It is well-known that philosophical conflicts exist among classical mechanics,quantum mechanics and relativistic mechanics.In order to use the framework of general system theory to unify these three mechanics subjects...It is well-known that philosophical conflicts exist among classical mechanics,quantum mechanics and relativistic mechanics.In order to use the framework of general system theory to unify these three mechanics subjects,a new general system theory is developed based on a new ontology of ether and minds as the fundamental existences in the world.The two-body problem is the simplest model in mechanics and in this paper,it is re-examined by using our new general system theory.It is found that the current description of the classical full two-body problem is inappropriate since the observer and the measurement apparatus have not been explicitly considered.After considering these,it is actually a three-body problem while only the special case of the Kepler problem is the two-body problem.By introducing the concepts of psychic force and psychic field,all the possible movement states in the two-body problem can be explained within the framework of classical mechanics.There is no need to change the meanings of many fundamental concepts,such as time,space,matter,mass,and energy as done in quantum mechanics and relativity theory.This points out a new direction for the unification of different theories.展开更多
A binary gravitational rotator, also called the two-body problem, is a pair of masses m<sub>1</sub>, m<sub>2</sub> moving around their center-of-mass (com) in their own gravitational field. In ...A binary gravitational rotator, also called the two-body problem, is a pair of masses m<sub>1</sub>, m<sub>2</sub> moving around their center-of-mass (com) in their own gravitational field. In Newtonian gravitation, the two-body problem can be described by a single reduced mass (gravitational rotator) m<sub>r</sub> = m<sub>1</sub>m<sub>2</sub>/(m<sub>1</sub>+m<sub>2</sub>) orbiting around the total mass m = m<sub>1</sub>+m<sub>2</sub> situated in com in the distance r, which is the distance between the two original masses. In this paper, we discuss the rotator in Newtonian, Schwarzschild and Kerr spacetime context. We formulate the corresponding Kerr orbit equations, and adapt the Kerr rotational parameter to the Newtonian correction of the rotator potential. We present a vacuum solution of Einstein equations (Manko-Ruiz), which is a generalized Kerr spacetime with five parameters g<sub>μν</sub> (m<sub>1</sub>, m<sub>2</sub>, R, a<sub>1</sub>, a<sub>2</sub>), and adapt it to the Newtonian correction for observer orbits. We show that the Manko-Ruiz metric is the exact solution of the GR-two-body problem (i.e. GR-rotator) and express the orbit energy and angular momentum in terms of the 5 parameters. We calculate and discuss Manko-Ruiz rotator orbits in their own field, and present numerical results for two examples. Finally, we carry out numerical calculations of observer orbits in the rotator field for all involved models and compare them.展开更多
Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubatio...Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius a<sub>H</sub> and planet mean radius R<sub>P </sub>and the ratio R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub>. Under very low R<sub>1 </sub>(less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub> =0.01 and 5.9862 × 10<sup>-3</sup> respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study.展开更多
This paper presents a novel machine learning approach designed to efficiently solve the classical two-body problem.The inherent structure of the two-body problem involves the integration of a system of second-order no...This paper presents a novel machine learning approach designed to efficiently solve the classical two-body problem.The inherent structure of the two-body problem involves the integration of a system of second-order nonlinear ordinary differential equations.Conventional numerical integration techniques that rely on small computation steps result in a prolonged computational time.Moreover,calculus has limitations in resolving the two-body problem,inevitably converging towards an unresolved Kepler equation of a transcendental nature.To address this issue,we integrate the conventional analytical solution based on true anomaly with a deep neural network representation of the Kepler equation.This results in a highly accurate closed-form solution that is solely dependent on time,which is termed a learning-based solution to the two-body problem.To enhance the precision,a correction module based on Halley iteration is introduced,which substantially improves the final solution in terms of precision and computational cost.Compared to stateof-the-art methods such as the piecewise Padéapproximation,Adomian decomposition method,and modified Mikkola's method,our approach achieves a computational speedup of several thousand to tens of thousands,while maintaining accuracy in large-scale orbit propagation scenarios.Empirical validation under simulated conditions underscores its effectiveness and potential value for long-term orbit determination.展开更多
During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive...During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.展开更多
Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when ta...Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.展开更多
Truncating at the second order of the mutual potential between two rigid bodies,time-explicit rst order solutions to the rotations and the orbital motion of the two bodies in the planar full two-body problem(F2BP)are ...Truncating at the second order of the mutual potential between two rigid bodies,time-explicit rst order solutions to the rotations and the orbital motion of the two bodies in the planar full two-body problem(F2BP)are constructed.Based on this analytical solution,equations of motion(EOMs)for the related restricted full three-body problem are given.In the case of the synchronous or double synchronous states for the full two-body problem,EOMs for the related restricted full three-body problem(RF3BP)are also given.At last,one example-the"collinear libration point"in the binary asteroid system-is given.展开更多
Background:Parenting exerts a profound influence on children’s mental health and behavioral development.Despite the high prevalence of children’s emotional and behavioral problems(CEBP)in China,evidence-based parent...Background:Parenting exerts a profound influence on children’s mental health and behavioral development.Despite the high prevalence of children’s emotional and behavioral problems(CEBP)in China,evidence-based parenting interventions remain scarcely investigated as preventive public health strategies.This pilot study evaluated a school-based intervention for preventing CEBP.Methods:We employed a quasi-experimental design with propensity score matching(PSM)to select 28 families(intervention:n=13;control:n=15)from two matched urban primary schools.Quantitative data from seven validated scales were analyzed using t-tests and ANCOVA.Qualitative insights were derived from 10 semi-structured interviews via thematic analysis.Results:Compared to the control group,the intervention group demonstrated significantly greater improvements in CEBP(p=0.020,Cohen’s d=0.92),parental adjustment(p=0.031,Cohen’s d=0.80),parenting confidence(p=0.003,Cohen’s d=1.04),and parentchild relationships(p=0.001,Cohen’s d=1.46).Non-significant effects were observed for parenting style,parental relationship,and parenting conflict(p>0.05).Qualitative analysis corroborated these findings and further identified contributing factors for non-significant outcomes,including challengeswithmeasurement adaptability and inconsistent co-parenting practices.Conclusions:This pilot study suggests that an authoritative parenting style may be effective and culturally adaptable in China.Positive parenting interventions appear to mitigate CEBP by reducing risk factors and enhancing protective factors.However,improving parental relationships and parenting conflict may require targeted strategies.Given the pilot nature of this PSM-matched study(n=28),the findings should be interpreted as exploratory and used primarily for intervention refinement.展开更多
Let Pr denote an almost-prime with at most r prime factors,counted according to multiplicity.In this paper,it is proved that,for every sufficiently large even integer N,the equation N=x^(2)+p_(2)^(2)+p_(3)^(3)+p_(4)^(...Let Pr denote an almost-prime with at most r prime factors,counted according to multiplicity.In this paper,it is proved that,for every sufficiently large even integer N,the equation N=x^(2)+p_(2)^(2)+p_(3)^(3)+p_(4)^(3)+p_(5)^(5)+_6^(5)is solvable with being an almost-prime P_(6) and the other variables primes.This result constitutes an enhancement upon the previous result of Hooley[Recent Progress in Analytic Number Theory,Vol.1(Durham,1979),London:Academic Press,1981,127-191].展开更多
Let d(n;r_(1),q_(1),r_(2),q_(2))be the number of factorization n=n_(1)n_(2)satisfying n_i≡r_i(mod q_i)(i=1,2)andΔ(x;r_(1),q_(1),r_(2),q_(2))be the error term of the summatory function of d(n;r_(1),q_(1),r_(2),q_(2))...Let d(n;r_(1),q_(1),r_(2),q_(2))be the number of factorization n=n_(1)n_(2)satisfying n_i≡r_i(mod q_i)(i=1,2)andΔ(x;r_(1),q_(1),r_(2),q_(2))be the error term of the summatory function of d(n;r_(1),q_(1),r_(2),q_(2)).Suppose x≥(q_(1)q_(2))^(1+ε),1≤r_i≤q_i,and(r_i,q_i)=1(i=1,2).This paper studies the power moments and sign changes ofΔ(x;r_(1),q_(1),r_(2),q_(2)).We prove that for sufficiently large constant C,Δ(q_(1)q_(2)x:r_(1),q_(1),r_(2),q_(2))changes sign in the interval[T,T+C√T]for any large T.Meanwhile,we show that for small constants c and c,there exist infinitely many subintervals of length c√log^(-7)T in[T,2T]where±Δ(q_(1)q_(2)x:r_(1),q_(1),r_(2),q_(2))>cx^(1/4)always holds.展开更多
Automatically answer math word problems is a challenging task in artificial intelligence.Previous solvers constructed mathematical expressions in sequence or binary tree.However,these approaches may suffer from the fo...Automatically answer math word problems is a challenging task in artificial intelligence.Previous solvers constructed mathematical expressions in sequence or binary tree.However,these approaches may suffer from the following issues:Models relying on such structures exhibit fixed-order reasoning(e.g.,left-to-right),limiting flexibility and increasing error susceptibility;prior models rely on autoregressive reasoning in a single pass,accumulating minor errors(e.g.,incorrect math symbols)during generation,resulting in reduced accuracy.To address the above issues,we emulate the human“check and modify”process in reasoning and propose a unified M-tree self-correction solver(UTSCSolver)by iterative inference with self-correction mechanism.First,we use an iterative,non-autoregressive process for generating mathematical expressions,free from fixed generation orders to handle complex and diverse problems.Additionally,we design a self-correction mechanism based on alternating execution between a generator and a discriminator.This module iteratively detects and rectifies errors in generated expressions,leveraging previous iteration information for subsequent generation guidance.Experimental results show that our UTSC-Solver outperforms traditional models in accuracy on two popular datasets,while it improves the interpretability of mathematical reasoning.展开更多
BACKGROUND Emotional reactions,such as anxiety,irritability,and aggressive behavior,have attracted clinical attention as behavioral and emotional problems in preschool-age children.AIM To investigate the current statu...BACKGROUND Emotional reactions,such as anxiety,irritability,and aggressive behavior,have attracted clinical attention as behavioral and emotional problems in preschool-age children.AIM To investigate the current status of family rearing,parental stress,and behavioral and emotional problems of preschool children and to analyze the mediating effect of the current status of family rearing on parental stress and behavioral/emo-tional problems.METHODS We use convenience sampling to select 258 preschool children in the physical examination center of our hospital from October 2021 to September 2023.The children and their parents were evaluated using a questionnaire survey.Pearson's correlation was used to analyze the correlation between child behavioral and emotional problems and parental stress and family rearing,and the structural equation model was constructed to test the mediating effect.RESULTS The score for behavioral/emotional problems of 258 preschool children was(27.54±3.63),the score for parental stress was(87.64±11.34),and the score for parental family rearing was(31.54±5.24).There was a positive correlation between the behavioral and emotional problems of the children and the“hostile/mandatory”parenting style;meanwhile,showed a negative correlation with the“support/participation”parenting style(all P<0.05).The intermediary effect value between the family upbringing of parents in parental stress and children's behavior problems was 29.89%.CONCLUSION Parental family upbringing has a mediating effect between parental stress and behavioral and emotional problems of children.Despite paying attention to the behavioral and emotional problems of preschool-age children,clinical medical staff should provide correct and reasonable parenting advice to their parents to promote the mental health of preschool-age children.展开更多
This case study explores the efficacy of school-based intervention to address psychosocial challenges faced by an 11-year-old adolescent. The case study aimed to decrease the agression and acting out behavior as resul...This case study explores the efficacy of school-based intervention to address psychosocial challenges faced by an 11-year-old adolescent. The case study aimed to decrease the agression and acting out behavior as result of being victimized at school by the peers. The aim was to assess and manage the child’s aggressive behavior and academic underperformance which played a significant role in the child’s low self-esteem and emotional regulation. A comprehensive assessment was conducted to rule out the difficulties and a multi-faceted intervention strategy was utilized including anger management and structured activity scheduling that helped that child to improve his academic performance as well as to learn to manage his emotional expression. Throughout 16 sessions, the intervention targeted key behavioural indicators such as emotional expression, and aggression;post-assessment results demonstrated a 22% improvement in the child’s behavioral and academic challenges. The findings suggest that a multi-faceted therapeutic approach can be effective in addressing complex issues of aggression and academic underperformance in children, highlighting the importance of integrated psychological and educational interventions.展开更多
The two-body fragmentation dynamics of water isotopologues dications(H_(2)O^(2+),HOD^(2+),and D_(2)O^(2+))induced by200 eV electron impact is investigated.Two fragment ions and an emitted electron are detected in coin...The two-body fragmentation dynamics of water isotopologues dications(H_(2)O^(2+),HOD^(2+),and D_(2)O^(2+))induced by200 eV electron impact is investigated.Two fragment ions and an emitted electron are detected in coincidence,and their momentum vectors are determined by employing a reaction microscope.The complete kinematical information of four two-body fragmentation channels of H^(+)+OH+,H^(+)+OD^(+),D^(+)+OH^(+),and D^(+)+OD+is obtained.By analyzing the projectile energy-loss spectrum,the initial electronic state of the two-body dissociation channel is determined.Upon examining the kinetic energy release(KER)distributions of the four fragmentation channels,a clear difference is found between the two-body fragmentation channel H^(+)+OD+and the other three channels.The isotopic effect in the two-body fragmentation is demonstrated by the analysis of the relative yields of the two-body fragmentation channels originating from different isotopologues,which shows preferential cleavage of the O-H bond over the O-D bond.These results provide deeper insight into the microscopic dynamic mechanisms in water radiolysis.展开更多
Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either dire...Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.展开更多
This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the chara...This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.展开更多
In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,where...In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.展开更多
As one of the world's three major food crops and an important economic and oil crop,soybean plays a crucial role in ensuring food safety.In recent years,there are many problems in soybean cultivation,production an...As one of the world's three major food crops and an important economic and oil crop,soybean plays a crucial role in ensuring food safety.In recent years,there are many problems in soybean cultivation,production and processing.In view of this situation,this paper comprehensively expounded and decomposed the cultivation situation,existing problems,specific countermeasures and conclusions,so as to re-recognize them.This study provides reference materials for the sustainable and healthy development of the soybean industry.展开更多
1.The price of a desk is 10 times the price of a chair.The desk costs 288 yuan more than the chair.How much does one desk and one chair cost?2.A and B start from two different places and walk toward each other.After 4...1.The price of a desk is 10 times the price of a chair.The desk costs 288 yuan more than the chair.How much does one desk and one chair cost?2.A and B start from two different places and walk toward each other.After 4 hours,they meet at a point that is 4 kilometres away from the midpoint between their starting points.A walks faster than B.How many more kilometres per hour does A walk than B?展开更多
基金supported by the“Construction of a Leading Innovation Team”project by the Hangzhou Municipal government,and the startup funding of New-Joined PI of Westlake University with grant number(041030150118).
文摘It is well-known that philosophical conflicts exist among classical mechanics,quantum mechanics and relativistic mechanics.In order to use the framework of general system theory to unify these three mechanics subjects,a new general system theory is developed based on a new ontology of ether and minds as the fundamental existences in the world.The two-body problem is the simplest model in mechanics and in this paper,it is re-examined by using our new general system theory.It is found that the current description of the classical full two-body problem is inappropriate since the observer and the measurement apparatus have not been explicitly considered.After considering these,it is actually a three-body problem while only the special case of the Kepler problem is the two-body problem.By introducing the concepts of psychic force and psychic field,all the possible movement states in the two-body problem can be explained within the framework of classical mechanics.There is no need to change the meanings of many fundamental concepts,such as time,space,matter,mass,and energy as done in quantum mechanics and relativity theory.This points out a new direction for the unification of different theories.
文摘A binary gravitational rotator, also called the two-body problem, is a pair of masses m<sub>1</sub>, m<sub>2</sub> moving around their center-of-mass (com) in their own gravitational field. In Newtonian gravitation, the two-body problem can be described by a single reduced mass (gravitational rotator) m<sub>r</sub> = m<sub>1</sub>m<sub>2</sub>/(m<sub>1</sub>+m<sub>2</sub>) orbiting around the total mass m = m<sub>1</sub>+m<sub>2</sub> situated in com in the distance r, which is the distance between the two original masses. In this paper, we discuss the rotator in Newtonian, Schwarzschild and Kerr spacetime context. We formulate the corresponding Kerr orbit equations, and adapt the Kerr rotational parameter to the Newtonian correction of the rotator potential. We present a vacuum solution of Einstein equations (Manko-Ruiz), which is a generalized Kerr spacetime with five parameters g<sub>μν</sub> (m<sub>1</sub>, m<sub>2</sub>, R, a<sub>1</sub>, a<sub>2</sub>), and adapt it to the Newtonian correction for observer orbits. We show that the Manko-Ruiz metric is the exact solution of the GR-two-body problem (i.e. GR-rotator) and express the orbit energy and angular momentum in terms of the 5 parameters. We calculate and discuss Manko-Ruiz rotator orbits in their own field, and present numerical results for two examples. Finally, we carry out numerical calculations of observer orbits in the rotator field for all involved models and compare them.
文摘Our Solar System contains eight planets and their respective natural satellites excepting the inner two planets Mercury and Venus. A satellite hosted by a given Planet is well protected by the gravitational pertubation of much heavier planets such as Jupiter and Saturn if the natural satellite lies deep inside the respective host Planet Hill sphere. Each planet has a Hill radius a<sub>H</sub> and planet mean radius R<sub>P </sub>and the ratio R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub>. Under very low R<sub>1 </sub>(less than 0.006) the approximation of CRTBP (centrally restricted three-body problem) to two-body problem is valid and planet has spacious Hill lobe to capture a satellite and retain it. This ensures a high probability of capture of natural satellite by the given planet and Sun’s perturbation on Planet-Satellite binary can be neglected. This is the case with Earth, Mars, Jupiter, Saturn, Neptune and Uranus. But Mercury and Venus has R<sub>1</sub>=R<sub>P</sub>/a<sub>H</sub> =0.01 and 5.9862 × 10<sup>-3</sup> respectively hence they have no satellites. There is a limit to the dimension of the captured body. It must be a much smaller body both dimensionally as well masswise. The qantitative limit is a subject of an independent study.
基金National Key R&D Program of China:Gravitational Wave Detection Project(No.2021YFC22026,No.2021YFC2202601,No.2021YFC2202603)National Natural Science Foundation of China(No.12172288).
文摘This paper presents a novel machine learning approach designed to efficiently solve the classical two-body problem.The inherent structure of the two-body problem involves the integration of a system of second-order nonlinear ordinary differential equations.Conventional numerical integration techniques that rely on small computation steps result in a prolonged computational time.Moreover,calculus has limitations in resolving the two-body problem,inevitably converging towards an unresolved Kepler equation of a transcendental nature.To address this issue,we integrate the conventional analytical solution based on true anomaly with a deep neural network representation of the Kepler equation.This results in a highly accurate closed-form solution that is solely dependent on time,which is termed a learning-based solution to the two-body problem.To enhance the precision,a correction module based on Halley iteration is introduced,which substantially improves the final solution in terms of precision and computational cost.Compared to stateof-the-art methods such as the piecewise Padéapproximation,Adomian decomposition method,and modified Mikkola's method,our approach achieves a computational speedup of several thousand to tens of thousands,while maintaining accuracy in large-scale orbit propagation scenarios.Empirical validation under simulated conditions underscores its effectiveness and potential value for long-term orbit determination.
基金supported by the National Natural Sci‐ence Foundation of China(Grant No.62306325)。
文摘During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.
基金funded by National Natural Science Foundation of China(Nos.12402142,11832013 and 11572134)Natural Science Foundation of Hubei Province(No.2024AFB235)+1 种基金Hubei Provincial Department of Education Science and Technology Research Project(No.Q20221714)the Opening Foundation of Hubei Key Laboratory of Digital Textile Equipment(Nos.DTL2023019 and DTL2022012).
文摘Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.
基金National Natural Science Foundation of China(Grant Nos.11322330 and 11673072)National Basic Research Program of China(Grant No.2013CB834100).
文摘Truncating at the second order of the mutual potential between two rigid bodies,time-explicit rst order solutions to the rotations and the orbital motion of the two bodies in the planar full two-body problem(F2BP)are constructed.Based on this analytical solution,equations of motion(EOMs)for the related restricted full three-body problem are given.In the case of the synchronous or double synchronous states for the full two-body problem,EOMs for the related restricted full three-body problem(RF3BP)are also given.At last,one example-the"collinear libration point"in the binary asteroid system-is given.
基金supported by the National Social Science Fund of China[18BSH146].
文摘Background:Parenting exerts a profound influence on children’s mental health and behavioral development.Despite the high prevalence of children’s emotional and behavioral problems(CEBP)in China,evidence-based parenting interventions remain scarcely investigated as preventive public health strategies.This pilot study evaluated a school-based intervention for preventing CEBP.Methods:We employed a quasi-experimental design with propensity score matching(PSM)to select 28 families(intervention:n=13;control:n=15)from two matched urban primary schools.Quantitative data from seven validated scales were analyzed using t-tests and ANCOVA.Qualitative insights were derived from 10 semi-structured interviews via thematic analysis.Results:Compared to the control group,the intervention group demonstrated significantly greater improvements in CEBP(p=0.020,Cohen’s d=0.92),parental adjustment(p=0.031,Cohen’s d=0.80),parenting confidence(p=0.003,Cohen’s d=1.04),and parentchild relationships(p=0.001,Cohen’s d=1.46).Non-significant effects were observed for parenting style,parental relationship,and parenting conflict(p>0.05).Qualitative analysis corroborated these findings and further identified contributing factors for non-significant outcomes,including challengeswithmeasurement adaptability and inconsistent co-parenting practices.Conclusions:This pilot study suggests that an authoritative parenting style may be effective and culturally adaptable in China.Positive parenting interventions appear to mitigate CEBP by reducing risk factors and enhancing protective factors.However,improving parental relationships and parenting conflict may require targeted strategies.Given the pilot nature of this PSM-matched study(n=28),the findings should be interpreted as exploratory and used primarily for intervention refinement.
基金Supported by NSFC (Nos.12471009,12301006,12001047,11901566)Beijing Natural Science Foundation (No.1242003)National Training Program of Innovation and Entrepreneurship for Undergraduates(No.202307011)。
文摘Let Pr denote an almost-prime with at most r prime factors,counted according to multiplicity.In this paper,it is proved that,for every sufficiently large even integer N,the equation N=x^(2)+p_(2)^(2)+p_(3)^(3)+p_(4)^(3)+p_(5)^(5)+_6^(5)is solvable with being an almost-prime P_(6) and the other variables primes.This result constitutes an enhancement upon the previous result of Hooley[Recent Progress in Analytic Number Theory,Vol.1(Durham,1979),London:Academic Press,1981,127-191].
基金supported by the Talent Fund of Beijing Jiaotong University(No.2020RC012)NSFC(No.11871295),supported by NSFC(No.11971476),supported by NSFC(No.12071421)。
文摘Let d(n;r_(1),q_(1),r_(2),q_(2))be the number of factorization n=n_(1)n_(2)satisfying n_i≡r_i(mod q_i)(i=1,2)andΔ(x;r_(1),q_(1),r_(2),q_(2))be the error term of the summatory function of d(n;r_(1),q_(1),r_(2),q_(2)).Suppose x≥(q_(1)q_(2))^(1+ε),1≤r_i≤q_i,and(r_i,q_i)=1(i=1,2).This paper studies the power moments and sign changes ofΔ(x;r_(1),q_(1),r_(2),q_(2)).We prove that for sufficiently large constant C,Δ(q_(1)q_(2)x:r_(1),q_(1),r_(2),q_(2))changes sign in the interval[T,T+C√T]for any large T.Meanwhile,we show that for small constants c and c,there exist infinitely many subintervals of length c√log^(-7)T in[T,2T]where±Δ(q_(1)q_(2)x:r_(1),q_(1),r_(2),q_(2))>cx^(1/4)always holds.
基金supported by the National Natural Science Foundation of China(62106244)the Fundamental Research Funds for the Central Universities(WK2150110021)the University Synergy Innovation Program of Anhui Province(GXXT-2022-042).
文摘Automatically answer math word problems is a challenging task in artificial intelligence.Previous solvers constructed mathematical expressions in sequence or binary tree.However,these approaches may suffer from the following issues:Models relying on such structures exhibit fixed-order reasoning(e.g.,left-to-right),limiting flexibility and increasing error susceptibility;prior models rely on autoregressive reasoning in a single pass,accumulating minor errors(e.g.,incorrect math symbols)during generation,resulting in reduced accuracy.To address the above issues,we emulate the human“check and modify”process in reasoning and propose a unified M-tree self-correction solver(UTSCSolver)by iterative inference with self-correction mechanism.First,we use an iterative,non-autoregressive process for generating mathematical expressions,free from fixed generation orders to handle complex and diverse problems.Additionally,we design a self-correction mechanism based on alternating execution between a generator and a discriminator.This module iteratively detects and rectifies errors in generated expressions,leveraging previous iteration information for subsequent generation guidance.Experimental results show that our UTSC-Solver outperforms traditional models in accuracy on two popular datasets,while it improves the interpretability of mathematical reasoning.
基金Supported by the Shijiazhuang Science and Technology Research and Development Program,No.221460383.
文摘BACKGROUND Emotional reactions,such as anxiety,irritability,and aggressive behavior,have attracted clinical attention as behavioral and emotional problems in preschool-age children.AIM To investigate the current status of family rearing,parental stress,and behavioral and emotional problems of preschool children and to analyze the mediating effect of the current status of family rearing on parental stress and behavioral/emo-tional problems.METHODS We use convenience sampling to select 258 preschool children in the physical examination center of our hospital from October 2021 to September 2023.The children and their parents were evaluated using a questionnaire survey.Pearson's correlation was used to analyze the correlation between child behavioral and emotional problems and parental stress and family rearing,and the structural equation model was constructed to test the mediating effect.RESULTS The score for behavioral/emotional problems of 258 preschool children was(27.54±3.63),the score for parental stress was(87.64±11.34),and the score for parental family rearing was(31.54±5.24).There was a positive correlation between the behavioral and emotional problems of the children and the“hostile/mandatory”parenting style;meanwhile,showed a negative correlation with the“support/participation”parenting style(all P<0.05).The intermediary effect value between the family upbringing of parents in parental stress and children's behavior problems was 29.89%.CONCLUSION Parental family upbringing has a mediating effect between parental stress and behavioral and emotional problems of children.Despite paying attention to the behavioral and emotional problems of preschool-age children,clinical medical staff should provide correct and reasonable parenting advice to their parents to promote the mental health of preschool-age children.
文摘This case study explores the efficacy of school-based intervention to address psychosocial challenges faced by an 11-year-old adolescent. The case study aimed to decrease the agression and acting out behavior as result of being victimized at school by the peers. The aim was to assess and manage the child’s aggressive behavior and academic underperformance which played a significant role in the child’s low self-esteem and emotional regulation. A comprehensive assessment was conducted to rule out the difficulties and a multi-faceted intervention strategy was utilized including anger management and structured activity scheduling that helped that child to improve his academic performance as well as to learn to manage his emotional expression. Throughout 16 sessions, the intervention targeted key behavioural indicators such as emotional expression, and aggression;post-assessment results demonstrated a 22% improvement in the child’s behavioral and academic challenges. The findings suggest that a multi-faceted therapeutic approach can be effective in addressing complex issues of aggression and academic underperformance in children, highlighting the importance of integrated psychological and educational interventions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12325406,92261201,12404305,11974272)the Shannxi Province Natural Science Fundamental Research Project(Grant Nos.2023JC-XJ-03 and 23JSQ013)the Fundamental Research Funds for the Central Universities(Grant No.xzy022024040)。
文摘The two-body fragmentation dynamics of water isotopologues dications(H_(2)O^(2+),HOD^(2+),and D_(2)O^(2+))induced by200 eV electron impact is investigated.Two fragment ions and an emitted electron are detected in coincidence,and their momentum vectors are determined by employing a reaction microscope.The complete kinematical information of four two-body fragmentation channels of H^(+)+OH+,H^(+)+OD^(+),D^(+)+OH^(+),and D^(+)+OD+is obtained.By analyzing the projectile energy-loss spectrum,the initial electronic state of the two-body dissociation channel is determined.Upon examining the kinetic energy release(KER)distributions of the four fragmentation channels,a clear difference is found between the two-body fragmentation channel H^(+)+OD+and the other three channels.The isotopic effect in the two-body fragmentation is demonstrated by the analysis of the relative yields of the two-body fragmentation channels originating from different isotopologues,which shows preferential cleavage of the O-H bond over the O-D bond.These results provide deeper insight into the microscopic dynamic mechanisms in water radiolysis.
基金funded by the National Key R&D Program of China(Grant No.2024YFE0102500)the National Natural Science Foundation of China(Grant No.12404568)+1 种基金the Guangzhou Municipal Science and Technology Project(Grant No.2023A03J00904)the Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area,China and the Undergraduate Research Project from HKUST(Guangzhou).
文摘Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.
基金supported by the Tianjin Municipal Science and Technology Program of China(No.23JCZDJC00070)。
文摘This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.
基金supported by the National Natural Science Foundation of China under Grant No.12147115the Discipline(Subject)Leader Cultivation Project of Universities in Anhui Province under Grant Nos.DTR2023052 and DTR2024046+2 种基金the Natural Science Research Project of Universities in Anhui Province under Grant No.2024AH040202the Young Top Notch Talents and Young Scholars of High End Talent Introduction and Cultivation Action Project in Anhui Provincethe Scientific Research Foundation Funded Project of Chuzhou University under Grant Nos.2022qd022 and 2022qd038。
文摘In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.
基金Supported by Special Fund for National Modern Agricultural Industry Technology System Construction(CARS-04-CES16).
文摘As one of the world's three major food crops and an important economic and oil crop,soybean plays a crucial role in ensuring food safety.In recent years,there are many problems in soybean cultivation,production and processing.In view of this situation,this paper comprehensively expounded and decomposed the cultivation situation,existing problems,specific countermeasures and conclusions,so as to re-recognize them.This study provides reference materials for the sustainable and healthy development of the soybean industry.
文摘1.The price of a desk is 10 times the price of a chair.The desk costs 288 yuan more than the chair.How much does one desk and one chair cost?2.A and B start from two different places and walk toward each other.After 4 hours,they meet at a point that is 4 kilometres away from the midpoint between their starting points.A walks faster than B.How many more kilometres per hour does A walk than B?
