This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic diff...This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.展开更多
The generation of synthetic trajectories has become essential in various fields for analyzing complex movement patterns.However,the use of real-world trajectory data poses significant privacy risks,such as location re...The generation of synthetic trajectories has become essential in various fields for analyzing complex movement patterns.However,the use of real-world trajectory data poses significant privacy risks,such as location reidentification and correlation attacks.To address these challenges,privacy-preserving trajectory generation methods are critical for applications relying on sensitive location data.This paper introduces DPIL-Traj,an advanced framework designed to generate synthetic trajectories while achieving a superior balance between data utility and privacy preservation.Firstly,the framework incorporates Differential Privacy Clustering,which anonymizes trajectory data by applying differential privacy techniques that add noise,ensuring the protection of sensitive user information.Secondly,Imitation Learning is used to replicate decision-making behaviors observed in real-world trajectories.By learning from expert trajectories,this component generates synthetic data that closely mimics real-world decision-making processes while optimizing the quality of the generated trajectories.Finally,Markov-based Trajectory Generation is employed to capture and maintain the inherent temporal dynamics of movement patterns.Extensive experiments conducted on the GeoLife trajectory dataset show that DPIL-Traj improves utility performance by an average of 19.85%,and in terms of privacy performance by an average of 12.51%,compared to state-of-the-art approaches.Ablation studies further reveal that DP clustering effectively safeguards privacy,imitation learning enhances utility under noise,and the Markov module strengthens temporal coherence.展开更多
Fractional differential equations(FDEs)provide a powerful tool for modeling systems with memory and non-local effects,but understanding their underlying structure remains a significant challenge.While numerous numeric...Fractional differential equations(FDEs)provide a powerful tool for modeling systems with memory and non-local effects,but understanding their underlying structure remains a significant challenge.While numerous numerical and semi-analytical methods exist to find solutions,new approaches are needed to analyze the intrinsic properties of the FDEs themselves.This paper introduces a novel computational framework for the structural analysis of FDEs involving iterated Caputo derivatives.The methodology is based on a transformation that recasts the original FDE into an equivalent higher-order form,represented as the sum of a closed-form,integer-order component G(y)and a residual fractional power seriesΨ(x).This transformed FDE is subsequently reduced to a first-order ordinary differential equation(ODE).The primary novelty of the proposed methodology lies in treating the structure of the integer-order component G(y)not as fixed,but as a parameterizable polynomial whose coefficients can be determined via global optimization.Using particle swarm optimization,the framework identifies an optimal ODE architecture by minimizing a dual objective that balances solution accuracy against a high-fidelity reference and the magnitude of the truncated residual series.The effectiveness of the approach is demonstrated on both a linear FDE and a nonlinear fractional Riccati equation.Results demonstrate that the framework successfully identifies an optimal,low-degree polynomial ODE architecture that is not necessarily identical to the forcing function of the original FDE.This work provides a new tool for analyzing the underlying structure of FDEs and gaining deeper insights into the interplay between local and non-local dynamics in fractional systems.展开更多
In this article,we study the meromorphic solutions of the following non-linear differential equation■where n and k are integers with n≥k≥3,P_(d)(z,f)is a differential polynomial in f of degree d≤n−1,p′js andα′j...In this article,we study the meromorphic solutions of the following non-linear differential equation■where n and k are integers with n≥k≥3,P_(d)(z,f)is a differential polynomial in f of degree d≤n−1,p′js andα′js are non-zero constants.We obtain the expressions of meromorphic solutions of the above equations under some restrictions onα′js.Some examples are given to illustrate the possibilities of our results.展开更多
Precisely estimating the state of health(SOH)of lithium-ion batteries is essential for battery management systems(BMS),as it plays a key role in ensuring the safe and reliable operation of battery systems.However,curr...Precisely estimating the state of health(SOH)of lithium-ion batteries is essential for battery management systems(BMS),as it plays a key role in ensuring the safe and reliable operation of battery systems.However,current SOH estimation methods often overlook the valuable temperature information that can effectively characterize battery aging during capacity degradation.Additionally,the Elman neural network,which is commonly employed for SOH estimation,exhibits several drawbacks,including slow training speed,a tendency to become trapped in local minima,and the initialization of weights and thresholds using pseudo-random numbers,leading to unstable model performance.To address these issues,this study addresses the challenge of precise and effective SOH detection by proposing a method for estimating the SOH of lithium-ion batteries based on differential thermal voltammetry(DTV)and an SSA-Elman neural network.Firstly,two health features(HFs)considering temperature factors and battery voltage are extracted fromthe differential thermal voltammetry curves and incremental capacity curves.Next,the Sparrow Search Algorithm(SSA)is employed to optimize the initial weights and thresholds of the Elman neural network,forming the SSA-Elman neural network model.To validate the performance,various neural networks,including the proposed SSA-Elman network,are tested using the Oxford battery aging dataset.The experimental results demonstrate that the method developed in this study achieves superior accuracy and robustness,with a mean absolute error(MAE)of less than 0.9%and a rootmean square error(RMSE)below 1.4%.展开更多
When a differential field K having n commuting derivations is given together with two finitely generated differential extensions L and M of K, an important problem in differential algebra is to exhibit a common differ...When a differential field K having n commuting derivations is given together with two finitely generated differential extensions L and M of K, an important problem in differential algebra is to exhibit a common differential extension N in order to define the new differential extensions L<span style="white-space:nowrap;"><span style="white-space:nowrap;">∩M and the smallest differential field <span style="white-space:nowrap;">(L,M ) <span style="white-space:nowrap;"><span style="white-space:nowrap;">⊂ N containing both L and M. Such a result allows to generalize the use of complex numbers in classical algebra. Having now two finitely generated differential modules L and M over the non-commutative ring <span style="white-space:nowrap;">D = K [d<sub>1</sub>,...,d<sub>n</sub>] = K [d] of differential operators with coefficients in K, we may similarly look for a differential module N containing both L and M in order to define <span style="white-space:nowrap;">L∩M and <span style="white-space:nowrap;">L+M. This is exactly the situation met in linear or non-linear OD or PD control theory by selecting the inputs and the outputs among the control variables. However, in many recent books and papers, we have shown that controllability was a built-in property of a control system, not depending on the choice of inputs and outputs. The purpose of this paper is thus to revisit control theory by showing the specific importance of the two previous problems and the part plaid by N in both cases for the parametrization of the control system. An important tool will be the study of differential correspondences, a modern name for what was called B<span style="white-space:nowrap;"><span style="white-space:nowrap;">äcklund problem during the last century, namely the elimination theory for groups of variables among systems of linear or nonlinear OD or PD equations. The main difficulty is to revisit differential homological algebra by using noncommutative localization as a way to generalize the symbolic calculus in the style of Heaviside and Mikusinski. Finally, when M is a D-module, this paper is using for the first time the fact that the system <span style="white-space:nowrap;">R = hom<sub>K</sub> (M,K) is a D-module for the Spencer operator acting on sections, avoiding thus behaviours, trajectories and signal spaces in a purely formal way, contrary to a few recent works on this difficult subject.展开更多
The lamina(combination)types,reservoir characteristics and shale oil occurrence states of organic-rich shale in the Triassic Yanchang Formation Chang 73 sub-member in the Ordos Basin were systematically investigated t...The lamina(combination)types,reservoir characteristics and shale oil occurrence states of organic-rich shale in the Triassic Yanchang Formation Chang 73 sub-member in the Ordos Basin were systematically investigated to reveal the main controlling factors of shale oil occurrence under different lamina combinations.The differential enrichment mechanisms and patterns of shale oil were discussed using the shale oil micro-migration characterization and evaluation methods from the perspectives of relay hydrocarbon supply,stepwise migration,and multi-stage differentiation.The results are obtained in five aspects.First,Chang 73 shale mainly develops five types of lamina combination,i.e.non-laminated shale,sandy laminated shale,tuffaceous laminated shale,mixed laminated shale,and organic-rich laminated shale.Second,shales with different lamina combinations are obviously different in the reservoir space.Specifically,shales with sandy laminae and tuffaceous laminae have a large number of intergranular pores,dissolution pores and hydrocarbon generation-induced fractures.The multi-scale pore and fracture system constitutes the main place for liquid hydrocarbon occurrence.Third,the occurrence and distribution of shale oil in shale with different lamina combinations are jointly controlled by organic matter abundance,reservoir property,thermal evolution degree,mineral composition and laminae scale.The micro-nano-scale pore-fracture networks within shales containing rigid laminae,particularly sandy and tuffaceous laminations,primarily contain free-state light hydrocarbon components.In contrast,adsorption-phase heavy hydrocarbon components predominantly occupy surfaces of organic matter assemblages,clay mineral matrices,and framework mineral particulates.Fourth,there is obvious shale oil micro-migration between shales with different lamina combinations in Chang 73.Generally,such micro-migration is stepwise in a sequence of organic-rich laminated shale→tuffaceous laminated shale→mixed laminated shale→sandy lamiated shale→non-laminated shale.Fifth,the relay hydrocarbon supply of organic matter under the control of the spatial superposition of shales with various laminae,the stepwise migration via multi-scale pore and fracture network,and the multi-differentiation in shales with different lamina combinations under the control of organic-inorganic interactions fundamentally decide the differences of shale oil components between shales with different lamina combinations.展开更多
Based on the coalbed methane(CBM)/coal-rock gas(CRG)geological,geophysical,and experimental testing data from the Daji block in the Ordos Basin,the coal-forming and hydrocarbon generation&accumulation characterist...Based on the coalbed methane(CBM)/coal-rock gas(CRG)geological,geophysical,and experimental testing data from the Daji block in the Ordos Basin,the coal-forming and hydrocarbon generation&accumulation characteristics across different zones were dissected,and the key factors controlling the differential CBM/CRG enrichment were identified.The No.8 coal seam of the Carboniferous Benxi Formation in the Daji block is 8-10 m thick,typically overlain by limestone.The primary hydrocarbon generation phase occurred during the Early Cretaceous.Based on the differences in tectonic evolution and CRG occurrence,and with the maximum vitrinite reflectance of 2.0%and burial depth of 1800 m as boundaries,the study area is divided into deeply buried and deeply preserved,deeply buried and shallowly preserved,and shallowly buried and shallowly preserved zones.The deeply buried and deeply preserved zone contains gas content of 22-35 m^(3)/t,adsorbed gas saturation of 95%-100%,and formation water with total dissolved solid(TDS)higher than 50000 mg/L.This zone features structural stability and strong sealing capacity,with high gas production rates.The deeply buried and shallowly preserved zone contains gas content of 16-20 m^(3)/t,adsorbed gas saturation of 80%-95%,and formation water with TDS of 5000-50000 mg/L.This zone exhibits localized structural modification and hydrodynamic sealing,with moderate gas production rate.The shallowly buried and shallowly preserved zone contains gas content of 8-16 m^(3)/t,adsorbed gas saturation of 50%-70%,and formation water with TDS lower than 5000 mg/L.This zone experienced intense uplift,resulting in poor sealing and secondary alteration of the primary gas reservoir,with partial adsorbed gas loss,and low gas production rate.A depositional unification and structural divergence model is proposed,that is,although coal seams across the basin experienced broadly similar depositional and tectonic histories,differences in tectonic intensity have led to spatial heterogeneity in the maximum burial depth(i.e.,thermal maturity of coal)and current burial depth and occurrence of CRG(i.e.,gas content and occurrence state).The research results provide valuable guidance for advancing the theoretical understanding of CBM/CRG enrichment and for improving exploration and development practices.展开更多
When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game ...When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game strategy,the game of kind is generally considered to be angle-optimized,which allows unlimited turns,but these practices do not take into account the effect of acceleration,which does not correspond to the actual situation,thus,based on the angle-optimized,the acceleration optimization and the acceleration upper bound constraint are added into the game for consideration.A two-to-one differential game problem is proposed in the three-dimensional space,and an improved multi-objective grey wolf optimization(IMOGWO)algorithm is proposed to solve the optimal game point of this problem.With the equations that describe the relative motions between the pursuers and the evader in the three-dimensional space,a multi-objective function with constraints is given as the performance index to design an optimal strategy for the differential game.Then the optimal game point is solved by using the IMOGWO algorithm.It is proved based on Markov chains that with the IMOGWO,the Pareto solution set is the solution of the differential game.Finally,it is verified through simulations that the pursuers can capture the escapee,and via comparative experiments,it is shown that the IMOGWO algorithm performs well in terms of running time and memory usage.展开更多
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error...In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.展开更多
This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–M...This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.展开更多
The two-player nonzero-sum linear-exponential-quadratic stochastic differential game is studied.The game takes into account the players'attitudes to risk.The nonlinear transformations and change of probability mea...The two-player nonzero-sum linear-exponential-quadratic stochastic differential game is studied.The game takes into account the players'attitudes to risk.The nonlinear transformations and change of probability measure techniques are used to study the existence of both open-loop and closed-loop Nash equilibria for the game.Some examples are constructed to illustrate their differences.Furthermore,theoretical results are applied to solve the risk-sensitive portfolio game problem in the financial market and show the effects of risk attitudes and economic performance on equilibria.展开更多
In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval...In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals.展开更多
This study aims to explore the clinical and CT imaging features of brucellosis spondylitis(BS)and to strengthen the clinical cognition to reduce misdiagnosis and mistreatment.In this study,clinical and CT imaging data...This study aims to explore the clinical and CT imaging features of brucellosis spondylitis(BS)and to strengthen the clinical cognition to reduce misdiagnosis and mistreatment.In this study,clinical and CT imaging data of 106 patients with BS diagnosed in the Second Hospital of Hohhot and the Third Hospital of Baotou were collected from March 2023 to September 2024 and retrospectively analyzed by clinical manifestations,CT imaging,and disease regression.In 106 patients,58.5%had fever,98.1%had malaise,96.2%had excessive sweating,81.1%had lumbosacral pain,79.3%had limitation of limb movement,76.4%had constipation,and 6.6%had urinary retention.For imaging manifestations,the involvement of lumbar,thoracic and cervical vertebrae were 80.2%,16.9%and 1.9%,respectively.Lesions<1.0 cm,1.0–2.0 cm,2.0–3.0 cm,and>3.0 cm were found in 49.4%,29.6%,19.4%,and 1.6%,respectively.In 106 patients,CT showed round,irregular or worm-like areas of bone destruction,with coexisting osteophytes in 61.5%and no signs of dead bone or pedicle destruction.Interdiscal destruction,spinal canal abscess,ligament injury,and signs of lumbar major muscle compression were rare,accounting for 11.7%,6.6%,4.7%,and 3.8%,respectively.Regarding regression,106 patients with BS treated with antimicrobial therapy or antimicrobial+surgery had a good prognosis.In conclusion,BS has its own characteristics in clinical and imaging aspects and it is easy to distinguish from other common causes of spondylitis bone damage.展开更多
Interstitial hypertension and extracellular matrix(ECM)barriers imposed by cancer-associated fibroblasts(CAFs)at the tumor site significantly impede the retention of intratumorally administered oncolytic viruses(OVs)a...Interstitial hypertension and extracellular matrix(ECM)barriers imposed by cancer-associated fibroblasts(CAFs)at the tumor site significantly impede the retention of intratumorally administered oncolytic viruses(OVs)as well as their efficacy in infecting and eradicating tumor cells.Herein,a stable,controllable,and easily prepared hydrogel was developed for employing a differential release strategy to deliver OVs.The oncolytic herpes simplex virus-2(oH2)particles were loaded within sodium alginate(ALG),together with the small molecule drug PT-100 targeting CAFs.The rapid release of PT-100 functions as an anti-CAFs agent,reducing ECM,and alleviating interstitial pressure at the tumor site.Consequently,the delayed release of oH2 could more effectively invade and eradicate tumor cells while also facilitating enhanced infiltration of immune cells into the tumor microenvironment,thereby establishing an immunologically favorable milieu against tumors.This approach holds significant potential for achieving highly efficient oncolytic virus therapy with minimal toxicity,particularly in tumors rich in stromal components.展开更多
Compared to discrete continental marginal basins,the mechanisms of hydrocarbon migration and enrichment in transform continental marginal basins are poorly understood.In this study,we conducted a comprehensive analysi...Compared to discrete continental marginal basins,the mechanisms of hydrocarbon migration and enrichment in transform continental marginal basins are poorly understood.In this study,we conducted a comprehensive analysis of the main source rocks,reservoirs,and vertical migration pathways within the Rovuma(RB)and Tanzania(TB)basins in East Africa utilizing drilling,logging,seismic,and geochemical data.The results indicate that the enhanced preservation conditions of the Lower Jurassic source rocks in the southwest could lead to the discovery of large natural gas fields in the southern TB and RB.The primary reservoir is a deep-water turbidite sandstone.Due to topographic differences,the expanse of the turbidite sandstones in the RB is significantly larger than those in Tanzania.The main vertical migration pathways are the western boundary fault zone of the Kerimbas Graben(WBFZ)and the Seagap fault zone(SFZ).In the RB,natural gas migrates vertically along the WBFZ and preferentially accumulates in the deep-water turbidite sandstones of the footwall under the control of the fluid potential.Conversely,in the southern TB,the deep natural gas first migrates upward along the SFZ,then moves along the shallow branch faults in the sandstones on both sides of the SFZ.展开更多
This study introduces a novel bargaining solution termed the"'min-distance bargaining solution"and applies it to a differential games model.A comprehensive algorithm for implementing this new solution is...This study introduces a novel bargaining solution termed the"'min-distance bargaining solution"and applies it to a differential games model.A comprehensive algorithm for implementing this new solution is presented,considering its time consistency within the differential games framework.Realistic scenarios are carefully analyzed to derive insightful findings regarding the mindistance solution,which are further validated through simulations using the resource extraction differential games model.Specifically,we examine scenarios such as managing a finite resource stock in the resource extraction game.Furthermore,a comparative analysis is conducted,pitting the mindistance bargaining solution against well-established alternatives such as Nash bargaining,Kalai-Smorodinsky,and Egalitarian solutions.By subjecting these solutions to numerical evaluations,the study offers valuable insights into decision-making processes.The findings not only contribute to negotiation theory by providing theoretical support but also have practical implications for decision-makers seeking effective strategies.This research significantly advances the field of negotiation theory,particularly in the context of differential games.The proposed min-distance bargaining solution demonstrates its applicability to real-world scenarios and enhances our understanding of strategic decision-making.展开更多
The rapid development and widespread adoption of massive open online courses(MOOCs)have indeed had a significant impact on China’s education curriculum.However,the problem of fake reviews and ratings on the platform ...The rapid development and widespread adoption of massive open online courses(MOOCs)have indeed had a significant impact on China’s education curriculum.However,the problem of fake reviews and ratings on the platform has seriously affected the authenticity of course evaluations and user trust,requiring effective anomaly detection techniques for screening.The textual characteristics of MOOCs reviews,such as varying lengths and diverse emotional tendencies,have brought complexity to text analysis.Traditional rule-based analysis methods are often inadequate in dealing with such unstructured data.We propose a Differential Privacy-Enabled Text Convolutional Neural Network(DP-TextCNN)framework,aiming to achieve high-precision identification of outliers in MOOCs course reviews and ratings while protecting user privacy.This framework leverages the advantages of Convolutional Neural Networks(CNN)in text feature extraction and combines differential privacy techniques.It balances data privacy protection with model performance by introducing controlled random noise during the data preprocessing stage.By embedding differential privacy into the model training process,we ensure the privacy security of the framework when handling sensitive data,while maintaining a high recognition accuracy.Experimental results indicate that the DP-TextCNN framework achieves an exceptional accuracy of over 95%in identifying fake reviews on the dataset,this outcome not only verifies the applicability of differential privacy techniques in TextCNN but also underscores its potential in handling sensitive educational data.Additionally,we analyze the specific impact of differential privacy parameters on framework performance,offering theoretical support and empirical analysis to strike an optimal balance between privacy protection and framework efficiency.展开更多
The traditional orbit determination method based on pulsar profile distortion can determine the six elements of the orbit.However,the estimation accuracies of these methods are limited and the computational load of a ...The traditional orbit determination method based on pulsar profile distortion can determine the six elements of the orbit.However,the estimation accuracies of these methods are limited and the computational load of a six-dimensional search is huge.To solve this problem,the differential-geometry-based Multi-dimensional Joint Position-Velocity Estimation(MJPVE)using Crab pulsar profile distortion is proposed in this paper.Firstly,through theoretical analysis,it is found that the pulsar profile distortion caused by the initial state error in some joint positionvelocity directions is very small.In other words,the accuracies of estimation in these directions are very low.Namely,the search dimension can be reduced,which in turn greatly reduces the computational load.Then,we construct the chi-squared function of the pulsar profile with respect to the estimation error in joint position-velocity direction and use differential geometry to find the joint position-velocity directions corresponding to different degrees of distortion.Finally,we utilize the grid search based on directory folding in these joint position-velocity directions corresponding to large degrees of distortion to obtain the joint position-velocity estimation.The experimental results show that compared with the grouping bi-chi-squared inversion method,MJPVE has high precision and extensive navigation information.展开更多
The principal stresses will increase or decrease during mining,leading to variations in surrounding rock strength and subsequently an influence on the risk of rockbursts.To address this issue,this study conducted theo...The principal stresses will increase or decrease during mining,leading to variations in surrounding rock strength and subsequently an influence on the risk of rockbursts.To address this issue,this study conducted theoretical analysis,numerical simulation,and field monitoring.A rockburst risk analysis method that integrates dynamic changes in the stress and strength of surrounding rock was proposed and verified in the field.The dynamic changes in maximum(σ_(1))and minimum(σ_(3))principal stresses are represented by the σ_(1) and σ_(3) differentials,respectively.The difference in principal stress differential(DPSD),defined as the difference between σ_(1) and σ_(3),was introduced as a novel indicator for rockburst risk analysis.The findings of this study demonstrate a positive correlation between increases in DPSD and heightened risks of rockbursts,as evidenced by an increase in both the frequency of rockbursts and the occurrence of large-energy microseismic events.Conversely,a decrease in DPSD is associated with a reduction in risk.Specifically,in the W1123 panel of a coal mine susceptible to rockbursts,areas exhibiting higher DPSD values experienced more frequent and severe rockbursts.The DPSD-based analysis aligned well with the observed rockburst occurrences.Subsequent optimization of rockburst prevention measures in areas with elevated DPSD led to a reduction in DPSD.Following these adjustments,the W1123 panel predominantly experienced low-energy microseismic events,with a significant decrease in large-energy microseismic events and no further rockbursts.The DPSD analysis is a valuable tool for evaluating rockburst risk and aiding in prevention,which is of great significance for disaster prevention.展开更多
基金Supported by the National Natural Science Foundation of China(12001074)the Research Innovation Program of Graduate Students in Hunan Province(CX20220258)+1 种基金the Research Innovation Program of Graduate Students of Central South University(1053320214147)the Key Scientific Research Project of Higher Education Institutions in Henan Province(25B110025)。
文摘This paper deals with Mckean-Vlasov backward stochastic differential equations with weak monotonicity coefficients.We first establish the existence and uniqueness of solutions to Mckean-Vlasov backward stochastic differential equations.Then we obtain a comparison theorem in one-dimensional situation.
基金supported by the Natural Science Foundation of Fujian Province of China(2025J01380)National Natural Science Foundation of China(No.62471139)+3 种基金the Major Health Research Project of Fujian Province(2021ZD01001)Fujian Provincial Units Special Funds for Education and Research(2022639)Fujian University of Technology Research Start-up Fund(GY-S24002)Fujian Research and Training Grants for Young and Middle-aged Leaders in Healthcare(GY-H-24179).
文摘The generation of synthetic trajectories has become essential in various fields for analyzing complex movement patterns.However,the use of real-world trajectory data poses significant privacy risks,such as location reidentification and correlation attacks.To address these challenges,privacy-preserving trajectory generation methods are critical for applications relying on sensitive location data.This paper introduces DPIL-Traj,an advanced framework designed to generate synthetic trajectories while achieving a superior balance between data utility and privacy preservation.Firstly,the framework incorporates Differential Privacy Clustering,which anonymizes trajectory data by applying differential privacy techniques that add noise,ensuring the protection of sensitive user information.Secondly,Imitation Learning is used to replicate decision-making behaviors observed in real-world trajectories.By learning from expert trajectories,this component generates synthetic data that closely mimics real-world decision-making processes while optimizing the quality of the generated trajectories.Finally,Markov-based Trajectory Generation is employed to capture and maintain the inherent temporal dynamics of movement patterns.Extensive experiments conducted on the GeoLife trajectory dataset show that DPIL-Traj improves utility performance by an average of 19.85%,and in terms of privacy performance by an average of 12.51%,compared to state-of-the-art approaches.Ablation studies further reveal that DP clustering effectively safeguards privacy,imitation learning enhances utility under noise,and the Markov module strengthens temporal coherence.
基金Research Council of Lithuania(LMTLT),agreement No.S-PD-24-120Research Council of Lithuania(LMTLT),agreement No.S-PD-24-120funded by the Research Council of Lithuania.
文摘Fractional differential equations(FDEs)provide a powerful tool for modeling systems with memory and non-local effects,but understanding their underlying structure remains a significant challenge.While numerous numerical and semi-analytical methods exist to find solutions,new approaches are needed to analyze the intrinsic properties of the FDEs themselves.This paper introduces a novel computational framework for the structural analysis of FDEs involving iterated Caputo derivatives.The methodology is based on a transformation that recasts the original FDE into an equivalent higher-order form,represented as the sum of a closed-form,integer-order component G(y)and a residual fractional power seriesΨ(x).This transformed FDE is subsequently reduced to a first-order ordinary differential equation(ODE).The primary novelty of the proposed methodology lies in treating the structure of the integer-order component G(y)not as fixed,but as a parameterizable polynomial whose coefficients can be determined via global optimization.Using particle swarm optimization,the framework identifies an optimal ODE architecture by minimizing a dual objective that balances solution accuracy against a high-fidelity reference and the magnitude of the truncated residual series.The effectiveness of the approach is demonstrated on both a linear FDE and a nonlinear fractional Riccati equation.Results demonstrate that the framework successfully identifies an optimal,low-degree polynomial ODE architecture that is not necessarily identical to the forcing function of the original FDE.This work provides a new tool for analyzing the underlying structure of FDEs and gaining deeper insights into the interplay between local and non-local dynamics in fractional systems.
基金supported by the National Natural Science Foundation of China(No.12001117)the Guangdong Basic and Applied Basic Research Foundation(No.2021A1515110654).
文摘In this article,we study the meromorphic solutions of the following non-linear differential equation■where n and k are integers with n≥k≥3,P_(d)(z,f)is a differential polynomial in f of degree d≤n−1,p′js andα′js are non-zero constants.We obtain the expressions of meromorphic solutions of the above equations under some restrictions onα′js.Some examples are given to illustrate the possibilities of our results.
基金supported by the National Natural Science Foundation of China(NSFC)under Grant(No.51677058).
文摘Precisely estimating the state of health(SOH)of lithium-ion batteries is essential for battery management systems(BMS),as it plays a key role in ensuring the safe and reliable operation of battery systems.However,current SOH estimation methods often overlook the valuable temperature information that can effectively characterize battery aging during capacity degradation.Additionally,the Elman neural network,which is commonly employed for SOH estimation,exhibits several drawbacks,including slow training speed,a tendency to become trapped in local minima,and the initialization of weights and thresholds using pseudo-random numbers,leading to unstable model performance.To address these issues,this study addresses the challenge of precise and effective SOH detection by proposing a method for estimating the SOH of lithium-ion batteries based on differential thermal voltammetry(DTV)and an SSA-Elman neural network.Firstly,two health features(HFs)considering temperature factors and battery voltage are extracted fromthe differential thermal voltammetry curves and incremental capacity curves.Next,the Sparrow Search Algorithm(SSA)is employed to optimize the initial weights and thresholds of the Elman neural network,forming the SSA-Elman neural network model.To validate the performance,various neural networks,including the proposed SSA-Elman network,are tested using the Oxford battery aging dataset.The experimental results demonstrate that the method developed in this study achieves superior accuracy and robustness,with a mean absolute error(MAE)of less than 0.9%and a rootmean square error(RMSE)below 1.4%.
文摘When a differential field K having n commuting derivations is given together with two finitely generated differential extensions L and M of K, an important problem in differential algebra is to exhibit a common differential extension N in order to define the new differential extensions L<span style="white-space:nowrap;"><span style="white-space:nowrap;">∩M and the smallest differential field <span style="white-space:nowrap;">(L,M ) <span style="white-space:nowrap;"><span style="white-space:nowrap;">⊂ N containing both L and M. Such a result allows to generalize the use of complex numbers in classical algebra. Having now two finitely generated differential modules L and M over the non-commutative ring <span style="white-space:nowrap;">D = K [d<sub>1</sub>,...,d<sub>n</sub>] = K [d] of differential operators with coefficients in K, we may similarly look for a differential module N containing both L and M in order to define <span style="white-space:nowrap;">L∩M and <span style="white-space:nowrap;">L+M. This is exactly the situation met in linear or non-linear OD or PD control theory by selecting the inputs and the outputs among the control variables. However, in many recent books and papers, we have shown that controllability was a built-in property of a control system, not depending on the choice of inputs and outputs. The purpose of this paper is thus to revisit control theory by showing the specific importance of the two previous problems and the part plaid by N in both cases for the parametrization of the control system. An important tool will be the study of differential correspondences, a modern name for what was called B<span style="white-space:nowrap;"><span style="white-space:nowrap;">äcklund problem during the last century, namely the elimination theory for groups of variables among systems of linear or nonlinear OD or PD equations. The main difficulty is to revisit differential homological algebra by using noncommutative localization as a way to generalize the symbolic calculus in the style of Heaviside and Mikusinski. Finally, when M is a D-module, this paper is using for the first time the fact that the system <span style="white-space:nowrap;">R = hom<sub>K</sub> (M,K) is a D-module for the Spencer operator acting on sections, avoiding thus behaviours, trajectories and signal spaces in a purely formal way, contrary to a few recent works on this difficult subject.
基金Supported by the National Natural Science Foundation of China(42302184)Innovation Group Project of Basic Research in Gansu Province,China(22JR5RA045)。
文摘The lamina(combination)types,reservoir characteristics and shale oil occurrence states of organic-rich shale in the Triassic Yanchang Formation Chang 73 sub-member in the Ordos Basin were systematically investigated to reveal the main controlling factors of shale oil occurrence under different lamina combinations.The differential enrichment mechanisms and patterns of shale oil were discussed using the shale oil micro-migration characterization and evaluation methods from the perspectives of relay hydrocarbon supply,stepwise migration,and multi-stage differentiation.The results are obtained in five aspects.First,Chang 73 shale mainly develops five types of lamina combination,i.e.non-laminated shale,sandy laminated shale,tuffaceous laminated shale,mixed laminated shale,and organic-rich laminated shale.Second,shales with different lamina combinations are obviously different in the reservoir space.Specifically,shales with sandy laminae and tuffaceous laminae have a large number of intergranular pores,dissolution pores and hydrocarbon generation-induced fractures.The multi-scale pore and fracture system constitutes the main place for liquid hydrocarbon occurrence.Third,the occurrence and distribution of shale oil in shale with different lamina combinations are jointly controlled by organic matter abundance,reservoir property,thermal evolution degree,mineral composition and laminae scale.The micro-nano-scale pore-fracture networks within shales containing rigid laminae,particularly sandy and tuffaceous laminations,primarily contain free-state light hydrocarbon components.In contrast,adsorption-phase heavy hydrocarbon components predominantly occupy surfaces of organic matter assemblages,clay mineral matrices,and framework mineral particulates.Fourth,there is obvious shale oil micro-migration between shales with different lamina combinations in Chang 73.Generally,such micro-migration is stepwise in a sequence of organic-rich laminated shale→tuffaceous laminated shale→mixed laminated shale→sandy lamiated shale→non-laminated shale.Fifth,the relay hydrocarbon supply of organic matter under the control of the spatial superposition of shales with various laminae,the stepwise migration via multi-scale pore and fracture network,and the multi-differentiation in shales with different lamina combinations under the control of organic-inorganic interactions fundamentally decide the differences of shale oil components between shales with different lamina combinations.
基金Supported by the China National Science and Technology Major Project(2025ZD1405700)CNPC Science and Technology Project(2023YQX20117).
文摘Based on the coalbed methane(CBM)/coal-rock gas(CRG)geological,geophysical,and experimental testing data from the Daji block in the Ordos Basin,the coal-forming and hydrocarbon generation&accumulation characteristics across different zones were dissected,and the key factors controlling the differential CBM/CRG enrichment were identified.The No.8 coal seam of the Carboniferous Benxi Formation in the Daji block is 8-10 m thick,typically overlain by limestone.The primary hydrocarbon generation phase occurred during the Early Cretaceous.Based on the differences in tectonic evolution and CRG occurrence,and with the maximum vitrinite reflectance of 2.0%and burial depth of 1800 m as boundaries,the study area is divided into deeply buried and deeply preserved,deeply buried and shallowly preserved,and shallowly buried and shallowly preserved zones.The deeply buried and deeply preserved zone contains gas content of 22-35 m^(3)/t,adsorbed gas saturation of 95%-100%,and formation water with total dissolved solid(TDS)higher than 50000 mg/L.This zone features structural stability and strong sealing capacity,with high gas production rates.The deeply buried and shallowly preserved zone contains gas content of 16-20 m^(3)/t,adsorbed gas saturation of 80%-95%,and formation water with TDS of 5000-50000 mg/L.This zone exhibits localized structural modification and hydrodynamic sealing,with moderate gas production rate.The shallowly buried and shallowly preserved zone contains gas content of 8-16 m^(3)/t,adsorbed gas saturation of 50%-70%,and formation water with TDS lower than 5000 mg/L.This zone experienced intense uplift,resulting in poor sealing and secondary alteration of the primary gas reservoir,with partial adsorbed gas loss,and low gas production rate.A depositional unification and structural divergence model is proposed,that is,although coal seams across the basin experienced broadly similar depositional and tectonic histories,differences in tectonic intensity have led to spatial heterogeneity in the maximum burial depth(i.e.,thermal maturity of coal)and current burial depth and occurrence of CRG(i.e.,gas content and occurrence state).The research results provide valuable guidance for advancing the theoretical understanding of CBM/CRG enrichment and for improving exploration and development practices.
基金National Natural Science Foundation of China(NSFC61773142,NSFC62303136)。
文摘When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game strategy,the game of kind is generally considered to be angle-optimized,which allows unlimited turns,but these practices do not take into account the effect of acceleration,which does not correspond to the actual situation,thus,based on the angle-optimized,the acceleration optimization and the acceleration upper bound constraint are added into the game for consideration.A two-to-one differential game problem is proposed in the three-dimensional space,and an improved multi-objective grey wolf optimization(IMOGWO)algorithm is proposed to solve the optimal game point of this problem.With the equations that describe the relative motions between the pursuers and the evader in the three-dimensional space,a multi-objective function with constraints is given as the performance index to design an optimal strategy for the differential game.Then the optimal game point is solved by using the IMOGWO algorithm.It is proved based on Markov chains that with the IMOGWO,the Pareto solution set is the solution of the differential game.Finally,it is verified through simulations that the pursuers can capture the escapee,and via comparative experiments,it is shown that the IMOGWO algorithm performs well in terms of running time and memory usage.
文摘In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.
基金supported by the PhD Research Startup Foundation of Hubei University of Economics(Grand No.XJ23BS42).
文摘This paper studies the Smoluchowski–Kramers approximation for a discrete-time dynamical system modeled as the motion of a particle in a force field.We show that the approximation holds for the drift-implicit Euler–Maruyama discretization and derive its convergence rate.In particular,the solution of the discretized system converges to the solution of the first-order limit equation in the mean-square sense,and this convergence is independent of the order in which the mass parameterμand the step size h tend to zero.
文摘The two-player nonzero-sum linear-exponential-quadratic stochastic differential game is studied.The game takes into account the players'attitudes to risk.The nonlinear transformations and change of probability measure techniques are used to study the existence of both open-loop and closed-loop Nash equilibria for the game.Some examples are constructed to illustrate their differences.Furthermore,theoretical results are applied to solve the risk-sensitive portfolio game problem in the financial market and show the effects of risk attitudes and economic performance on equilibria.
基金Supported by NSFC (No.12361027)NSF of Inner Mongolia (No.2018MS01021)+1 种基金NSF of Shandong Province (No.ZR2020QA009)Science and Technology Innovation Program for Higher Education Institutions of Shanxi Province (No.2024L533)。
文摘In this paper,we give a complete characterization of all self-adjoint domains of odd order differential operators on two intervals.These two intervals with all four endpoints are singular(one endpoint of each interval is singular or all four endpoints are regulars are the special cases).And these extensions yield"new"self-adjoint operators,which involve interactions between the two intervals.
文摘This study aims to explore the clinical and CT imaging features of brucellosis spondylitis(BS)and to strengthen the clinical cognition to reduce misdiagnosis and mistreatment.In this study,clinical and CT imaging data of 106 patients with BS diagnosed in the Second Hospital of Hohhot and the Third Hospital of Baotou were collected from March 2023 to September 2024 and retrospectively analyzed by clinical manifestations,CT imaging,and disease regression.In 106 patients,58.5%had fever,98.1%had malaise,96.2%had excessive sweating,81.1%had lumbosacral pain,79.3%had limitation of limb movement,76.4%had constipation,and 6.6%had urinary retention.For imaging manifestations,the involvement of lumbar,thoracic and cervical vertebrae were 80.2%,16.9%and 1.9%,respectively.Lesions<1.0 cm,1.0–2.0 cm,2.0–3.0 cm,and>3.0 cm were found in 49.4%,29.6%,19.4%,and 1.6%,respectively.In 106 patients,CT showed round,irregular or worm-like areas of bone destruction,with coexisting osteophytes in 61.5%and no signs of dead bone or pedicle destruction.Interdiscal destruction,spinal canal abscess,ligament injury,and signs of lumbar major muscle compression were rare,accounting for 11.7%,6.6%,4.7%,and 3.8%,respectively.Regarding regression,106 patients with BS treated with antimicrobial therapy or antimicrobial+surgery had a good prognosis.In conclusion,BS has its own characteristics in clinical and imaging aspects and it is easy to distinguish from other common causes of spondylitis bone damage.
基金supported by the National Key R&D Program of China(No.2022YFC2403401)the National Natural Science Foundation of China(Nos.82073368,82303766)+2 种基金the Liaoning Revitalization Talents Program(No.XLYC2007071)the China Postdoctoral Science Foundation(No.2023M743908)the Joint Program of Science and Technology Program of Liaoning Province(No.2023JH2/101700094).
文摘Interstitial hypertension and extracellular matrix(ECM)barriers imposed by cancer-associated fibroblasts(CAFs)at the tumor site significantly impede the retention of intratumorally administered oncolytic viruses(OVs)as well as their efficacy in infecting and eradicating tumor cells.Herein,a stable,controllable,and easily prepared hydrogel was developed for employing a differential release strategy to deliver OVs.The oncolytic herpes simplex virus-2(oH2)particles were loaded within sodium alginate(ALG),together with the small molecule drug PT-100 targeting CAFs.The rapid release of PT-100 functions as an anti-CAFs agent,reducing ECM,and alleviating interstitial pressure at the tumor site.Consequently,the delayed release of oH2 could more effectively invade and eradicate tumor cells while also facilitating enhanced infiltration of immune cells into the tumor microenvironment,thereby establishing an immunologically favorable milieu against tumors.This approach holds significant potential for achieving highly efficient oncolytic virus therapy with minimal toxicity,particularly in tumors rich in stromal components.
基金financially supported by the National Natural Science Foundation of China(Grant No.42002150)the Open Foundation of Cooperative Innovation Center of Unconventional Oil and Gas,Yangtze University(Ministry of Education&Hubei Province,Grant No.UOG2024-12)+1 种基金the Open Foundation Project of the Key Laboratory of Polar Geology and Marine Mineral Resources(China University of Geosciences,Beijing,China),Ministry of Education(Grant No.PGMR-2023-201)the National Key Research Program of China(Grant No.2017ZX05032-002)。
文摘Compared to discrete continental marginal basins,the mechanisms of hydrocarbon migration and enrichment in transform continental marginal basins are poorly understood.In this study,we conducted a comprehensive analysis of the main source rocks,reservoirs,and vertical migration pathways within the Rovuma(RB)and Tanzania(TB)basins in East Africa utilizing drilling,logging,seismic,and geochemical data.The results indicate that the enhanced preservation conditions of the Lower Jurassic source rocks in the southwest could lead to the discovery of large natural gas fields in the southern TB and RB.The primary reservoir is a deep-water turbidite sandstone.Due to topographic differences,the expanse of the turbidite sandstones in the RB is significantly larger than those in Tanzania.The main vertical migration pathways are the western boundary fault zone of the Kerimbas Graben(WBFZ)and the Seagap fault zone(SFZ).In the RB,natural gas migrates vertically along the WBFZ and preferentially accumulates in the deep-water turbidite sandstones of the footwall under the control of the fluid potential.Conversely,in the southern TB,the deep natural gas first migrates upward along the SFZ,then moves along the shallow branch faults in the sandstones on both sides of the SFZ.
文摘This study introduces a novel bargaining solution termed the"'min-distance bargaining solution"and applies it to a differential games model.A comprehensive algorithm for implementing this new solution is presented,considering its time consistency within the differential games framework.Realistic scenarios are carefully analyzed to derive insightful findings regarding the mindistance solution,which are further validated through simulations using the resource extraction differential games model.Specifically,we examine scenarios such as managing a finite resource stock in the resource extraction game.Furthermore,a comparative analysis is conducted,pitting the mindistance bargaining solution against well-established alternatives such as Nash bargaining,Kalai-Smorodinsky,and Egalitarian solutions.By subjecting these solutions to numerical evaluations,the study offers valuable insights into decision-making processes.The findings not only contribute to negotiation theory by providing theoretical support but also have practical implications for decision-makers seeking effective strategies.This research significantly advances the field of negotiation theory,particularly in the context of differential games.The proposed min-distance bargaining solution demonstrates its applicability to real-world scenarios and enhances our understanding of strategic decision-making.
文摘The rapid development and widespread adoption of massive open online courses(MOOCs)have indeed had a significant impact on China’s education curriculum.However,the problem of fake reviews and ratings on the platform has seriously affected the authenticity of course evaluations and user trust,requiring effective anomaly detection techniques for screening.The textual characteristics of MOOCs reviews,such as varying lengths and diverse emotional tendencies,have brought complexity to text analysis.Traditional rule-based analysis methods are often inadequate in dealing with such unstructured data.We propose a Differential Privacy-Enabled Text Convolutional Neural Network(DP-TextCNN)framework,aiming to achieve high-precision identification of outliers in MOOCs course reviews and ratings while protecting user privacy.This framework leverages the advantages of Convolutional Neural Networks(CNN)in text feature extraction and combines differential privacy techniques.It balances data privacy protection with model performance by introducing controlled random noise during the data preprocessing stage.By embedding differential privacy into the model training process,we ensure the privacy security of the framework when handling sensitive data,while maintaining a high recognition accuracy.Experimental results indicate that the DP-TextCNN framework achieves an exceptional accuracy of over 95%in identifying fake reviews on the dataset,this outcome not only verifies the applicability of differential privacy techniques in TextCNN but also underscores its potential in handling sensitive educational data.Additionally,we analyze the specific impact of differential privacy parameters on framework performance,offering theoretical support and empirical analysis to strike an optimal balance between privacy protection and framework efficiency.
基金supported in part by the National Natural Science Foundation of China(Nos.61873196,62373030,61772187)the Innovation Program for Quantum Science and Technology(No.2021ZD0303400)。
文摘The traditional orbit determination method based on pulsar profile distortion can determine the six elements of the orbit.However,the estimation accuracies of these methods are limited and the computational load of a six-dimensional search is huge.To solve this problem,the differential-geometry-based Multi-dimensional Joint Position-Velocity Estimation(MJPVE)using Crab pulsar profile distortion is proposed in this paper.Firstly,through theoretical analysis,it is found that the pulsar profile distortion caused by the initial state error in some joint positionvelocity directions is very small.In other words,the accuracies of estimation in these directions are very low.Namely,the search dimension can be reduced,which in turn greatly reduces the computational load.Then,we construct the chi-squared function of the pulsar profile with respect to the estimation error in joint position-velocity direction and use differential geometry to find the joint position-velocity directions corresponding to different degrees of distortion.Finally,we utilize the grid search based on directory folding in these joint position-velocity directions corresponding to large degrees of distortion to obtain the joint position-velocity estimation.The experimental results show that compared with the grouping bi-chi-squared inversion method,MJPVE has high precision and extensive navigation information.
基金support from the National Natural Science Foundation of China(Grant Nos.52374180 and 52327804).
文摘The principal stresses will increase or decrease during mining,leading to variations in surrounding rock strength and subsequently an influence on the risk of rockbursts.To address this issue,this study conducted theoretical analysis,numerical simulation,and field monitoring.A rockburst risk analysis method that integrates dynamic changes in the stress and strength of surrounding rock was proposed and verified in the field.The dynamic changes in maximum(σ_(1))and minimum(σ_(3))principal stresses are represented by the σ_(1) and σ_(3) differentials,respectively.The difference in principal stress differential(DPSD),defined as the difference between σ_(1) and σ_(3),was introduced as a novel indicator for rockburst risk analysis.The findings of this study demonstrate a positive correlation between increases in DPSD and heightened risks of rockbursts,as evidenced by an increase in both the frequency of rockbursts and the occurrence of large-energy microseismic events.Conversely,a decrease in DPSD is associated with a reduction in risk.Specifically,in the W1123 panel of a coal mine susceptible to rockbursts,areas exhibiting higher DPSD values experienced more frequent and severe rockbursts.The DPSD-based analysis aligned well with the observed rockburst occurrences.Subsequent optimization of rockburst prevention measures in areas with elevated DPSD led to a reduction in DPSD.Following these adjustments,the W1123 panel predominantly experienced low-energy microseismic events,with a significant decrease in large-energy microseismic events and no further rockbursts.The DPSD analysis is a valuable tool for evaluating rockburst risk and aiding in prevention,which is of great significance for disaster prevention.
