In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to ...In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.展开更多
Highly accurate spatial discretization is essentially required to perform numerical climate and weather prediction. The difference between the differential and the finite-difference operator is however a primitive err...Highly accurate spatial discretization is essentially required to perform numerical climate and weather prediction. The difference between the differential and the finite-difference operator is however a primitive error source in the numerics. This paper presents an optimization of centered finite-difference operator based on the principle of constrained cost function, which can reduce the truncation error to minimum. In the optimization point of view, such optimal operator is in fact an attempt to minimize spatial truncation er-rors in atmospheric modeling, in a simple way and indeed a quite innovative way to implement Variational Continuous Assimilation (VCA) technique. Furthermore, the optimizing difference operator is consciously designed to be meshing-independent, so that it can be used for most Arakawa-mesh configurations, such as un-staggered (Arakawa-A) or com-monly staggered (Arakawa-B, Arakawa-C, Arakawa-D) mesh. But for the calibration purpose, the pro-posed operator is implemented on an un-staggered mesh in which the truncation oscillation is mostly ex-cited, and it thus makes a severe and indeed a benchmark test for the proposed optimal scheme. Both theo-retical investigation and practical modeling indicate that the aforementioned numerical noise can be significantly eliminated.展开更多
In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery p...In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.展开更多
A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exist...A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exists an n dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n dimensional optimal approximations to be unique is obtained.展开更多
For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln（ψ） =∑k=0^n akψ（k） where the constant coefficients...For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln（ψ） =∑k=0^n akψ（k） where the constant coefficients ak C R may be adapted to f.展开更多
In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy sys...In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.展开更多
The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(...The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.展开更多
In radiology,magnetic resonance imaging(MRI)is an essential diagnostic tool that provides detailed images of a patient’s anatomical and physiological structures.MRI is particularly effective for detecting soft tissue...In radiology,magnetic resonance imaging(MRI)is an essential diagnostic tool that provides detailed images of a patient’s anatomical and physiological structures.MRI is particularly effective for detecting soft tissue anomalies.Traditionally,radiologists manually interpret these images,which can be labor-intensive and time-consuming due to the vast amount of data.To address this challenge,machine learning,and deep learning approaches can be utilized to improve the accuracy and efficiency of anomaly detection in MRI scans.This manuscript presents the use of the Deep AlexNet50 model for MRI classification with discriminative learning methods.There are three stages for learning;in the first stage,the whole dataset is used to learn the features.In the second stage,some layers of AlexNet50 are frozen with an augmented dataset,and in the third stage,AlexNet50 with an augmented dataset with the augmented dataset.This method used three publicly available MRI classification datasets:Harvard whole brain atlas(HWBA-dataset),the School of Biomedical Engineering of Southern Medical University(SMU-dataset),and The National Institute of Neuroscience and Hospitals brain MRI dataset(NINS-dataset)for analysis.Various hyperparameter optimizers like Adam,stochastic gradient descent(SGD),Root mean square propagation(RMS prop),Adamax,and AdamW have been used to compare the performance of the learning process.HWBA-dataset registers maximum classification performance.We evaluated the performance of the proposed classification model using several quantitative metrics,achieving an average accuracy of 98%.展开更多
This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV i...This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.展开更多
In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimizatio...In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimization objective functions caused by their physical dimensions.These deviations seriously affect the scheduling process.A novel standardization fusion method has been established to address this issue by analyzing the variation process of each objective function’s values.The optimal scheduling results of IEHS with HESS indicate that the economy and overall energy loss can be improved 2–3 times under different optimization methods.The proposed method better balances all optimization objective functions and reduces the impact of their dimensionality.When the cost of BESS decreases by approximately 30%,its participation deepens by about 1 time.Moreover,if the price of the electrolyzer is less than 15¥/kWh or if the cost of the fuel cell drops below 4¥/kWh,their participation will increase substantially.This study aims to provide a more reasonable approach to solving multi-objective optimization problems.展开更多
Rapid and reliable onboard optimization of bank angle profiles is crucial for mitigating uncertainties during Mars atmospheric entry.This paper presents a neural-network-accelerated methodology for optimizing parametr...Rapid and reliable onboard optimization of bank angle profiles is crucial for mitigating uncertainties during Mars atmospheric entry.This paper presents a neural-network-accelerated methodology for optimizing parametric bank angle profiles in Mars atmospheric entry missions.The methodology includes a universal approach to handling path constraints and a reliable solution method based on the Particle Swarm Optimization(PSO)algorithm.For illustrative purposes,a mission with the objective of maximizing terminal altitude is considered.The original entry optimization problem is converted into optimizing three coefficients for the bank angle profiles with terminal constraints by formulating a parametric Mars entry bank angle profile and constraint handling methods.The parameter optimization problem is addressed using the PSO algorithm,with reliability enhanced by increasing the PSO swarm size.To improve computational efficiency,an enhanced Deep Operator Network(Deep ONet)is used as a dynamics solver to predict terminal states under various bank angle profiles rapidly.Numerical simulations demonstrate that the proposed methodology ensures reliable convergence with a sufficiently large PSO swarm while maintaining high computational efficiency facilitated by the neural-network-based dynamics solver.Compared to the existing methodologies,this methodology offers a streamlined process,the reduced sensitivity to initial guesses,and the improved computational efficiency.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
Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(...Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.展开更多
Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective to...Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective tools to address these challenges.In this paper,new mathematical approaches for handling uncertainty in medical diagnosis are introduced using q-rung orthopair fuzzy sets(q-ROFS)and interval-valued q-rung orthopair fuzzy sets(IVq-ROFS).Three aggregation operators are proposed in our methodologies:the q-ROF weighted averaging(q-ROFWA),the q-ROF weighted geometric(q-ROFWG),and the q-ROF weighted neutrality averaging(qROFWNA),which enhance decision-making under uncertainty.These operators are paired with ranking methods such as the similarity measure,score function,and inverse score function to improve the accuracy of disease identification.Additionally,the impact of varying q-rung values is explored through a sensitivity analysis,extending the analysis beyond the typical maximum value of 3.The Basic Uncertain Information(BUI)method is employed to simulate expert opinions,and aggregation operators are used to combine these opinions in a group decisionmaking context.Our results provide a comprehensive comparison of methodologies,highlighting their strengths and limitations in diagnosing diseases based on uncertain patient data.展开更多
Assessing the impact of anthropogenic volatile organic compounds(VOCs)on ozone(O_(3))formation is vital for themanagement of emission reduction and pollution control.Continuousmeasurement of O_(3)and the major precurs...Assessing the impact of anthropogenic volatile organic compounds(VOCs)on ozone(O_(3))formation is vital for themanagement of emission reduction and pollution control.Continuousmeasurement of O_(3)and the major precursorswas conducted in a typical light industrial city in the YRD region from 1 May to 25 July in 2021.Alkanes were the most abundant VOC group,contributing to 55.0%of TVOCs concentration(56.43±21.10 ppb).OVOCs,aromatics,halides,alkenes,and alkynes contributed 18.7%,9.6%,9.3%,5.2%and 1.9%,respectively.The observational site shifted from a typical VOC control regime to a mixed regime from May to July,which can be explained by the significant increase of RO_(x)production,resulting in the transition of environment from NOx saturation to radical saturation with respect to O_(3)production.The optimal O_(3)control strategy should be dynamically changed depending on the transition of control regime.Under NOx saturation condition,minimizing the proportion of NOx in reduction could lead to better achievement of O_(3)alleviation.Under mixed control regime,the cut percentage gets the top priority for the effectiveness of O_(3)control.Five VOCs sources were identified:temperature dependent source(28.1%),vehicular exhausts(19.9%),petrochemical industries(7.2%),solvent&gasoline usage(32.3%)and manufacturing industries(12.6%).The increase of temperature and radiation would enhance the evaporation related VOC emissions,resulting in the increase of VOC concentration and the change of RO_(x)circulation.Our results highlight determination of the optimal control strategies for O_(3)pollution in a typical YRD industrial city.展开更多
The work takes a new liquid-cooling plate in a power battery with pin fins inside the channel as the object.A mathematical model is established via the central composite design of the response surface to study the rel...The work takes a new liquid-cooling plate in a power battery with pin fins inside the channel as the object.A mathematical model is established via the central composite design of the response surface to study the relationships among the length,width,height,and spacing of pin fins;the maximum temperature and temperature difference of the battery module;and the pressure drop of the liquid-cooling plate.Model accuracy is verified via variance analysis.The new liquid-cooling plate enables the power battery to work within an optimal temperature range.Appropriately increasing the length,width,and height and reducing the spacing of pin fins could reduce the temperature of the power battery module and improve the temperature uniformity.However,the pressure drop of the liquid-cooling plate increases.The structural parameters of the pin fins are optimized to minimize the maximum temperature and the temperature difference of the battery module as well as the pressure drop of the liquid-cooling plate.The errors between the values predicted and actual by the simulation test are 0.58%,4%,and 0.48%,respectively,which further verifies the model accuracy.The results reveal the influence of the structural parameters of the pin fins inside the liquid-cooling plate on its heat dissipation performance and pressure drop characteristics.A theoretical basis is provided for the design of liquid-cooling plates in power batteries and the optimization of structural parameters.展开更多
To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target...To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target location. Since trajectory optimization struggles to meet real-time requirements, the emergence of data-based generation methods has become a significant focus in contemporary research. However, due to the large differences in the characteristics of the optimal control laws caused by the diversity of tasks, it is difficult to achieve good prediction results by modeling all data with one single model.Therefore, the modeling idea of the mixture of experts(MoE) is adopted. Firstly, the K-means clustering algorithm is used to partition the sample data set, and the corresponding neural network classification model is established as the gate switch of MoE. Then, the expert models, i.e., the mappings from the generation conditions to the optimal control law represented by the results of principal component analysis(PCA), are represented by Kriging models. Finally, multiple rounds of accuracy evaluation, sample supplementation, and model updating are conducted to improve the generation accuracy. The Monte Carlo simulation shows that the accuracy of the proposed model reaches 96% and the generation efficiency meets the real-time requirement.展开更多
The quantum alternating operator ansatz algorithm(QAOA+)is widely used for constrained combinatorial optimization problems(CCOPs)due to its ability to construct feasible solution spaces.In this paper,we propose a prog...The quantum alternating operator ansatz algorithm(QAOA+)is widely used for constrained combinatorial optimization problems(CCOPs)due to its ability to construct feasible solution spaces.In this paper,we propose a progressive quantum algorithm(PQA)to reduce qubit requirements for QAOA+in solving the maximum independent set(MIS)problem.PQA iteratively constructs a subgraph likely to include the MIS solution of the original graph and solves the problem on it to approximate the global solution.Specifically,PQA starts with a small-scale subgraph and progressively expands its graph size utilizing heuristic expansion strategies.After each expansion,PQA solves the MIS problem on the newly generated subgraph using QAOA+.In each run,PQA repeats the expansion and solving process until a predefined stopping condition is reached.Simulation results show that PQA achieves an approximation ratio of 0.95 using only 5.57%(2.17%)of the qubits and 17.59%(6.43%)of the runtime compared with directly solving the original problem with QAOA+on Erd?s-Rényi(3-regular)graphs,highlighting the efficiency and scalability of PQA.展开更多
In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and the...In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and therefore,the foreign exchange rate model is incorporated.Under the allowing of selling and borrowing,the problem of maximizing the expected exponential utility of terminal wealth is studied.By solving the corresponding Hamilton-Jacobi-Bellman equations,the optimal investment strategies and value functions are obtained.Finally,numerical analysis is presented.展开更多
This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis...This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.展开更多
基金Supported in part by Natural Science Foundation of Guangxi(2023GXNSFAA026246)in part by the Central Government's Guide to Local Science and Technology Development Fund(GuikeZY23055044)in part by the National Natural Science Foundation of China(62363003)。
文摘In this paper,we consider the maximal positive definite solution of the nonlinear matrix equation.By using the idea of Algorithm 2.1 in ZHANG(2013),a new inversion-free method with a stepsize parameter is proposed to obtain the maximal positive definite solution of nonlinear matrix equation X+A^(*)X|^(-α)A=Q with the case 0<α≤1.Based on this method,a new iterative algorithm is developed,and its convergence proof is given.Finally,two numerical examples are provided to show the effectiveness of the proposed method.
基金We acknowledge the anonymous reviewers for their helpful comments and criticism on an earlier manuscript.The authors are indebted to the supports from the National Natural Science Foundation of China under Grant Nos.40175025and 40028504the State key Bas
文摘Highly accurate spatial discretization is essentially required to perform numerical climate and weather prediction. The difference between the differential and the finite-difference operator is however a primitive error source in the numerics. This paper presents an optimization of centered finite-difference operator based on the principle of constrained cost function, which can reduce the truncation error to minimum. In the optimization point of view, such optimal operator is in fact an attempt to minimize spatial truncation er-rors in atmospheric modeling, in a simple way and indeed a quite innovative way to implement Variational Continuous Assimilation (VCA) technique. Furthermore, the optimizing difference operator is consciously designed to be meshing-independent, so that it can be used for most Arakawa-mesh configurations, such as un-staggered (Arakawa-A) or com-monly staggered (Arakawa-B, Arakawa-C, Arakawa-D) mesh. But for the calibration purpose, the pro-posed operator is implemented on an un-staggered mesh in which the truncation oscillation is mostly ex-cited, and it thus makes a severe and indeed a benchmark test for the proposed optimal scheme. Both theo-retical investigation and practical modeling indicate that the aforementioned numerical noise can be significantly eliminated.
基金Supported by the National Fund of Natural Sciences.
文摘In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.
文摘A method of approaching to the infinite dimensional linear operators by the finite dimensional operators is discussed. It is shown that,for every infinite dimensional operator A and every natural number n, there exists an n dimensional optimal approximation to A. The norm error is found and the necessary and sufficient condition for such n dimensional optimal approximations to be unique is obtained.
文摘For a real valued function f defined on a finite interval I we consider the problem of approximating f from null spaces of differential operators of the form Ln（ψ） =∑k=0^n akψ（k） where the constant coefficients ak C R may be adapted to f.
基金supported by the Central Government Guides Local Science and Technology Development Fund Project(2023ZY0020)Key R&D and Achievement Transformation Project in InnerMongolia Autonomous Region(2022YFHH0019)+3 种基金the Fundamental Research Funds for Inner Mongolia University of Science&Technology(2022053)Natural Science Foundation of Inner Mongolia(2022LHQN05002)National Natural Science Foundation of China(52067018)Metallurgical Engineering First-Class Discipline Construction Project in Inner Mongolia University of Science and Technology,Control Science and Engineering Quality Improvement and Cultivation Discipline Project in Inner Mongolia University of Science and Technology。
文摘In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.
基金Supported by Sichuan Science and Technology Program (No.2022ZYD0010)。
文摘The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.
文摘In radiology,magnetic resonance imaging(MRI)is an essential diagnostic tool that provides detailed images of a patient’s anatomical and physiological structures.MRI is particularly effective for detecting soft tissue anomalies.Traditionally,radiologists manually interpret these images,which can be labor-intensive and time-consuming due to the vast amount of data.To address this challenge,machine learning,and deep learning approaches can be utilized to improve the accuracy and efficiency of anomaly detection in MRI scans.This manuscript presents the use of the Deep AlexNet50 model for MRI classification with discriminative learning methods.There are three stages for learning;in the first stage,the whole dataset is used to learn the features.In the second stage,some layers of AlexNet50 are frozen with an augmented dataset,and in the third stage,AlexNet50 with an augmented dataset with the augmented dataset.This method used three publicly available MRI classification datasets:Harvard whole brain atlas(HWBA-dataset),the School of Biomedical Engineering of Southern Medical University(SMU-dataset),and The National Institute of Neuroscience and Hospitals brain MRI dataset(NINS-dataset)for analysis.Various hyperparameter optimizers like Adam,stochastic gradient descent(SGD),Root mean square propagation(RMS prop),Adamax,and AdamW have been used to compare the performance of the learning process.HWBA-dataset registers maximum classification performance.We evaluated the performance of the proposed classification model using several quantitative metrics,achieving an average accuracy of 98%.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-RP23066).
文摘This study directs the discussion of HIV disease with a novel kind of complex dynamical generalized and piecewise operator in the sense of classical and Atangana Baleanu(AB)derivatives having arbitrary order.The HIV infection model has a susceptible class,a recovered class,along with a case of infection divided into three sub-different levels or categories and the recovered class.The total time interval is converted into two,which are further investigated for ordinary and fractional order operators of the AB derivative,respectively.The proposed model is tested separately for unique solutions and existence on bi intervals.The numerical solution of the proposed model is treated by the piece-wise numerical iterative scheme of Newtons Polynomial.The proposed method is established for piece-wise derivatives under natural order and non-singular Mittag-Leffler Law.The cross-over or bending characteristics in the dynamical system of HIV are easily examined by the aspect of this research having a memory effect for controlling the said disease.This study uses the neural network(NN)technique to obtain a better set of weights with low residual errors,and the epochs number is considered 1000.The obtained figures represent the approximate solution and absolute error which are tested with NN to train the data accurately.
基金sponsored by R&D Program of Beijing Municipal Education Commission(KM202410009013).
文摘In the independent electro-hydrogen system(IEHS)with hybrid energy storage(HESS),achieving optimal scheduling is crucial.Still,it presents a challenge due to the significant deviations in values ofmultiple optimization objective functions caused by their physical dimensions.These deviations seriously affect the scheduling process.A novel standardization fusion method has been established to address this issue by analyzing the variation process of each objective function’s values.The optimal scheduling results of IEHS with HESS indicate that the economy and overall energy loss can be improved 2–3 times under different optimization methods.The proposed method better balances all optimization objective functions and reduces the impact of their dimensionality.When the cost of BESS decreases by approximately 30%,its participation deepens by about 1 time.Moreover,if the price of the electrolyzer is less than 15¥/kWh or if the cost of the fuel cell drops below 4¥/kWh,their participation will increase substantially.This study aims to provide a more reasonable approach to solving multi-objective optimization problems.
基金supported in part by the National Defense Basic Scientific Research Program of China(No.JCKY2021603B030)the Shenzhen Fundamental Research Program,China(No.JCYJ20220818102601004)the Science Center Program of National Natural Science Foundation of China(No.62188101)。
文摘Rapid and reliable onboard optimization of bank angle profiles is crucial for mitigating uncertainties during Mars atmospheric entry.This paper presents a neural-network-accelerated methodology for optimizing parametric bank angle profiles in Mars atmospheric entry missions.The methodology includes a universal approach to handling path constraints and a reliable solution method based on the Particle Swarm Optimization(PSO)algorithm.For illustrative purposes,a mission with the objective of maximizing terminal altitude is considered.The original entry optimization problem is converted into optimizing three coefficients for the bank angle profiles with terminal constraints by formulating a parametric Mars entry bank angle profile and constraint handling methods.The parameter optimization problem is addressed using the PSO algorithm,with reliability enhanced by increasing the PSO swarm size.To improve computational efficiency,an enhanced Deep Operator Network(Deep ONet)is used as a dynamics solver to predict terminal states under various bank angle profiles rapidly.Numerical simulations demonstrate that the proposed methodology ensures reliable convergence with a sufficiently large PSO swarm while maintaining high computational efficiency facilitated by the neural-network-based dynamics solver.Compared to the existing methodologies,this methodology offers a streamlined process,the reduced sensitivity to initial guesses,and the improved computational efficiency.
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 NSFC(No.11971295)Guangdong Higher Education Teaching Reform Project(No.2023307)。
文摘Let Ω be homogeneous of degree zero,integrable on S^(n−1) and have mean value zero,T_(Ω) be the homogeneous singular integral operator with kernel Ω(x)/|x|^(n) and[b,T_(Ω)]be the commutator of T_(Ω)with symbol b∈BMO(R^(n)).In this paper,the authors prove that if sup ζ∈S^(n−1)∫Sn−1^(|Ω(θ)|log^(β)(1/|θ·ζ|)dθ<∞ with β>2,then[b,T_(Ω)]is bounded on Triebel–Lizorkin space F^(0,q)p(R^(n))provided that 1+1/β−1<p,q<β.
文摘Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective tools to address these challenges.In this paper,new mathematical approaches for handling uncertainty in medical diagnosis are introduced using q-rung orthopair fuzzy sets(q-ROFS)and interval-valued q-rung orthopair fuzzy sets(IVq-ROFS).Three aggregation operators are proposed in our methodologies:the q-ROF weighted averaging(q-ROFWA),the q-ROF weighted geometric(q-ROFWG),and the q-ROF weighted neutrality averaging(qROFWNA),which enhance decision-making under uncertainty.These operators are paired with ranking methods such as the similarity measure,score function,and inverse score function to improve the accuracy of disease identification.Additionally,the impact of varying q-rung values is explored through a sensitivity analysis,extending the analysis beyond the typical maximum value of 3.The Basic Uncertain Information(BUI)method is employed to simulate expert opinions,and aggregation operators are used to combine these opinions in a group decisionmaking context.Our results provide a comprehensive comparison of methodologies,highlighting their strengths and limitations in diagnosing diseases based on uncertain patient data.
基金supported by the National Natural Science Foundation of China(Nos.42005086,91844301,and 41805100)the National Key Research and Development Programof China(No.2022YFC3703500)+2 种基金China Postdoctoral Science Foundation(No.2023M733028)the Key Research and Development Program of Zhejiang Province(Nos.2021C03165 and 2022C03084)the Ecological and Environmental Scientific Research and Achievement Promotion Project of Zhejiang Province(No.2020HT0048).
文摘Assessing the impact of anthropogenic volatile organic compounds(VOCs)on ozone(O_(3))formation is vital for themanagement of emission reduction and pollution control.Continuousmeasurement of O_(3)and the major precursorswas conducted in a typical light industrial city in the YRD region from 1 May to 25 July in 2021.Alkanes were the most abundant VOC group,contributing to 55.0%of TVOCs concentration(56.43±21.10 ppb).OVOCs,aromatics,halides,alkenes,and alkynes contributed 18.7%,9.6%,9.3%,5.2%and 1.9%,respectively.The observational site shifted from a typical VOC control regime to a mixed regime from May to July,which can be explained by the significant increase of RO_(x)production,resulting in the transition of environment from NOx saturation to radical saturation with respect to O_(3)production.The optimal O_(3)control strategy should be dynamically changed depending on the transition of control regime.Under NOx saturation condition,minimizing the proportion of NOx in reduction could lead to better achievement of O_(3)alleviation.Under mixed control regime,the cut percentage gets the top priority for the effectiveness of O_(3)control.Five VOCs sources were identified:temperature dependent source(28.1%),vehicular exhausts(19.9%),petrochemical industries(7.2%),solvent&gasoline usage(32.3%)and manufacturing industries(12.6%).The increase of temperature and radiation would enhance the evaporation related VOC emissions,resulting in the increase of VOC concentration and the change of RO_(x)circulation.Our results highlight determination of the optimal control strategies for O_(3)pollution in a typical YRD industrial city.
基金supported by the Education and Teaching Research Project of Universities in Fujian Province(FBJY20230167).
文摘The work takes a new liquid-cooling plate in a power battery with pin fins inside the channel as the object.A mathematical model is established via the central composite design of the response surface to study the relationships among the length,width,height,and spacing of pin fins;the maximum temperature and temperature difference of the battery module;and the pressure drop of the liquid-cooling plate.Model accuracy is verified via variance analysis.The new liquid-cooling plate enables the power battery to work within an optimal temperature range.Appropriately increasing the length,width,and height and reducing the spacing of pin fins could reduce the temperature of the power battery module and improve the temperature uniformity.However,the pressure drop of the liquid-cooling plate increases.The structural parameters of the pin fins are optimized to minimize the maximum temperature and the temperature difference of the battery module as well as the pressure drop of the liquid-cooling plate.The errors between the values predicted and actual by the simulation test are 0.58%,4%,and 0.48%,respectively,which further verifies the model accuracy.The results reveal the influence of the structural parameters of the pin fins inside the liquid-cooling plate on its heat dissipation performance and pressure drop characteristics.A theoretical basis is provided for the design of liquid-cooling plates in power batteries and the optimization of structural parameters.
基金Defense Industrial Technology Development Program (JCKY2020204B016)National Natural Science Foundation of China (92471206)。
文摘To better complete various missions, it is necessary to plan an optimal trajectory or provide the optimal control law for the multirole missile according to the actual situation, including launch conditions and target location. Since trajectory optimization struggles to meet real-time requirements, the emergence of data-based generation methods has become a significant focus in contemporary research. However, due to the large differences in the characteristics of the optimal control laws caused by the diversity of tasks, it is difficult to achieve good prediction results by modeling all data with one single model.Therefore, the modeling idea of the mixture of experts(MoE) is adopted. Firstly, the K-means clustering algorithm is used to partition the sample data set, and the corresponding neural network classification model is established as the gate switch of MoE. Then, the expert models, i.e., the mappings from the generation conditions to the optimal control law represented by the results of principal component analysis(PCA), are represented by Kriging models. Finally, multiple rounds of accuracy evaluation, sample supplementation, and model updating are conducted to improve the generation accuracy. The Monte Carlo simulation shows that the accuracy of the proposed model reaches 96% and the generation efficiency meets the real-time requirement.
基金supported by the National Natural Science Foundation of China(Grant Nos.62371069,62372048,and 62272056)BUPT Excellent Ph.D.Students Foundation(Grant No.CX2023123)。
文摘The quantum alternating operator ansatz algorithm(QAOA+)is widely used for constrained combinatorial optimization problems(CCOPs)due to its ability to construct feasible solution spaces.In this paper,we propose a progressive quantum algorithm(PQA)to reduce qubit requirements for QAOA+in solving the maximum independent set(MIS)problem.PQA iteratively constructs a subgraph likely to include the MIS solution of the original graph and solves the problem on it to approximate the global solution.Specifically,PQA starts with a small-scale subgraph and progressively expands its graph size utilizing heuristic expansion strategies.After each expansion,PQA solves the MIS problem on the newly generated subgraph using QAOA+.In each run,PQA repeats the expansion and solving process until a predefined stopping condition is reached.Simulation results show that PQA achieves an approximation ratio of 0.95 using only 5.57%(2.17%)of the qubits and 17.59%(6.43%)of the runtime compared with directly solving the original problem with QAOA+on Erd?s-Rényi(3-regular)graphs,highlighting the efficiency and scalability of PQA.
基金supported by the National Natural Science Foundation of China(Grant No.12301603).
文摘In this paper,we study the optimal investment problem of an insurer whose surplus process follows the diffusion approximation of the classical Cramer-Lundberg model.Investment in the foreign markets is allowed,and therefore,the foreign exchange rate model is incorporated.Under the allowing of selling and borrowing,the problem of maximizing the expected exponential utility of terminal wealth is studied.By solving the corresponding Hamilton-Jacobi-Bellman equations,the optimal investment strategies and value functions are obtained.Finally,numerical analysis is presented.
文摘This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.
