexible wearable optoelectronic devices fabricated fromorganic–inorganic hybrid perovskites significantly accelerate the developmentof portable energy,biomedicine,and sensing fields,but their poor thermal stabilityh...Flexible wearable optoelectronic devices fabricated fromorganic–inorganic hybrid perovskites significantly accelerate the developmentof portable energy,biomedicine,and sensing fields,but their poor thermal stabilityhinders further applications.Conversely,all-inorganic perovskites possessexcellent thermal stability,but black-phase all-inorganic perovskite filmusually requires high-temperature annealing steps,which increases energy consumptionand is not conducive to the fabrication of flexible wearable devices.In this work,an unprecedented low-temperature fabrication of stable blackphaseCsPbI3perovskite films is demonstrated by the in situ hydrolysis reactionof diphenylphosphinic chloride additive.The released diphenyl phosphateand chloride ions during the hydrolysis reaction significantly lower the phasetransition temperature and effectively passivate the defects in the perovskitefilms,yielding high-performance photodetectors with a responsivity of 42.1 AW−1 and a detectivity of 1.3×10^(14)Jones.Furthermore,high-fidelity imageand photoplethysmography sensors are demonstrated based on the fabricated flexible wearable photodetectors.This work provides a newperspective for the low-temperature fabrication of large-area all-inorganic perovskite flexible optoelectronic devices.展开更多
Surrounding rock deterioration and large deformation have always been a significant difficulty in designing and constructing tunnels in soft rock.The key lies in real-time perception and quantitative assessment of the...Surrounding rock deterioration and large deformation have always been a significant difficulty in designing and constructing tunnels in soft rock.The key lies in real-time perception and quantitative assessment of the damaged area around the tunnel.An in situ microseismic(MS)monitoring system is established in the plateau soft tock tunnel.This technique facilitates spatiotemporal monitoring of the rock mass's fracturing expansion and squeezing deformation,which agree well with field convergence deformation results.The formation mechanisms of progressive failure evolution of soft rock tunnels were discussed and analyzed with MS data and numerical results.The results demonstrate that:(1)Localized stress concentration and layered rock result in significant asymmetry in micro-fractures propagation in the tunnel radial section.As excavation continues,the fracture extension area extends into the deep surrounding rockmass on the east side affected by the weak bedding;(2)Tunnel excavation and long-term deformation can induce tensile shear action on the rock mass,vertical tension fractures(account for 45%)exist in deep rockmass,which play a crucial role in controlling the macroscopic failure of surrounding rock;and(3)Based on the radiated MS energy,a three-dimensional model was created to visualize the damage zone of the tunnel surrounding rock.The model depicted varying degrees of damage,and three high damage zones were identified.Generally,the depth of high damage zone ranged from 4 m to 12 m.This study may be a valuable reference for the warning and controlling of large deformations in similar projects.展开更多
With the rapid development of wearable electronic skin technology, flexible strain sensors have shown great application prospects in the fields of human motion and physiological signal detection, medical diagnostics, ...With the rapid development of wearable electronic skin technology, flexible strain sensors have shown great application prospects in the fields of human motion and physiological signal detection, medical diagnostics, and human-computer interaction owing to their outstanding sensing performance. This paper reports a strain sensor with synergistic conductive network, consisting of stable carbon nanotube dispersion (CNT) layer and brittle MXene layer by dip-coating and electrostatic self-assembly method, and breathable three-dimensional (3D) flexible substrate of thermoplastic polyurethane (TPU) fibrous membrane prepared through electrospinning technology. The MXene/CNT@PDA-TPU (MC@p-TPU) flexible strain sensor had excellent air permeability, wide operating range (0–450 %), high sensitivity (Gauge Factor, GFmax = 8089.7), ultra-low detection limit (0.05 %), rapid response and recovery times (40 ms/60 ms), and excellent cycle stability and durability (10,000 cycles). Given its superior strain sensing capabilities, this sensor can be applied in physiological signals detection, human motion pattern recognition, and driving exoskeleton robots. In addition, MC@p-TPU fibrous membrane also exhibited excellent photothermal conversion performance and can be used as a wearable photo-heater, which has far-reaching application potential in the photothermal therapy of human joint diseases.展开更多
A novel near-infrared all-fiber mode monitor based on a mini-two-path Mach-Zehnder interferometer(MTP-MZI)is proposed.The MTP-MZI mode monitor is created by fusing a section of(no-core fiber,NCF)and a(single-mode fibe...A novel near-infrared all-fiber mode monitor based on a mini-two-path Mach-Zehnder interferometer(MTP-MZI)is proposed.The MTP-MZI mode monitor is created by fusing a section of(no-core fiber,NCF)and a(single-mode fiber,SMF)together with an optical fiber fusion splicer,establishing two distinct centimeter-level optical transmission paths.Since the high-order modes in NCF transmit near-infrared light more sensitively to curvature-induced energy leakage than the fundamental mode in SMF,the near-infrared high-order mode light leaks out of NCF when the curvature changes,causing the MTP-MZI transmission spectrum to change.By ana⁃lyzing the relationship between the curvature,transmission spectrum,and spatial frequency spectrum,the modes involved in the interference can be studied,thereby revealing the mode transmission characteristics of near-infra⁃red light in optical fibers.In the verification experiments,higher-order modes were excited by inserting a novel hollow-core fiber(HCF)into the MTP-MZI.When the curvature of the MTP-MZI changes,the near-infrared light high-order mode introduced into the device leaks out,causing the transmission spectrum to return to its origi⁃nal state before bending and before the HCF was spliced.The experimental results demonstrate that the MTP-MZI mode monitor can monitor the fiber modes introduced from the external environment,providing both theoretical and experimental foundations for near-infrared all-fiber mode monitoring in optical information systems.展开更多
In recent decades,control performance monitoring(CPM)has experienced remarkable progress in research and industrial applications.While CPM research has been investigated using various benchmarks,the historical data be...In recent decades,control performance monitoring(CPM)has experienced remarkable progress in research and industrial applications.While CPM research has been investigated using various benchmarks,the historical data benchmark(HIS)has garnered the most attention due to its practicality and effectiveness.However,existing CPM reviews usually focus on the theoretical benchmark,and there is a lack of an in-depth review that thoroughly explores HIS-based methods.In this article,a comprehensive overview of HIS-based CPM is provided.First,we provide a novel static-dynamic perspective on data-level manifestations of control performance underlying typical controller capacities including regulation and servo:static and dynamic properties.The static property portrays time-independent variability in system output,and the dynamic property describes temporal behavior driven by closed-loop feedback.Accordingly,existing HIS-based CPM approaches and their intrinsic motivations are classified and analyzed from these two perspectives.Specifically,two mainstream solutions for CPM methods are summarized,including static analysis and dynamic analysis,which match data-driven techniques with actual controlling behavior.Furthermore,this paper also points out various opportunities and challenges faced in CPM for modern industry and provides promising directions in the context of artificial intelligence for inspiring future research.展开更多
Potential high-temperature risks exist in heat-prone components of electric moped charging devices,such as sockets,interfaces,and controllers.Traditional detection methods have limitations in terms of real-time perfor...Potential high-temperature risks exist in heat-prone components of electric moped charging devices,such as sockets,interfaces,and controllers.Traditional detection methods have limitations in terms of real-time performance and monitoring scope.To address this,a temperature detection method based on infrared image processing has been proposed:utilizing the median filtering algorithm to denoise the original infrared image,then applying an image segmentation algorithm to divide the image.展开更多
In order to address the current inability of screen printing to monitor printing pressure online,an online printing pressure monitoring system applied to screen printing machines was designed in this study.In this stu...In order to address the current inability of screen printing to monitor printing pressure online,an online printing pressure monitoring system applied to screen printing machines was designed in this study.In this study,the consistency of printed electrodes was measured by using a confocal microscope and the pressure distribution detected by online pressure monitoring system was compared to investigate the relationship.The results demonstrated the relationship between printing pressure and the consistency of printed electrodes.As printing pressure increases,the ink layer at the corresponding position becomes thicker and that higher printing pressure enhances the consistency of the printed electrodes.The experiment confirms the feasibility of the online pressure monitoring system,which aids in predicting and controlling the consistency of printed electrodes,thereby improving their performance.展开更多
Mooring cable tension is a crucial parameter for evaluating the safety and reliability of a floating platform mooring system.The real-time mooring tension in an actual marine environment has always been essential data...Mooring cable tension is a crucial parameter for evaluating the safety and reliability of a floating platform mooring system.The real-time mooring tension in an actual marine environment has always been essential data that mooring system designers aim to acquire.To address the need for long-term continuous monitoring of mooring tension in deep-sea marine environments,this paper presents a mooring cable tension monitoring method based on the principle of direct mechanical measurement.The developed tension monitoring sensors were installed and applied in the mooring system of the"Yongle"scientific experimental platform.Over the course of one year,a substantial amount of in-situ tension monitoring data was obtained.Under wave heights of up to 1.24 m,the mooring tension on the floating platform reached 16.5 tons.Through frequency domain and time domain analysis,the spectral characteristics of mooring tension,including waveinduced force,slow drift force,and mooring cable elastic restoring force,were determined.The mooring cable elastic restoring force frequency was approximately half of that of the wave signal.Due to the characteristics of the hinge connection structure of the dual module floating platform,under some specific working conditions the wave-induced force was the maximum of the three different frequency forces,and restoring force was the smallest.展开更多
基金Supported by The National Undergraduate Innovation Training Program(Grant No.202310290069Z).
文摘In this article,the multi-parameters Mittag-Leffler function is studied in detail.As a consequence,a series of novel results such as the integral representation,series representation and Mellin transform to the above function,are obtained.Especially,we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions.Meanwhile,some interesting integral operators and derivative operators of this function,are also discussed.
基金supported by the National Natural Science Foundation of China(Grant No.12075323)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0300702).
文摘Multi-parameter quantum estimation has attracted considerable attention due to its broad applications.Due to the complexity of quantum dynamics,existing research places significant emphasis on estimating parameters in time-independent Hamiltonians.Here,our work makes an effort to explore multi-parameter estimation with time-dependent Hamiltonians.In particular,we focus on the discrimination of two close frequencies of a magnetic field by using a single qubit.We optimize the quantum controls by employing both traditional optimization methods and reinforcement learning to improve the precision for estimating the frequencies of the two magnetic fields.In addition to the estimation precision,we also evaluate the robustness of the optimization schemes against the shift of the control parameters.The results demonstrate that the hybrid reinforcement learning approach achieves the highest estimation precision,and exhibits superior robustness.Moreover,a fundamental challenge in multi-parameter quantum estimation stems from the incompatibility of the optimal control strategies for different parameters.We demonstrate that the hybrid control strategies derived through numerical optimization remain effective in enhancing the precision of multi-parameter estimation in spite of the incompatibilities,thereby mitigating incompatibilities between control strategies on the estimation precision.Finally,we investigate the trade-offs in estimation precision among different parameters for different scenarios,revealing the inherent challenges in balancing the optimization of multiple parameters simultaneously and providing insights into the fundamental distinction between quantum single-parameter estimation and multi-parameter estimation.
基金supported by the Marine S&T Fund of Shandong Province for Pilot National Laboratory for Marine Science and Technology(Qingdao)(Grant No.2021QNLM020001)the National Key R&D Program of China(Grant No.2019YFC0605503C)+2 种基金the Major Scientific and Technological Projects of China National Petroleum Corporation(CNPC)(Grant No.ZD2019-183-003)the National Outstanding Youth Science Foundation(Grant No.41922028)the National Innovation Group Project(Grant No.41821002).
文摘Based on waveform fitting,full waveform inversion(FWI)is an important inversion method with the ability to reconstruct multi-parameter models in high precision.However,the strong nonlinear equation used in FWI presents the following challenges,such as low convergence efficiency,high dependence on the initial model,and the energy imbalance in deep region of the inverted model.To solve these inherent problems,we develop a timedomain elastic FWI method based on gradient preconditioning with the following details:(1)the limited memory Broyden Fletcher Goldfarb Shanno method with faster convergence is adopted to im-prove the inversion stability;(2)a multi-scaled inversion strategy is used to alleviate the nonlinear inversion instead of falling into the local minimum;(3)in addition,the pseudo-Hessian preconditioned illumination operator is involved for preconditioning the parameter gradients to improve the illumination equilibrium degree of deep structures.Based on the programming implementation of the new method,a deep depression model with five diffractors is used for testing.Compared with the conventional elastic FWI method,the technique proposed by this study has better effectiveness and accuracy on the inversion effect and con-vergence,respectively.
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
基金supported by the International Science and Technology Cooperation Program of China(2010DFB20190)the Key Project of Earthquake Science(201008007)
文摘In this paper, the progress and development on remote sensing technology applied in earthquake monitoring research are summarized, such as differential interference synthetic aperture radar （D-InSAR）, infrared remote sensing, and seismo-ionospheric detecting. Many new monitoring data in this domain have been used, and new data processing methods have been developed to obtain high-precision images about crustal deformation, outgoing longwave radiation （OLR）, surface latent heat flux （SLHF）, and ionospheric parameters. The development in monitoring technology and data processing technique largely enriches earthquake research information and provides new tools for earthquake stereoscope monitoring system, especially on the space part. Finally, new developing trend in this area was introduced, and some key problems in future work were pointed out.
基金financial support from the Fundamental Research Funds for the Central Universities of China (No. 2015QNB19)the financial support from the Open Fund of Key Laboratory of Safety and High-efficiency Coal Mining, Ministry of Education of China (No. JYBSYS2015107)+2 种基金the National Natural Science Foundation of China (Nos. 51404254, 41430317 and U1261202)the China Postdoctoral Science Foundation of China (No. 2014M560465)the Jiangsu Planned Projects for Postdoctoral Research Funds of China (No. 1302050B)
文摘The level of deformation development of surrounding rocks is a vital predictor to evaluate impending coal mine disasters and it is important to establish accurate measurements of the deformed status to ensure coal mine safety. Traditional deformation monitoring methods are mostly based on single parameter, in this paper, multiple approaches are integrated: firstly, both electric and elastic models are established,from which electric field distribution and seismic wave recording are calculated and finally, the resistivity profiles and source position information are determined using inversion methods, from which then the deformation and failure of mine floor are evaluated. According to the inversion results of both electric and seismic field signals, multiple-parameter dynamic monitoring of surrounding rock deformation in deep mine can be performed. The methodology is validated using numerical simulation results which shows that the multi-parameter dynamic monitoring methods have better results for surrounding rock deformation in deep mine monitoring than single parameter methods.
基金financially supported by the National Natural Science Foundation of China(No.52371049)the Young Elite Scientists Sponsorship Program by the China Association for Science and Technology(YESS,No.2020QNRC001)the National Science and Technology Resources Investigation Program of China(Nos.2021FY100603 and 2019FY101404)。
文摘The atmospheric corrosion monitoring(ACM)technique has been widely employed to track the real-time corrosion behavior of metal materials.However,limited studies have applied ACM to the corrosion protection properties of organic coatings.This study compared a bare epoxy coating with one containing zinc phosphate corrosion inhibitors,both applied on ACM sensors,to observe their corrosion protection properties over time.Coatings with artificial damage via scratches were exposed to immersion and alternating dry and wet environments,which allowed for monitoring galvanic corrosion currents in real-time.Throughout the corrosion tests,the ACM currents of the zinc phosphate/epoxy coating were considerably lower than those of the blank epoxy coating.The trend in ACM current variations closely matched the results obtained from regular electrochemical tests and surface analysis.This alignment highlights the potential of the ACM technique in evaluating the corrosion protection capabilities of organic coatings.Compared with the blank epoxy coating,the zinc phosphate/epoxy coating showed much-decreased ACM current values that confirmed the effective inhibition of zinc phosphate against steel corrosion beneath the damaged coating.
文摘Global efforts for environmental cleanliness through the control of gaseous emissions from vehicles are gaining momentum and attracting increasing attention. Calibration plays a crucial role in these efforts by ensuring the quantitative assessment of emissions for informed decisions on environmental treatments. This paper describes a method for the calibration of CO/CO<sub>2</sub> monitors used for periodic inspections of vehicles in cites. The calibration was performed in the selected ranges: 900 - 12,000 µmol/mol for CO and 2000 - 20,000 µmol/mol for CO<sub>2</sub>. The traceability of the measurement results to the SI units was ensured by using certified reference materials from CO/N<sub>2</sub> and CO<sub>2</sub>/N<sub>2</sub> primary gas mixtures. The method performance was evaluated by assessing its linearity, accuracy, precision, bias, and uncertainty of the calibration results. The calibration data exhibited a strong linear trend with R² values close to 1, indicating an excellent fit between the measured values and the calibration lines. Precision, expressed as relative standard deviation (%RSD), ranged from 0.48 to 4.56% for CO and from 0.97 to 3.53% for CO<sub>2</sub>, staying well below the 5% threshold for reporting results at a 95% confidence level. Accuracy measured as percent recovery, was consistently high (≥ 99.1%) for CO and ranged from 84.90% to 101.54% across the calibration range for CO<sub>2</sub>. In addition, the method exhibited minimal bias for both CO and CO<sub>2</sub> calibrations and thus provided a reliable and accurate approach for calibrating CO/CO<sub>2</sub> monitors used in vehicle inspections. Thus, it ensures the effectiveness of exhaust emission control for better environment.
基金supported by the National Natural Science Foundation of China(Grant Nos.41661134012 and 41501012)Foundation for selected young scientists,Institute of Mountain Hazards and Environment,CAS(Grant Nos.SDSQN-1306,Y3L1340340,sds-135-1202-02)
文摘In recent years, the increasing frequency of debris flow demands enhanced effectiveness and efficiency of warning systems. Effective warning systems are essential not only from an economic point of view but are also considered as a frontline approach to alleviate hazards. Currently, the key issues are the imbalance between the limited lifespan of equipment, the relatively long period between the recurrences of such hazards, and the wide range of critical rainfall that trigger these disasters. This paper attempts to provide a stepwise multi-parameter debris flow warning system after taking into account the shortcomings observed in other warning systems. The whole system is divided into five stages. Differentwarning levels can be issued based on the critical rainfall thresholds. Monitoring starts when early warning is issued and it continues with debris flow near warning, triggering warning, movement warning and hazard warning stages. For early warning, historical archives of earthquake and drought are used to choose a debris flow-susceptible site for further monitoring. Secondly, weather forecasts provide an alert of possible near warning. Hazardous precipitation, model calculation and debris flow initiation tests, pore pressure sensors and water content sensors are combined to check the critical rainfall and to publically announce a triggering warning. In the final two stages, equipment such as rainfall gauges, flow stage sensors, vibration sensors, low sound sensors and infrasound meters are used to assess movement processes and issue hazardwarnings. In addition to these warnings, communitybased knowledge and information is also obtained and discussed in detail. The proposed stepwise, multiparameter debris flow monitoring and warning system has been applied in Aizi valley China which continuously monitors the debris flow activities.
基金supported by the National Natural Science Foundation of China(No.51605054).
文摘Environmentalmonitoring systems based on remote sensing technology have a wider monitoringrange and longer timeliness, which makes them widely used in the detection andmanagement of pollution sources. However, haze weather conditions degrade image qualityand reduce the precision of environmental monitoring systems. To address this problem,this research proposes a remote sensing image dehazingmethod based on the atmosphericscattering model and a dark channel prior constrained network. The method consists ofa dehazing network, a dark channel information injection network (DCIIN), and a transmissionmap network. Within the dehazing network, the branch fusion module optimizesfeature weights to enhance the dehazing effect. By leveraging dark channel information,the DCIIN enables high-quality estimation of the atmospheric veil. To ensure the outputof the deep learning model aligns with physical laws, we reconstruct the haze image usingthe prediction results from the three networks. Subsequently, we apply the traditionalloss function and dark channel loss function between the reconstructed haze image and theoriginal haze image. This approach enhances interpretability and reliabilitywhile maintainingadherence to physical principles. Furthermore, the network is trained on a synthesizednon-homogeneous haze remote sensing dataset using dark channel information from cloudmaps. The experimental results show that the proposed network can achieve better imagedehazing on both synthetic and real remote sensing images with non-homogeneous hazedistribution. This research provides a new idea for solving the problem of decreased accuracyof environmental monitoring systems under haze weather conditions and has strongpracticability.
基金the Talent Management Project of Prince of Songkla University
文摘Wearable sensing systems have been designed to monitor health conditions in real-time by detecting analytes in human biofluids.Wound diagnosis remains challenging,necessitating suitable materials for high-performance wearable sensors to offer prompt feedback.Existing devices have limitations in measuring pH and the concentration of pH-dependent electroactive species simultaneously,which is crucial for obtaining a comprehensive understanding of wound status and optimizing biosensors.Therefore,improving materials and analysis system accuracy is essential.This article introduces the first example of a flexible array capable of detecting pyocyanin,a bacterial virulence factor,while correcting dynamic pH fluctuations.We demonstrate that this combined sensor enhances accuracy by mitigating the impact of pH variability on pyocyanin sensor response.Customized screen-printable inks were developed to enhance analytical performance.The analytical performances of two sensitive sensor systems(i.e.,fully-printed porous graphene/multiwalled carbon nanotube(CNT)and polyaniline/CNT composites for pyocyanin and pH sensors)are evaluated.Partial least square regression is employed to analyze nonzero-order data arrays from square wave voltammetric and potentiometric measurements of pyocyanin and pH sensors to establish a predictive model for pyocyanin concentration in complex fluids.This sensitive and effective strategy shows potential for personalized applications due to its affordability,ease of use,and ability to adjust for dynamic pH changes.
基金Supported by the Shaanxi Provincial Key Research and Development Plan Project,No.2020ZDLSF01-02.
文摘BACKGROUND At present,the conventional methods for diagnosing cerebral edema in clinical practice are computed tomography(CT)and magnetic resonance imaging(MRI),which can evaluate the location and degree of peripheral cerebral edema,but cannot realize quantification.When patients have symptoms of diffuse cerebral edema or high cranial pressure,CT or MRI often suggests that cerebral edema is lagging and cannot be dynamically monitored in real time.Intracranial pressure monitoring is the gold standard,but it is an invasive operation with high cost and complications.For clinical purposes,the ideal cerebral edema monitoring should be non-invasive,real-time,bedside,and continuous dynamic monitoring.The dis-turbance coefficient(DC)was used in this study to dynamically monitor the occu-rrence,development,and evolution of cerebral edema in patients with cerebral hemorrhage in real time,and review head CT or MRI to evaluate the development of the disease and guide further treatment,so as to improve the prognosis of patients with cerebral hemorrhage.AIM To offer a promising new approach for non-invasive adjuvant therapy in cerebral edema treatment.METHODS A total of 160 patients with hypertensive cerebral hemorrhage admitted to the Department of Neurosurgery,Second Affiliated Hospital of Xi’an Medical University from September 2018 to September 2019 were recruited.The patients were randomly divided into a control group(n=80)and an experimental group(n=80).Patients in the control group received conventional empirical treatment,while those in the experimental group were treated with mannitol dehydration under the guidance of DC.Subsequently,we compared the two groups with regards to the total dosage of mannitol,the total course of treatment,the incidence of complications,and prognosis.RESULTS The mean daily consumption of mannitol,the total course of treatment,and the mean hospitalization days were 362.7±117.7 mL,14.8±5.2 days,and 29.4±7.9 in the control group and 283.1±93.6 mL,11.8±4.2 days,and 23.9±8.3 in the experimental group(P<0.05).In the control group,there were 20 patients with pulmonary infection(25%),30 with electrolyte disturbance(37.5%),20 with renal impairment(25%),and 16 with stress ulcer(20%).In the experimental group,pulmonary infection occurred in 18 patients(22.5%),electrolyte disturbance in 6(7.5%),renal impairment in 2(2.5%),and stress ulcers in 15(18.8%)(P<0.05).According to the Glasgow coma scale score 6 months after discharge,the prognosis of the control group was good in 20 patients(25%),fair in 26(32.5%),and poor in 34(42.5%);the prognosis of the experimental group was good in 32(40%),fair in 36(45%),and poor in 12(15%)(P<0.05).CONCLUSION Using DC for non-invasive dynamic monitoring of cerebral edema demonstrates considerable clinical potential.It reduces mannitol dosage,treatment duration,complication rates,and hospital stays,ultimately lowering hospital-ization costs.Additionally,it improves overall patient prognosis,offering a promising new approach for non-invasive adjuvant therapy in cerebral edema treatment.
基金supported by the National Natural Science Foundation of China(52303257,52321006,T2394480,and T2394484)the National Key R&D Program of China(Grant No.2023YFE0111500)+3 种基金Key Research&Development and Promotion of Special Project(Scientific Problem Tackling)of Henan Province(242102211090)the China Postdoctoral Science Foundation(2023TQ0300,and 2023M743171)the Postdoctoral Fellowship Program(Grade B)of China Postdoctoral Science Foundation(GZB20230666)College Student Innovation and Entrepreneurship Training Program of Zhengzhou University(202410459200)。
文摘Flexible wearable optoelectronic devices fabricated fromorganic–inorganic hybrid perovskites significantly accelerate the developmentof portable energy,biomedicine,and sensing fields,but their poor thermal stabilityhinders further applications.Conversely,all-inorganic perovskites possessexcellent thermal stability,but black-phase all-inorganic perovskite filmusually requires high-temperature annealing steps,which increases energy consumptionand is not conducive to the fabrication of flexible wearable devices.In this work,an unprecedented low-temperature fabrication of stable blackphaseCsPbI3perovskite films is demonstrated by the in situ hydrolysis reactionof diphenylphosphinic chloride additive.The released diphenyl phosphateand chloride ions during the hydrolysis reaction significantly lower the phasetransition temperature and effectively passivate the defects in the perovskitefilms,yielding high-performance photodetectors with a responsivity of 42.1 AW−1 and a detectivity of 1.3×10^(14)Jones.Furthermore,high-fidelity imageand photoplethysmography sensors are demonstrated based on the fabricated flexible wearable photodetectors.This work provides a newperspective for the low-temperature fabrication of large-area all-inorganic perovskite flexible optoelectronic devices.
基金the funding support from the National Natural Science Foundation of China(Grant Nos.U23A2060,42177143 and 42277461).
文摘Surrounding rock deterioration and large deformation have always been a significant difficulty in designing and constructing tunnels in soft rock.The key lies in real-time perception and quantitative assessment of the damaged area around the tunnel.An in situ microseismic(MS)monitoring system is established in the plateau soft tock tunnel.This technique facilitates spatiotemporal monitoring of the rock mass's fracturing expansion and squeezing deformation,which agree well with field convergence deformation results.The formation mechanisms of progressive failure evolution of soft rock tunnels were discussed and analyzed with MS data and numerical results.The results demonstrate that:(1)Localized stress concentration and layered rock result in significant asymmetry in micro-fractures propagation in the tunnel radial section.As excavation continues,the fracture extension area extends into the deep surrounding rockmass on the east side affected by the weak bedding;(2)Tunnel excavation and long-term deformation can induce tensile shear action on the rock mass,vertical tension fractures(account for 45%)exist in deep rockmass,which play a crucial role in controlling the macroscopic failure of surrounding rock;and(3)Based on the radiated MS energy,a three-dimensional model was created to visualize the damage zone of the tunnel surrounding rock.The model depicted varying degrees of damage,and three high damage zones were identified.Generally,the depth of high damage zone ranged from 4 m to 12 m.This study may be a valuable reference for the warning and controlling of large deformations in similar projects.
基金supported by the National Natural Science Foundation of China(Nos.52373093 and 12072325)the Outstanding Youth Fund of Henan Province(No.242300421062)+1 种基金National Key R&D Program of China(No.2019YFA0706802)the 111 project(No.D18023).
文摘With the rapid development of wearable electronic skin technology, flexible strain sensors have shown great application prospects in the fields of human motion and physiological signal detection, medical diagnostics, and human-computer interaction owing to their outstanding sensing performance. This paper reports a strain sensor with synergistic conductive network, consisting of stable carbon nanotube dispersion (CNT) layer and brittle MXene layer by dip-coating and electrostatic self-assembly method, and breathable three-dimensional (3D) flexible substrate of thermoplastic polyurethane (TPU) fibrous membrane prepared through electrospinning technology. The MXene/CNT@PDA-TPU (MC@p-TPU) flexible strain sensor had excellent air permeability, wide operating range (0–450 %), high sensitivity (Gauge Factor, GFmax = 8089.7), ultra-low detection limit (0.05 %), rapid response and recovery times (40 ms/60 ms), and excellent cycle stability and durability (10,000 cycles). Given its superior strain sensing capabilities, this sensor can be applied in physiological signals detection, human motion pattern recognition, and driving exoskeleton robots. In addition, MC@p-TPU fibrous membrane also exhibited excellent photothermal conversion performance and can be used as a wearable photo-heater, which has far-reaching application potential in the photothermal therapy of human joint diseases.
基金Supported by the Central Government Guidance on Local Science and Technology Development Funds(2023ZY1023)the Six Talent Peaks Project in Jiangsu Province(KTHY-052).
文摘A novel near-infrared all-fiber mode monitor based on a mini-two-path Mach-Zehnder interferometer(MTP-MZI)is proposed.The MTP-MZI mode monitor is created by fusing a section of(no-core fiber,NCF)and a(single-mode fiber,SMF)together with an optical fiber fusion splicer,establishing two distinct centimeter-level optical transmission paths.Since the high-order modes in NCF transmit near-infrared light more sensitively to curvature-induced energy leakage than the fundamental mode in SMF,the near-infrared high-order mode light leaks out of NCF when the curvature changes,causing the MTP-MZI transmission spectrum to change.By ana⁃lyzing the relationship between the curvature,transmission spectrum,and spatial frequency spectrum,the modes involved in the interference can be studied,thereby revealing the mode transmission characteristics of near-infra⁃red light in optical fibers.In the verification experiments,higher-order modes were excited by inserting a novel hollow-core fiber(HCF)into the MTP-MZI.When the curvature of the MTP-MZI changes,the near-infrared light high-order mode introduced into the device leaks out,causing the transmission spectrum to return to its origi⁃nal state before bending and before the HCF was spliced.The experimental results demonstrate that the MTP-MZI mode monitor can monitor the fiber modes introduced from the external environment,providing both theoretical and experimental foundations for near-infrared all-fiber mode monitoring in optical information systems.
基金supported in part by the National Natural Science Foundation of China(62125306)Zhejiang Key Research and Development Project(2024C01163)the State Key Laboratory of Industrial Control Technology,China(ICT2024A06)
文摘In recent decades,control performance monitoring(CPM)has experienced remarkable progress in research and industrial applications.While CPM research has been investigated using various benchmarks,the historical data benchmark(HIS)has garnered the most attention due to its practicality and effectiveness.However,existing CPM reviews usually focus on the theoretical benchmark,and there is a lack of an in-depth review that thoroughly explores HIS-based methods.In this article,a comprehensive overview of HIS-based CPM is provided.First,we provide a novel static-dynamic perspective on data-level manifestations of control performance underlying typical controller capacities including regulation and servo:static and dynamic properties.The static property portrays time-independent variability in system output,and the dynamic property describes temporal behavior driven by closed-loop feedback.Accordingly,existing HIS-based CPM approaches and their intrinsic motivations are classified and analyzed from these two perspectives.Specifically,two mainstream solutions for CPM methods are summarized,including static analysis and dynamic analysis,which match data-driven techniques with actual controlling behavior.Furthermore,this paper also points out various opportunities and challenges faced in CPM for modern industry and provides promising directions in the context of artificial intelligence for inspiring future research.
基金supported by the National Key Research and Development Project of China(No.2023YFB3709605)the National Natural Science Foundation of China(No.62073193)the National College Student Innovation Training Program(No.202310422122)。
文摘Potential high-temperature risks exist in heat-prone components of electric moped charging devices,such as sockets,interfaces,and controllers.Traditional detection methods have limitations in terms of real-time performance and monitoring scope.To address this,a temperature detection method based on infrared image processing has been proposed:utilizing the median filtering algorithm to denoise the original infrared image,then applying an image segmentation algorithm to divide the image.
文摘In order to address the current inability of screen printing to monitor printing pressure online,an online printing pressure monitoring system applied to screen printing machines was designed in this study.In this study,the consistency of printed electrodes was measured by using a confocal microscope and the pressure distribution detected by online pressure monitoring system was compared to investigate the relationship.The results demonstrated the relationship between printing pressure and the consistency of printed electrodes.As printing pressure increases,the ink layer at the corresponding position becomes thicker and that higher printing pressure enhances the consistency of the printed electrodes.The experiment confirms the feasibility of the online pressure monitoring system,which aids in predicting and controlling the consistency of printed electrodes,thereby improving their performance.
文摘Mooring cable tension is a crucial parameter for evaluating the safety and reliability of a floating platform mooring system.The real-time mooring tension in an actual marine environment has always been essential data that mooring system designers aim to acquire.To address the need for long-term continuous monitoring of mooring tension in deep-sea marine environments,this paper presents a mooring cable tension monitoring method based on the principle of direct mechanical measurement.The developed tension monitoring sensors were installed and applied in the mooring system of the"Yongle"scientific experimental platform.Over the course of one year,a substantial amount of in-situ tension monitoring data was obtained.Under wave heights of up to 1.24 m,the mooring tension on the floating platform reached 16.5 tons.Through frequency domain and time domain analysis,the spectral characteristics of mooring tension,including waveinduced force,slow drift force,and mooring cable elastic restoring force,were determined.The mooring cable elastic restoring force frequency was approximately half of that of the wave signal.Due to the characteristics of the hinge connection structure of the dual module floating platform,under some specific working conditions the wave-induced force was the maximum of the three different frequency forces,and restoring force was the smallest.
