The finite element method has established itself as an efficient numerical procedure for the solution of arbitrary-shaped field problems in space. Basically, the finite element method transforms the underlying differe...The finite element method has established itself as an efficient numerical procedure for the solution of arbitrary-shaped field problems in space. Basically, the finite element method transforms the underlying differential equation into a system of algebraic equations by application of the method of weighted residuals in conjunction with a finite element ansatz. However, this procedure is restricted to even-ordered differential equations and leads to symmetric system matrices as a key property of the finite element method. This paper aims in a generalization of the finite element method towards the solution of first-order differential equations. This is achieved by an approach which replaces the first-order derivative by fractional powers of operators making use of the square root of a Sturm-Liouville operator. The resulting procedure incorporates a finite element formulation and leads to a symmetric but dense system matrix. Finally, the scheme is applied to the barometric equation where the results are compared with the analytical solution and other numerical approaches. It turns out that the resulting numerical scheme shows excellent convergence properties.展开更多
This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differenti...This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.展开更多
This paper focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equati...This paper focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equations, from which a kind of conserved quantity is deduced, are presented. And their general conclusion is applied to a Hamilton system, a Birkhoff system and a generalized Hamilton system. Two examples are given to illustrate the application of the results.展开更多
In this article we consider via critical point theory the existence of homoclinic orbits of the first-order differential difference equation z（t）＋B（t）z（t）＋f（t,z（t＋τ）,z（t）,z（t-τ））=0.
Differential equation is very important in science and engineering, because it required the description of some measurable quantities (position, temperature, population, concentration, electrical current, etc.) in mat...Differential equation is very important in science and engineering, because it required the description of some measurable quantities (position, temperature, population, concentration, electrical current, etc.) in mathematical form of ordinary differential equations (ODEs). In this research, we determine heat transferred by convection in fluid problems by first-order ordinary differential equations. So in this research work first we discuss the solution of ordinary homogeneous and non-homogeneous differential equation and then apply the solution of first-order ODEs to heat transferring particularly in heat convection in fluid.展开更多
In this paper,we formulate two new families of fourth-order explicit exponential Runge–Kutta(ERK)methods with four stages for solving first-order differential systems y'(t)+M y(t)=f(y(t)).The order conditions of ...In this paper,we formulate two new families of fourth-order explicit exponential Runge–Kutta(ERK)methods with four stages for solving first-order differential systems y'(t)+M y(t)=f(y(t)).The order conditions of these ERK methods are derived by comparing the Taylor series of the exact solution,which are exactly identical to the order conditions of explicit Runge–Kutta methods,and these ERK methods reduce to classical Runge–Kutta methods once M→0.Moreover,we analyze the stability properties and the convergence of these new methods.Several numerical examples are implemented to illustrate the accuracy and efficiency of these ERK methods by comparison with standard exponential integrators.展开更多
In this paper, a novel class of exponential Fourier collocation methods （EFCMs） is presented for solving systems of first-order ordinary differential equations. These so-called exponential Fourier collocation method...In this paper, a novel class of exponential Fourier collocation methods （EFCMs） is presented for solving systems of first-order ordinary differential equations. These so-called exponential Fourier collocation methods are based on the variation-of-constants formula, incorporating a local Fourier expansion of the underlying problem with collocation meth- ods. We discuss in detail the connections of EFCMs with trigonometric Fourier colloca- tion methods （TFCMs）, the well-known Hamiltonian Boundary Value Methods （HBVMs）, Gauss methods and Radau IIA methods. It turns out that the novel EFCMs are an es- sential extension of these existing methods. We also analyse the accuracy in preserving the quadratic invariants and the Hamiltonian energy when the underlying system is a Hamiltonian system. Other properties of EFCMs including the order of approximations and the convergence of fixed-point iterations are investigated as well. The analysis given in this paper proves further that EFCMs can achieve arbitrarily high order in a routine manner which allows us to construct higher-order methods for solving systems of first- order ordinary differential equations conveniently. We also derive a practical fourth-order EFCM denoted by EFCM（2,2） as an illustrative example. The numerical experiments using EFCM（2,2） are implemented in comparison with an existing fourth-order HBVM, an energy-preserving collocation method and a fourth-order exponential integrator in the literature. The numerical results demonstrate the remarkable efficiency and robustness of the novel EFCM（2,2）.展开更多
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
Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna...Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.展开更多
In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed poi...In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.展开更多
A type of Inconsistent Mathematics structured on Paraconsistent Logic (PL) and that has, as the main purpose, the study of common mathematical objects such as sets, numbers and functions, where some contradictions are...A type of Inconsistent Mathematics structured on Paraconsistent Logic (PL) and that has, as the main purpose, the study of common mathematical objects such as sets, numbers and functions, where some contradictions are allowed, is called Paraconsistent Mathematics. The PL is a non-Classical logic and its main property is to present tolerance for contradiction in its fundamentals without the invalidation of the conclusions. In this paper (part 1), we use the PL in its annotated form, denominated Paraconsistent Annotated Logic with annotation of two values—PAL2v for present a first-order Paraconsistent Derivative. The PAL2v has, in its representation, an associated lattice FOUR based on Hasse Diagram. This PAL2v-Lattice allows development of a Para-consistent Differential Calculus based on fundamentals and equations obtained by geometric interpretations. In this first article it is presented some examples applying derivatives of first-order with the concepts of Paraconsistent Mathematics. In the second part of this work we will show the Paraconsistent Derivative of second-order with application examples.展开更多
The existence of at feast one solution and the existence of extreme solutions of periodic boundary value problems for first-order integro-differential equations of mixed type are studied, in the presence of generalize...The existence of at feast one solution and the existence of extreme solutions of periodic boundary value problems for first-order integro-differential equations of mixed type are studied, in the presence of generalized upper and laver solutions. The discussion is based an new comparison theorems and coincidence degree and monotone iterative methods.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
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
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 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
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
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
文摘The finite element method has established itself as an efficient numerical procedure for the solution of arbitrary-shaped field problems in space. Basically, the finite element method transforms the underlying differential equation into a system of algebraic equations by application of the method of weighted residuals in conjunction with a finite element ansatz. However, this procedure is restricted to even-ordered differential equations and leads to symmetric system matrices as a key property of the finite element method. This paper aims in a generalization of the finite element method towards the solution of first-order differential equations. This is achieved by an approach which replaces the first-order derivative by fractional powers of operators making use of the square root of a Sturm-Liouville operator. The resulting procedure incorporates a finite element formulation and leads to a symmetric but dense system matrix. Finally, the scheme is applied to the barometric equation where the results are compared with the analytical solution and other numerical approaches. It turns out that the resulting numerical scheme shows excellent convergence properties.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Programme Foundation of Institution of Higher Education of China (Grant No 20040007022)
文摘This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.
基金Project supported by the National Natural Science Foundation of China （Grant No 10272021） and the Doctoral Program Foundation of Institution of Higher Education of China （Grant No 20040007022）.
文摘This paper focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equations, from which a kind of conserved quantity is deduced, are presented. And their general conclusion is applied to a Hamilton system, a Birkhoff system and a generalized Hamilton system. Two examples are given to illustrate the application of the results.
基金supported by National Natural Science Foundation of China(51275094)by High-Level Personnel Project of Guangdong Province(2014011)by China Postdoctoral Science Foundation(20110490893)
文摘In this article we consider via critical point theory the existence of homoclinic orbits of the first-order differential difference equation z（t）＋B（t）z（t）＋f（t,z（t＋τ）,z（t）,z（t-τ））=0.
文摘Differential equation is very important in science and engineering, because it required the description of some measurable quantities (position, temperature, population, concentration, electrical current, etc.) in mathematical form of ordinary differential equations (ODEs). In this research, we determine heat transferred by convection in fluid problems by first-order ordinary differential equations. So in this research work first we discuss the solution of ordinary homogeneous and non-homogeneous differential equation and then apply the solution of first-order ODEs to heat transferring particularly in heat convection in fluid.
基金Supported by NSFC(Grant No.12071419)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2024MA056)。
文摘In this paper,we formulate two new families of fourth-order explicit exponential Runge–Kutta(ERK)methods with four stages for solving first-order differential systems y'(t)+M y(t)=f(y(t)).The order conditions of these ERK methods are derived by comparing the Taylor series of the exact solution,which are exactly identical to the order conditions of explicit Runge–Kutta methods,and these ERK methods reduce to classical Runge–Kutta methods once M→0.Moreover,we analyze the stability properties and the convergence of these new methods.Several numerical examples are implemented to illustrate the accuracy and efficiency of these ERK methods by comparison with standard exponential integrators.
文摘In this paper, a novel class of exponential Fourier collocation methods （EFCMs） is presented for solving systems of first-order ordinary differential equations. These so-called exponential Fourier collocation methods are based on the variation-of-constants formula, incorporating a local Fourier expansion of the underlying problem with collocation meth- ods. We discuss in detail the connections of EFCMs with trigonometric Fourier colloca- tion methods （TFCMs）, the well-known Hamiltonian Boundary Value Methods （HBVMs）, Gauss methods and Radau IIA methods. It turns out that the novel EFCMs are an es- sential extension of these existing methods. We also analyse the accuracy in preserving the quadratic invariants and the Hamiltonian energy when the underlying system is a Hamiltonian system. Other properties of EFCMs including the order of approximations and the convergence of fixed-point iterations are investigated as well. The analysis given in this paper proves further that EFCMs can achieve arbitrarily high order in a routine manner which allows us to construct higher-order methods for solving systems of first- order ordinary differential equations conveniently. We also derive a practical fourth-order EFCM denoted by EFCM（2,2） as an illustrative example. The numerical experiments using EFCM（2,2） are implemented in comparison with an existing fourth-order HBVM, an energy-preserving collocation method and a fourth-order exponential integrator in the literature. The numerical results demonstrate the remarkable efficiency and robustness of the novel EFCM（2,2）.
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.
文摘Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.
基金Supported by the Youth Science Foundation of China（l1201272） Supported by the Youth Science Foundatioa of Shanxi Province（2010021002-1）
文摘In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.
文摘A type of Inconsistent Mathematics structured on Paraconsistent Logic (PL) and that has, as the main purpose, the study of common mathematical objects such as sets, numbers and functions, where some contradictions are allowed, is called Paraconsistent Mathematics. The PL is a non-Classical logic and its main property is to present tolerance for contradiction in its fundamentals without the invalidation of the conclusions. In this paper (part 1), we use the PL in its annotated form, denominated Paraconsistent Annotated Logic with annotation of two values—PAL2v for present a first-order Paraconsistent Derivative. The PAL2v has, in its representation, an associated lattice FOUR based on Hasse Diagram. This PAL2v-Lattice allows development of a Para-consistent Differential Calculus based on fundamentals and equations obtained by geometric interpretations. In this first article it is presented some examples applying derivatives of first-order with the concepts of Paraconsistent Mathematics. In the second part of this work we will show the Paraconsistent Derivative of second-order with application examples.
文摘The existence of at feast one solution and the existence of extreme solutions of periodic boundary value problems for first-order integro-differential equations of mixed type are studied, in the presence of generalized upper and laver solutions. The discussion is based an new comparison theorems and coincidence degree and monotone iterative methods.
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.
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.
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 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.
