Brazil’s deforestation monitoring integrates accuracy and current monitoring for land use and land cover applications.Regular monitoring of deforestation and non-deforestation requires Sentinel-2 multispectral satell...Brazil’s deforestation monitoring integrates accuracy and current monitoring for land use and land cover applications.Regular monitoring of deforestation and non-deforestation requires Sentinel-2 multispectral satellite images of several bands at various frequencies,the mix of high-and low-resolution images that make object classification difficult because of the mixed pixel problem.Accuracy is impacted by the mixed pixel problem,which occurs when pixels belong to different classes and makes detection challenging.To identify mixed pixels,Band Math is used to merge numerous bands to generate a new band NDVI.Thresholding is used to analyze the edges of deforested and non-deforested areas.Segmentation is then used to analyze the pixels which helps to identify the number of mixed pixels to compute the deforested and non-deforested areas.Segmented image pixels are used to categorize the deforestation of the Brazilian Amazon Forest between 2019 and 2023.Verify how many pixels are mixed to improve accuracy and identify mixed pixel issues;compare the mixed and pure pixels of fuzzy clustering with the subtracted morphological image pixels.With the help of segmentation and clustering researchers effectively validate mixed pixels in a specific area.The proposed methodology is easy to analyze and helpful for an appropriate calculation of deforested and non-deforested areas.展开更多
In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms...In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms to solve the problem of multi-UAV path planning.The Dung Beetle Optimization(DBO)algorithm has been widely applied due to its diverse search patterns in the above algorithms.However,the update strategies for the rolling and thieving dung beetles of the DBO algorithm are overly simplistic,potentially leading to an inability to fully explore the search space and a tendency to converge to local optima,thereby not guaranteeing the discovery of the optimal path.To address these issues,we propose an improved DBO algorithm guided by the Landmark Operator(LODBO).Specifically,we first use tent mapping to update the population strategy,which enables the algorithm to generate initial solutions with enhanced diversity within the search space.Second,we expand the search range of the rolling ball dung beetle by using the landmark factor.Finally,by using the adaptive factor that changes with the number of iterations.,we improve the global search ability of the stealing dung beetle,making it more likely to escape from local optima.To verify the effectiveness of the proposed method,extensive simulation experiments are conducted,and the result shows that the LODBO algorithm can obtain the optimal path using the shortest time compared with the Genetic Algorithm(GA),the Gray Wolf Optimizer(GWO),the Whale Optimization Algorithm(WOA)and the original DBO algorithm in the disaster search and rescue task set.展开更多
Safe and efficient sortie scheduling on the confined flight deck is crucial for maintaining high combat effectiveness of the aircraft carrier.The primary difficulty exactly lies in the spatiotemporal coordination,i.e....Safe and efficient sortie scheduling on the confined flight deck is crucial for maintaining high combat effectiveness of the aircraft carrier.The primary difficulty exactly lies in the spatiotemporal coordination,i.e.,allocation of limited supporting resources and collision-avoidance between heterogeneous dispatch entities.In this paper,the problem is investigated in the perspective of hybrid flow-shop scheduling problem by synthesizing the precedence,space and resource constraints.Specifically,eight processing procedures are abstracted,where tractors,preparing spots,catapults,and launching are virtualized as machines.By analyzing the constraints in sortie scheduling,a mixed-integer planning model is constructed.In particular,the constraint on preparing spot occupancy is improved to further enhance the sortie efficiency.The basic trajectory library for each dispatch entity is generated and a delayed strategy is integrated to address the collision-avoidance issue.To efficiently solve the formulated HFSP,which is essentially a combinatorial problem with tightly coupled constraints,a chaos-initialized genetic algorithm is developed.The solution framework is validated by the simulation environment referring to the Fort-class carrier,exhibiting higher sortie efficiency when compared to existing strategies.And animation of the simulation results is available at www.bilibili.com/video/BV14t421A7Tt/.The study presents a promising supporting technique for autonomous flight deck operation in the foreseeable future,and can be easily extended to other supporting scenarios,e.g.,ammunition delivery and aircraft maintenance.展开更多
Solar energy, as a renewable resource, is an effective solution to the current global energy shortage problem. To actively respond to the call for "carbon peak" and "carbon neutrality", solar cell ...Solar energy, as a renewable resource, is an effective solution to the current global energy shortage problem. To actively respond to the call for "carbon peak" and "carbon neutrality", solar cell industry has experienced unprecedented development. The full utilization of solar energy resources remains an urgent issue to be addressed.展开更多
Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate...Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.展开更多
Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectiv...Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the system.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
Control signaling is mandatory for the operation and management of all types of communication networks,including the Third Generation Partnership Project(3GPP)mobile broadband networks.However,they consume important a...Control signaling is mandatory for the operation and management of all types of communication networks,including the Third Generation Partnership Project(3GPP)mobile broadband networks.However,they consume important and scarce network resources such as bandwidth and processing power.There have been several reports of these control signaling turning into signaling storms halting network operations and causing the respective Telecom companies big financial losses.This paper draws its motivation from such real network disaster incidents attributed to signaling storms.In this paper,we present a thorough survey of the causes,of the signaling storm problems in 3GPP-based mobile broadband networks and discuss in detail their possible solutions and countermeasures.We provide relevant analytical models to help quantify the effect of the potential causes and benefits of their corresponding solutions.Another important contribution of this paper is the comparison of the possible causes and solutions/countermeasures,concerning their effect on several important network aspects such as architecture,additional signaling,fidelity,etc.,in the form of a table.This paper presents an update and an extension of our earlier conference publication.To our knowledge,no similar survey study exists on the subject.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
We study the two-dimensional(2D)Cauchy problem of nonhomogeneous Boussinesq system for magnetohydrodynamics convection without heat diffusion in the whole plane.Based on delicate weighted estimates,we derive the globa...We study the two-dimensional(2D)Cauchy problem of nonhomogeneous Boussinesq system for magnetohydrodynamics convection without heat diffusion in the whole plane.Based on delicate weighted estimates,we derive the global existence and uniqueness of strong solutions.In particular,the initial data can be arbitrarily large and the initial density may contain vacuum states and even have compact support.展开更多
In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise c...In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.展开更多
In maths,some calculations are just as hard as word problems.Actually,they are word problems.Strategies of solving problems must be applied,while you are doing such calculations.Now,let's discuss a few questions a...In maths,some calculations are just as hard as word problems.Actually,they are word problems.Strategies of solving problems must be applied,while you are doing such calculations.Now,let's discuss a few questions as examples.展开更多
This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the ty...This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness.展开更多
“Integration is a hallmark of our era's development and a magic key to solve epochal problems.”“Medicine originated from humanity's initial expression of suffering and the primary desire to alleviate that s...“Integration is a hallmark of our era's development and a magic key to solve epochal problems.”“Medicine originated from humanity's initial expression of suffering and the primary desire to alleviate that suffering.”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 study provides a comprehensive summary of the current development status of the potato industry in Liangshan Prefecture,and analyzes the primary factors that hinder the advancement of this industry,including a lo...This study provides a comprehensive summary of the current development status of the potato industry in Liangshan Prefecture,and analyzes the primary factors that hinder the advancement of this industry,including a low degree of scale,a limited popularization rate of high-quality seeds,insufficient mechanization,a low level of commercialization,inadequate technological support,minimal integration between the secondary and tertiary industries,and an ineffective mechanism for connecting and benefiting farmers.Furthermore,it presents a problem-oriented approach that is grounded in the current climatic,resource,water,and soil conditions of Liangshan Prefecture,and proposes several pathways to promote the high-quality development of the potato industry.The strategies include:expanding coverage and increasing production volume as foundational steps to ensure food security;enhancing quality and efficiency as key drivers to stimulate agricultural advancement through scientific and technological innovation;focusing on the integration of the three industries to achieve industrial revitalization;implementing risk management measures as a preventive strategy to ensure industrial stability;establishing incentive policies to foster production enthusiasm;and ultimately assisting farmers in increasing their income to achieve the overarching goal of improving the livelihoods of the population.展开更多
文摘Brazil’s deforestation monitoring integrates accuracy and current monitoring for land use and land cover applications.Regular monitoring of deforestation and non-deforestation requires Sentinel-2 multispectral satellite images of several bands at various frequencies,the mix of high-and low-resolution images that make object classification difficult because of the mixed pixel problem.Accuracy is impacted by the mixed pixel problem,which occurs when pixels belong to different classes and makes detection challenging.To identify mixed pixels,Band Math is used to merge numerous bands to generate a new band NDVI.Thresholding is used to analyze the edges of deforested and non-deforested areas.Segmentation is then used to analyze the pixels which helps to identify the number of mixed pixels to compute the deforested and non-deforested areas.Segmented image pixels are used to categorize the deforestation of the Brazilian Amazon Forest between 2019 and 2023.Verify how many pixels are mixed to improve accuracy and identify mixed pixel issues;compare the mixed and pure pixels of fuzzy clustering with the subtracted morphological image pixels.With the help of segmentation and clustering researchers effectively validate mixed pixels in a specific area.The proposed methodology is easy to analyze and helpful for an appropriate calculation of deforested and non-deforested areas.
基金supported by the National Natural Science Foundation of China(No.62373027).
文摘In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms to solve the problem of multi-UAV path planning.The Dung Beetle Optimization(DBO)algorithm has been widely applied due to its diverse search patterns in the above algorithms.However,the update strategies for the rolling and thieving dung beetles of the DBO algorithm are overly simplistic,potentially leading to an inability to fully explore the search space and a tendency to converge to local optima,thereby not guaranteeing the discovery of the optimal path.To address these issues,we propose an improved DBO algorithm guided by the Landmark Operator(LODBO).Specifically,we first use tent mapping to update the population strategy,which enables the algorithm to generate initial solutions with enhanced diversity within the search space.Second,we expand the search range of the rolling ball dung beetle by using the landmark factor.Finally,by using the adaptive factor that changes with the number of iterations.,we improve the global search ability of the stealing dung beetle,making it more likely to escape from local optima.To verify the effectiveness of the proposed method,extensive simulation experiments are conducted,and the result shows that the LODBO algorithm can obtain the optimal path using the shortest time compared with the Genetic Algorithm(GA),the Gray Wolf Optimizer(GWO),the Whale Optimization Algorithm(WOA)and the original DBO algorithm in the disaster search and rescue task set.
基金the financial support of the National Key Research and Development Plan(2021YFB3302501)the financial support of the National Natural Science Foundation of China(12102077)。
文摘Safe and efficient sortie scheduling on the confined flight deck is crucial for maintaining high combat effectiveness of the aircraft carrier.The primary difficulty exactly lies in the spatiotemporal coordination,i.e.,allocation of limited supporting resources and collision-avoidance between heterogeneous dispatch entities.In this paper,the problem is investigated in the perspective of hybrid flow-shop scheduling problem by synthesizing the precedence,space and resource constraints.Specifically,eight processing procedures are abstracted,where tractors,preparing spots,catapults,and launching are virtualized as machines.By analyzing the constraints in sortie scheduling,a mixed-integer planning model is constructed.In particular,the constraint on preparing spot occupancy is improved to further enhance the sortie efficiency.The basic trajectory library for each dispatch entity is generated and a delayed strategy is integrated to address the collision-avoidance issue.To efficiently solve the formulated HFSP,which is essentially a combinatorial problem with tightly coupled constraints,a chaos-initialized genetic algorithm is developed.The solution framework is validated by the simulation environment referring to the Fort-class carrier,exhibiting higher sortie efficiency when compared to existing strategies.And animation of the simulation results is available at www.bilibili.com/video/BV14t421A7Tt/.The study presents a promising supporting technique for autonomous flight deck operation in the foreseeable future,and can be easily extended to other supporting scenarios,e.g.,ammunition delivery and aircraft maintenance.
文摘Solar energy, as a renewable resource, is an effective solution to the current global energy shortage problem. To actively respond to the call for "carbon peak" and "carbon neutrality", solar cell industry has experienced unprecedented development. The full utilization of solar energy resources remains an urgent issue to be addressed.
基金supported in part by the National Natural Science Foundation of China(62173051)the Fundamental Research Funds for the Central Universities(2024CDJCGJ012,2023CDJXY-010)+1 种基金the Chongqing Technology Innovation and Application Development Special Key Project(CSTB2022TIADCUX0015,CSTB2022TIAD-KPX0162)the China Postdoctoral Science Foundation(2024M763865)
文摘Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.
基金supported in part by the National Natural Science Foundation of China(62173255,62188101)Shenzhen Key Laboratory of Control Theory and Intelligent Systems(ZDSYS20220330161800001)
文摘Dear Editor,In this letter,a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated(HOFA)systems with noises.The method can effectively deal with nonlinearities,constraints,and noises in the system,optimize the performance metric,and present an upper bound on the stable output of the system.
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.
基金the Deanship of Graduate Studies and Scientific Research at Qassim University for financial support(QU-APC-2024-9/1).
文摘Control signaling is mandatory for the operation and management of all types of communication networks,including the Third Generation Partnership Project(3GPP)mobile broadband networks.However,they consume important and scarce network resources such as bandwidth and processing power.There have been several reports of these control signaling turning into signaling storms halting network operations and causing the respective Telecom companies big financial losses.This paper draws its motivation from such real network disaster incidents attributed to signaling storms.In this paper,we present a thorough survey of the causes,of the signaling storm problems in 3GPP-based mobile broadband networks and discuss in detail their possible solutions and countermeasures.We provide relevant analytical models to help quantify the effect of the potential causes and benefits of their corresponding solutions.Another important contribution of this paper is the comparison of the possible causes and solutions/countermeasures,concerning their effect on several important network aspects such as architecture,additional signaling,fidelity,etc.,in the form of a table.This paper presents an update and an extension of our earlier conference publication.To our knowledge,no similar survey study exists on the subject.
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We study the two-dimensional(2D)Cauchy problem of nonhomogeneous Boussinesq system for magnetohydrodynamics convection without heat diffusion in the whole plane.Based on delicate weighted estimates,we derive the global existence and uniqueness of strong solutions.In particular,the initial data can be arbitrarily large and the initial density may contain vacuum states and even have compact support.
文摘In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.
文摘In maths,some calculations are just as hard as word problems.Actually,they are word problems.Strategies of solving problems must be applied,while you are doing such calculations.Now,let's discuss a few questions as examples.
基金co-supported by the National Natural Science Foundation of China(No.62003019)the Young Talents Support Program of Beihang University,China(No.YWF21-BJ-J-1180)。
文摘This paper addresses the Singular Optimal Control Problem(SOCP)for a surface-to-air missile with limited control,fully considering aerodynamic effects with a parabolic drag polar.This problem is an extension of the typical Goddard problem.First,the classical Legendre-Clebsch condition is applied to derive optimal conditions for the singular angle of attack,revealing that the missile turns by gravity along the singular arc.Second,the higher-order differentiation of the switching function provides the necessary conditions to determine the optimal thrust,expressed as linear functions of the costate variables.The vanishing coefficient determinant is then employed to decouple the control and costate variables,yielding the singular thrust solely dependent on state variables and identifying the singular surface.Moreover,the analytical singular control can be regarded as path constraints subject to the typical Optimal Control Problem(OCP),enabling the GPOPS-Ⅱ,a direct method framework that does not involve the singular condition,to solve the SOCP.Finally,three cases with different structures are presented to evaluate the performance of the proposed method.The results show that it takes a few steps to obtain the numerical optimal solution,which is consistent with the analytical solution derived from the calculus of variations,highlighting its great computational accuracy and effectiveness.
基金released in Chengdu on June 22,2024,jointly signed and advocated by over 100 academicians from Chinese Academy of Sciences and Chinese Academy of Engineering,and more than 100 presidents from medical universities across China.
文摘“Integration is a hallmark of our era's development and a magic key to solve epochal problems.”“Medicine originated from humanity's initial expression of suffering and the primary desire to alleviate that suffering.”
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 the Construction of China Agricultural Industry Research System(CARS-09-ES22).
文摘This study provides a comprehensive summary of the current development status of the potato industry in Liangshan Prefecture,and analyzes the primary factors that hinder the advancement of this industry,including a low degree of scale,a limited popularization rate of high-quality seeds,insufficient mechanization,a low level of commercialization,inadequate technological support,minimal integration between the secondary and tertiary industries,and an ineffective mechanism for connecting and benefiting farmers.Furthermore,it presents a problem-oriented approach that is grounded in the current climatic,resource,water,and soil conditions of Liangshan Prefecture,and proposes several pathways to promote the high-quality development of the potato industry.The strategies include:expanding coverage and increasing production volume as foundational steps to ensure food security;enhancing quality and efficiency as key drivers to stimulate agricultural advancement through scientific and technological innovation;focusing on the integration of the three industries to achieve industrial revitalization;implementing risk management measures as a preventive strategy to ensure industrial stability;establishing incentive policies to foster production enthusiasm;and ultimately assisting farmers in increasing their income to achieve the overarching goal of improving the livelihoods of the population.
