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
近日,河北师范大学数学科学学院Alexander A.Ivanov教授以“Geometry of the Thompson Group”为题在代数学领域权威期刊《Journal of Algebra》上发表文章,针对著名数学家Thompson和Smith所关注的单群E构造法进行了改进,通过探究相关...近日,河北师范大学数学科学学院Alexander A.Ivanov教授以“Geometry of the Thompson Group”为题在代数学领域权威期刊《Journal of Algebra》上发表文章,针对著名数学家Thompson和Smith所关注的单群E构造法进行了改进,通过探究相关子群的陪集几何结构,将其几何呈现与Havas-Soicher-Wilson的成果相统一,由此为群E提供了新的几何构造方法及唯一性证明。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
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
This work investigates thermal enhancement in fluid flow over a nonlinear stretching sheet.The thickness of the sheet is variable and the flow of the fluid is affected by solar radiation energy with Thompson and Troia...This work investigates thermal enhancement in fluid flow over a nonlinear stretching sheet.The thickness of the sheet is variable and the flow of the fluid is affected by solar radiation energy with Thompson and Troian slip effects.The flow is magnetized by applying a magnetic field in the normal direction to the flow system.Moreover,thermal transport is controlled by incorporating the Cattaneo-Christov heat fluid model into the flow problem.The governing equations,initially framed in their dimensional form,are meticulously transformed into a dimensionless framework to simplify the analysis.These dimensionless equations are then solved using the homotopy analysis method(HAM).It is observed in this study that upsurges in the stagnation parameter,critical shear rate and velocity slip factor augment the velocity distribution while reducing the thermal profiles.The velocity distribution deteriorates while the thermal profiles are amplified with expansions in the magnetic factor and power law index.The thermal distribution also increases with rising Prandtl number and radiation factor.Augmentation of the power-law index,velocity slip parameter,critical shear rate,magnetic factor and stagnation parameter leads to an increased Nusselt number.The modeled problem is validated by comparing the current results with established work for different values of nonlinear stretching factor n in terms of the drag force and thermal flow rate at η=0,and a good agreement is observed between the current and established results.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
A family of neural networks is proposed to solve linear complementarity problems(LCP).The neural networks are constructed from the novel equivalent model of LCP,which is reformulated by utilizing the modulus and smoot...A family of neural networks is proposed to solve linear complementarity problems(LCP).The neural networks are constructed from the novel equivalent model of LCP,which is reformulated by utilizing the modulus and smoothing technologies.Some important properties of the proposed novel equivalent model are summarized.In addition,the stability properties of the proposed steepest descent-based neural networks for LCP are analyzed.In order to illustrate the theoretical results,we provide some numerical simulations and compare the proposed neural networks with existing neural networks based on the NCP-functions.Numerical results indicate that the performance of the proposed neural networks is effective and robust.展开更多
With the economic and social development of the country,vocational education is playing an increasingly significant role in cultivating highly skilled talents.However,the mechanical drawing courses in vocational colle...With the economic and social development of the country,vocational education is playing an increasingly significant role in cultivating highly skilled talents.However,the mechanical drawing courses in vocational colleges still face numerous challenges in the teaching process,such as outdated textbook content,inadequate practical resources,weak teaching staff,and low student interest.This paper aims to explore these issues and propose corresponding coping strategies.The findings of this study not only provide specific improvement suggestions for vocational colleges but also emphasize the importance of these strategies in enhancing students’comprehensive abilities and promoting the development of vocational education.By addressing these challenges,this paper contributes to the enhancement of teaching quality and the overall advancement of vocational skills education.展开更多
Formalizing complex processes and phenomena of a real-world problem may require a large number of variables and constraints,resulting in what is termed a large-scale optimization problem.Nowadays,such large-scale opti...Formalizing complex processes and phenomena of a real-world problem may require a large number of variables and constraints,resulting in what is termed a large-scale optimization problem.Nowadays,such large-scale optimization problems are solved using computing machines,leading to an enormous computational time being required,which may delay deriving timely solutions.Decomposition methods,which partition a large-scale optimization problem into lower-dimensional subproblems,represent a key approach to addressing time-efficiency issues.There has been significant progress in both applied mathematics and emerging artificial intelligence approaches on this front.This work aims at providing an overview of the decomposition methods from both the mathematics and computer science points of view.We also remark on the state-of-the-art developments and recent applications of the decomposition methods,and discuss the future research and development perspectives.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
This paper systematically reviews the latest research developments in Vehicle Routing Problems(VRP).It examines classical VRP models and their classifications across different dimensions,including load capacity,operat...This paper systematically reviews the latest research developments in Vehicle Routing Problems(VRP).It examines classical VRP models and their classifications across different dimensions,including load capacity,operational characteristics,optimization objectives,vehicle types,and time constraints.Based on literature retrieval results from the Web of Science database,the paper analyzes the current state and trends in VRP research,providing detailed explanations of VRP models and algorithms applied to various scenarios in recent years.Additionally,the article discusses limitations in existing research and provides perspectives on future development trends in VRP research.This review offers researchers in the VRP field a comprehensive overview while identifying future research directions.展开更多
The Traveling Salesman Problem(TSP)is a well-known NP-Hard problem,particularly challenging for conventional solving methods due to the curse of dimensionality in high-dimensional instances.This paper proposes a novel...The Traveling Salesman Problem(TSP)is a well-known NP-Hard problem,particularly challenging for conventional solving methods due to the curse of dimensionality in high-dimensional instances.This paper proposes a novel Double-stage Surrogate-assisted Pigeon-inspired Optimization algorithm(DOSA-PIO)to address this issue.DOSA-PIO integrates the ordering points to identify the clustering structure method for data clustering and employs a local surrogate model to assist the evolution of the Pigeon-inspired Optimization(PIO)algorithm.This combination enhances the algorithm’s ability to explore the solution space and converge to optimal solutions more effectively.Additionally,two novel approaches are introduced to extend the generalizability of continuous algorithms for solving discrete problems,enabling the adaptation of continuous optimization techniques to the discrete nature of TSP.Extensive experiments using benchmark functions and high-dimensional TSP instances demonstrate that DOSA-PIO significantly outperforms comparative algorithms in various dimensions(10D,20D,30D,50D,and 100D).The proposed algorithm provides superior solutions compared to traditional methods,highlighting its potential for solving high-dimensional TSPs.By leveraging advanced data clustering techniques and surrogate-assisted optimization,DOSA-PIO offers an effective solution for high-dimensional TSP instances,with experimental results confirming its superior performance and potential for practical applications in complex optimization problems.展开更多
With the widespread adoption of smartphones,parental phubbing behaviors have become increasingly prevalent,potentially affecting preschool children’s development.Current research primarily focuses on adolescent popul...With the widespread adoption of smartphones,parental phubbing behaviors have become increasingly prevalent,potentially affecting preschool children’s development.Current research primarily focuses on adolescent populations,while the mechanisms through which parental phubbing and authoritarian parenting style influence preschool children’s behavioral problems within the Chinese cultural context remain to be explored.Our investigation seeks to examine the factors contributing to behavioral difficulties among children of preschool age and provide theoretical guidance for prevention.Methods In our research,we utilized a convenience sampling approach to collect data from parents whose children(n=612)were between 3 and 7 years of age.The questionnaire distribution was facilitated via the Wenjuanxing online survey platform.Research instruments included the Parental Phubbing Scale,Parent-Child Relationship Scale,Authoritarian Parenting Style Scale,and Conners Child Behavior Rating Scale.For analytical procedures,we employed SPSS 24.0 to generate descriptive statistics and correlation analysis.Chain mediation effects were examined via Process macro,while significance assessment of the mediating effects relied on the Bootstrap method for constructing 95%confidence intervals.Results A statistically significant positive association was observed between parental phubbing and behavioral problems exhibited by children(r=0.251,p<0.001).Parental phubbing exhibited a significant direct effect on children’s behavioral problems(β=0.088,p<0.001).Analysis of sequential mediation demonstrated that authoritarian parenting style together with parent-child conflict functioned as significant intermediary variables in the relationship between parental phubbing and children’s problem behaviors(β=0.163,p<0.001),with these indirect pathways constituting 64.94%of the total effect.Conclusion Parental phubbing significantly contributes to behavioral problems in preschool children.Parents should monitor their media use,improve their parenting approach,and enhance parent-child relationships to reduce behavioral problems in preschool children.展开更多
In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hil...In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.展开更多
BACKGROUND As the aging process has accelerated,psychological problems in older patients with chronic heart failure(CHF)have become increasingly prominent,significantly affecting their quality of life and prognosis.Th...BACKGROUND As the aging process has accelerated,psychological problems in older patients with chronic heart failure(CHF)have become increasingly prominent,significantly affecting their quality of life and prognosis.This study explored a sports rehabilitation program based on the concept of medical care-family integration to provide patients with comprehensive and effective rehabilitation interventions and improve their health status.AIM To explore the effects of medical care-family integration-based exercise rehabilitation in older patients with CHF and psychological problems.METHODS Data from 118 older patients with CHF and psychological problems were retrospectively analyzed.Patients were divided into conventional(n=56)and exercise rehabilitation groups(n=62).The results of the 6-min walking distance(6 MWD),N-terminal B-type natriuretic peptide(NT-proBNP),left ventricular end-diastolic diameter(LVEDD),left ventricular ejection fraction(LVEF),Minnesota living with heart failure questionnaire(MLHFQ),generalized anxiety disorder-7(GAD-7)scale,9-item patient health questionnaire(PHQ-9)and Athens insomnia scale(AIS)were compared before and after intervention.RESULTS After intervention,there were significant differences in the number of patients with depression and anxiety between the two groups.There was also a significant difference in the distribution of sleep disorders.The PHQ-9 score,GAD-7 score,AIS score,NT-proBNP value,LVEDD value,physical field,emotional field,other fields,and MLHFQ total scores were lower in the exercise rehabilitation group compared to the conventional rehabilitation group,while the 6 MWD and LVEF values were higher compared to the conventional rehabilitation group(P<0.05).During the intervention period,the readmission rate of the exercise rehabilitation group(1.61%)was significantly lower than that of the conventional rehabilitation group(12.50%)(χ^(2)=3.930,P=0.047).CONCLUSION This exercise rehabilitation program with medical care-family integration can improve cardiac function and quality of life,alleviate psychological problems,and reduce readmission rates in older patients with CHF.展开更多
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.
文摘近日,河北师范大学数学科学学院Alexander A.Ivanov教授以“Geometry of the Thompson Group”为题在代数学领域权威期刊《Journal of Algebra》上发表文章,针对著名数学家Thompson和Smith所关注的单群E构造法进行了改进,通过探究相关子群的陪集几何结构,将其几何呈现与Havas-Soicher-Wilson的成果相统一,由此为群E提供了新的几何构造方法及唯一性证明。
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 via funding from Prince Sattam bin Abdulaziz University project number(PSAU/2025/R/1446)。
文摘This work investigates thermal enhancement in fluid flow over a nonlinear stretching sheet.The thickness of the sheet is variable and the flow of the fluid is affected by solar radiation energy with Thompson and Troian slip effects.The flow is magnetized by applying a magnetic field in the normal direction to the flow system.Moreover,thermal transport is controlled by incorporating the Cattaneo-Christov heat fluid model into the flow problem.The governing equations,initially framed in their dimensional form,are meticulously transformed into a dimensionless framework to simplify the analysis.These dimensionless equations are then solved using the homotopy analysis method(HAM).It is observed in this study that upsurges in the stagnation parameter,critical shear rate and velocity slip factor augment the velocity distribution while reducing the thermal profiles.The velocity distribution deteriorates while the thermal profiles are amplified with expansions in the magnetic factor and power law index.The thermal distribution also increases with rising Prandtl number and radiation factor.Augmentation of the power-law index,velocity slip parameter,critical shear rate,magnetic factor and stagnation parameter leads to an increased Nusselt number.The modeled problem is validated by comparing the current results with established work for different values of nonlinear stretching factor n in terms of the drag force and thermal flow rate at η=0,and a good agreement is observed between the current and established results.
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.
基金Supported by the National Natural Science Foundation of China(12371378,41725017,11901098).
文摘A family of neural networks is proposed to solve linear complementarity problems(LCP).The neural networks are constructed from the novel equivalent model of LCP,which is reformulated by utilizing the modulus and smoothing technologies.Some important properties of the proposed novel equivalent model are summarized.In addition,the stability properties of the proposed steepest descent-based neural networks for LCP are analyzed.In order to illustrate the theoretical results,we provide some numerical simulations and compare the proposed neural networks with existing neural networks based on the NCP-functions.Numerical results indicate that the performance of the proposed neural networks is effective and robust.
基金support from the Science and Technology Key Project of Beijing Polytechnic(Project Leader:Jinru Ma,No.2024X008-KXZ).
文摘With the economic and social development of the country,vocational education is playing an increasingly significant role in cultivating highly skilled talents.However,the mechanical drawing courses in vocational colleges still face numerous challenges in the teaching process,such as outdated textbook content,inadequate practical resources,weak teaching staff,and low student interest.This paper aims to explore these issues and propose corresponding coping strategies.The findings of this study not only provide specific improvement suggestions for vocational colleges but also emphasize the importance of these strategies in enhancing students’comprehensive abilities and promoting the development of vocational education.By addressing these challenges,this paper contributes to the enhancement of teaching quality and the overall advancement of vocational skills education.
基金The Australian Research Council(DP200101197,DP230101107).
文摘Formalizing complex processes and phenomena of a real-world problem may require a large number of variables and constraints,resulting in what is termed a large-scale optimization problem.Nowadays,such large-scale optimization problems are solved using computing machines,leading to an enormous computational time being required,which may delay deriving timely solutions.Decomposition methods,which partition a large-scale optimization problem into lower-dimensional subproblems,represent a key approach to addressing time-efficiency issues.There has been significant progress in both applied mathematics and emerging artificial intelligence approaches on this front.This work aims at providing an overview of the decomposition methods from both the mathematics and computer science points of view.We also remark on the state-of-the-art developments and recent applications of the decomposition methods,and discuss the future research and development perspectives.
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.
文摘This paper systematically reviews the latest research developments in Vehicle Routing Problems(VRP).It examines classical VRP models and their classifications across different dimensions,including load capacity,operational characteristics,optimization objectives,vehicle types,and time constraints.Based on literature retrieval results from the Web of Science database,the paper analyzes the current state and trends in VRP research,providing detailed explanations of VRP models and algorithms applied to various scenarios in recent years.Additionally,the article discusses limitations in existing research and provides perspectives on future development trends in VRP research.This review offers researchers in the VRP field a comprehensive overview while identifying future research directions.
基金funded by National Natural Science Foundation of China(Project No.52072314,52172321,52102391)China Shenhua Energy Co.,Ltd.,Science and Technology Program(Project No.GJNY-22-7)+2 种基金China State Railway Group Co.,Ltd.Science and Technology Program(P2022×013,K2023×030)Key science and technology projects in the transportation industry of the Ministry of Transport(2022-ZD7-131)the fundamental research funds for the central universities(2682022ZTPY068).
文摘The Traveling Salesman Problem(TSP)is a well-known NP-Hard problem,particularly challenging for conventional solving methods due to the curse of dimensionality in high-dimensional instances.This paper proposes a novel Double-stage Surrogate-assisted Pigeon-inspired Optimization algorithm(DOSA-PIO)to address this issue.DOSA-PIO integrates the ordering points to identify the clustering structure method for data clustering and employs a local surrogate model to assist the evolution of the Pigeon-inspired Optimization(PIO)algorithm.This combination enhances the algorithm’s ability to explore the solution space and converge to optimal solutions more effectively.Additionally,two novel approaches are introduced to extend the generalizability of continuous algorithms for solving discrete problems,enabling the adaptation of continuous optimization techniques to the discrete nature of TSP.Extensive experiments using benchmark functions and high-dimensional TSP instances demonstrate that DOSA-PIO significantly outperforms comparative algorithms in various dimensions(10D,20D,30D,50D,and 100D).The proposed algorithm provides superior solutions compared to traditional methods,highlighting its potential for solving high-dimensional TSPs.By leveraging advanced data clustering techniques and surrogate-assisted optimization,DOSA-PIO offers an effective solution for high-dimensional TSP instances,with experimental results confirming its superior performance and potential for practical applications in complex optimization problems.
文摘With the widespread adoption of smartphones,parental phubbing behaviors have become increasingly prevalent,potentially affecting preschool children’s development.Current research primarily focuses on adolescent populations,while the mechanisms through which parental phubbing and authoritarian parenting style influence preschool children’s behavioral problems within the Chinese cultural context remain to be explored.Our investigation seeks to examine the factors contributing to behavioral difficulties among children of preschool age and provide theoretical guidance for prevention.Methods In our research,we utilized a convenience sampling approach to collect data from parents whose children(n=612)were between 3 and 7 years of age.The questionnaire distribution was facilitated via the Wenjuanxing online survey platform.Research instruments included the Parental Phubbing Scale,Parent-Child Relationship Scale,Authoritarian Parenting Style Scale,and Conners Child Behavior Rating Scale.For analytical procedures,we employed SPSS 24.0 to generate descriptive statistics and correlation analysis.Chain mediation effects were examined via Process macro,while significance assessment of the mediating effects relied on the Bootstrap method for constructing 95%confidence intervals.Results A statistically significant positive association was observed between parental phubbing and behavioral problems exhibited by children(r=0.251,p<0.001).Parental phubbing exhibited a significant direct effect on children’s behavioral problems(β=0.088,p<0.001).Analysis of sequential mediation demonstrated that authoritarian parenting style together with parent-child conflict functioned as significant intermediary variables in the relationship between parental phubbing and children’s problem behaviors(β=0.163,p<0.001),with these indirect pathways constituting 64.94%of the total effect.Conclusion Parental phubbing significantly contributes to behavioral problems in preschool children.Parents should monitor their media use,improve their parenting approach,and enhance parent-child relationships to reduce behavioral problems in preschool children.
基金supported by the National Natural Science Foundation of China(No.12461086)the Natural Science Foundation of Hubei Province(No.2022CFC016)。
文摘In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.
文摘BACKGROUND As the aging process has accelerated,psychological problems in older patients with chronic heart failure(CHF)have become increasingly prominent,significantly affecting their quality of life and prognosis.This study explored a sports rehabilitation program based on the concept of medical care-family integration to provide patients with comprehensive and effective rehabilitation interventions and improve their health status.AIM To explore the effects of medical care-family integration-based exercise rehabilitation in older patients with CHF and psychological problems.METHODS Data from 118 older patients with CHF and psychological problems were retrospectively analyzed.Patients were divided into conventional(n=56)and exercise rehabilitation groups(n=62).The results of the 6-min walking distance(6 MWD),N-terminal B-type natriuretic peptide(NT-proBNP),left ventricular end-diastolic diameter(LVEDD),left ventricular ejection fraction(LVEF),Minnesota living with heart failure questionnaire(MLHFQ),generalized anxiety disorder-7(GAD-7)scale,9-item patient health questionnaire(PHQ-9)and Athens insomnia scale(AIS)were compared before and after intervention.RESULTS After intervention,there were significant differences in the number of patients with depression and anxiety between the two groups.There was also a significant difference in the distribution of sleep disorders.The PHQ-9 score,GAD-7 score,AIS score,NT-proBNP value,LVEDD value,physical field,emotional field,other fields,and MLHFQ total scores were lower in the exercise rehabilitation group compared to the conventional rehabilitation group,while the 6 MWD and LVEF values were higher compared to the conventional rehabilitation group(P<0.05).During the intervention period,the readmission rate of the exercise rehabilitation group(1.61%)was significantly lower than that of the conventional rehabilitation group(12.50%)(χ^(2)=3.930,P=0.047).CONCLUSION This exercise rehabilitation program with medical care-family integration can improve cardiac function and quality of life,alleviate psychological problems,and reduce readmission rates in older patients with CHF.
