In this paper, the multiple stochastic integral with respect to a Wiener D'-process is defined. And also it is shown that for a D'-valued nonlinear random functional there exists a sequence of multiple integra...In this paper, the multiple stochastic integral with respect to a Wiener D'-process is defined. And also it is shown that for a D'-valued nonlinear random functional there exists a sequence of multiple integral kernels such that the nonlinear functional can be expanded by series of multiple Wiener integrals of the integral kernels with respect to the Wiener D'-process.展开更多
In this paper,a kind of boundary value problems for Volterra functional differential equation is studied.\$\$εx″(t)=f(t,x(t),\(t),x(t-τ),x′(t),ε),t∈(0,1), x(t)=φ(t,ε),t∈[-τ,0], ax(1)+bx′(1)=A(ε).\$\$\ \ B...In this paper,a kind of boundary value problems for Volterra functional differential equation is studied.\$\$εx″(t)=f(t,x(t),\(t),x(t-τ),x′(t),ε),t∈(0,1), x(t)=φ(t,ε),t∈[-τ,0], ax(1)+bx′(1)=A(ε).\$\$\ \ By using the theory of differential inequality,the author proves the existence of the solutions and a uniformly valid asymptotic expansion of the solution is given as well.展开更多
Policy evaluation(PE)is a critical sub-problem in reinforcement learning,which estimates the value function for a given policy and can be used for policy improvement.However,there still exist some limitations in curre...Policy evaluation(PE)is a critical sub-problem in reinforcement learning,which estimates the value function for a given policy and can be used for policy improvement.However,there still exist some limitations in current PE methods,such as low sample efficiency and local convergence,especially on complex tasks.In this study,a novel PE algorithm called Least-Squares Truncated Temporal-Difference learning(LST2D)is proposed.In LST2D,an adaptive truncation mechanism is designed,which effectively takes advantage of the fast convergence property of Least-Squares Temporal Difference learning and the asymptotic convergence property of Temporal Difference learning(TD).Then,two feature pre-training methods are utilised to improve the approximation ability of LST2D.Furthermore,an Actor-Critic algorithm based on LST2D and pre-trained feature representations(ACLPF)is proposed,where LST2D is integrated into the critic network to improve learning-prediction efficiency.Comprehensive simulation studies were conducted on four robotic tasks,and the corresponding results illustrate the effectiveness of LST2D.The proposed ACLPF algorithm outperformed DQN,ACER and PPO in terms of sample efficiency and stability,which demonstrated that LST2D can be applied to online learning control problems by incorporating it into the actor-critic architecture.展开更多
By examining the current status of tourism and transport research both domestically and internationally,and analyzing the development trends of Chongqing’s tourism and transport industry,this study evaluates the weig...By examining the current status of tourism and transport research both domestically and internationally,and analyzing the development trends of Chongqing’s tourism and transport industry,this study evaluates the weight indices and performs a coupling and coordination analysis of various indicators of Chongqing’s tourism and transport industry from 2011 to 2019.The following conclusions are drawn:(1)The value of the comprehensive evaluation function for tourism is higher than that of the transport industry,indicating that Chongqing’s tourism industry is in a period of vigorous development;(2)The degree of coupling coordination development between Chongqing’s tourism and transportation industries from 2011 to 2019 is rising.As the coupling coordination stage continues to improve,the level of coupling coordination also improves,with the overall trend showing a progression from mild dysfunction to primary coordination.Based on these conclusions,corresponding countermeasures are proposed to promote the coupling coordination between tourism and transport in Chongqing,and suggestions are made for the overall improvement of the transport industry and the sustainable development of the tourism industry.展开更多
The author proves that if f : C → C^n is a transcendental vector valued mero-morphic function of finite order and assume, This result extends the related results for meromorphic function by Singh and Kulkarni.
Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ <em>x</em>)</span>, has been resolved and extended to complex valued functio...Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ <em>x</em>)</span>, has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function <span style="white-space:nowrap;">1/(1+ e<sup><em>x</em> </sup>)</span> . Grandi-type complex valued functions such as <span style="white-space:nowrap;">1/(<em>i</em> + <em>x</em>)</span> are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function <img src="Edit_f4efd7cd-6853-4ca4-b4dc-00f0b798c277.png" width="80" height="24" alt="" /> is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.展开更多
[ Objective] The study aimed to quantitatively assess the values of water ecosystem services. [ Method] Combining the market value, travel cost and restoration cost method, the ecological services and their economic v...[ Objective] The study aimed to quantitatively assess the values of water ecosystem services. [ Method] Combining the market value, travel cost and restoration cost method, the ecological services and their economic values of the lake Taodangmian were assessed from aspects of water supply, recreation and tourism, water purification and biodiversity maintenance. [ Resultl For the lake Taodangmian, its freshwater supply and tourism played more positive roles in the society than the others, while the functions of water purification and biodiversity maintenance brought negative effects, which shows that the ecological environment of Taodangmian has become increasingly worse and needs to be controlled and and protected further. [ Conclusion] The research could provide scientific references for the reasonable exploitation and utilization of water resources.展开更多
When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Li...When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained.展开更多
To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-...To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.展开更多
We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, wher...We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.展开更多
The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of ...The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem.Also,we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems.After that,we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem.Next,we have shown that both the saddle point conditions(Fritz-John and Kuhn-Tucker)are sufficient without any convexity requirements.Then with the convexity requirements,we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints.Here,all the results are derived with the help of interval order relations.Finally,we illustrate all the results with the help of a numerical example.展开更多
A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some f...A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some families of simultaneous best approximation problems.展开更多
In this paper, we investigate uniqueness problems of differential polynomials of meromorphic functions. Let a, b be non-zero constants and let n, k be positive integers satisfying n ≥ 3k + 12. If f^n+ af^(k)and ...In this paper, we investigate uniqueness problems of differential polynomials of meromorphic functions. Let a, b be non-zero constants and let n, k be positive integers satisfying n ≥ 3k + 12. If f^n+ af^(k)and g^n+ ag^(k)share b CM and the b-points of f^n+ af^(k)are not the zeros of f and g, then f and g are either equal or closely related.展开更多
[Objective]Returning farmland to forest and mountain enclosure for grazing prohibition ecological effect and economy rationality were explored.[Methods]A case study of returning farmland to forest and barren hills gra...[Objective]Returning farmland to forest and mountain enclosure for grazing prohibition ecological effect and economy rationality were explored.[Methods]A case study of returning farmland to forest and barren hills grazing prohibition in Yongxing Township of Jingyuan County was used to discuss and estimate the relative ecological function and relative ecological value.[Results]1)The ecological value of the forest of returning farmland was far more than the sum of the ecological value of farm crops and the agricultural output,and also more than the national subsidy standard.So the state policy of returning farmland to forests is not only favorable to local eco-environment restoration,but also reasonable in economic development.2)The ecological value of mountain enclosure for grazing prohibition was less than the opportunity cost of prohibiting grazing,also less than the national subsidy standard.The sum of the relative ecological value of prohibiting grazing and the state subsidies was more than the opportunity cost of prohibiting grazing.However,the ecological value of new vegetation through returning farmland to forest project was greater than the China's average ecological value of grassland.[Conclusion]The relative ecological value can be used to solve the problems in the equivalent conversion among various ecological indexes and between ecological indexes and economic indexes.展开更多
This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t&l...This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t<0), u (j) (0)=u(1)=0,(1≤j≤n-2).Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.An example to illustrate the application of this theorem is given. [FQ(6*2。39,X-W]展开更多
The kinetic theory is employed to analyze influence of agent competence and psychological factors on investment decision-making.We assume that the wealth held by agents in the financial market is non-negative,and agen...The kinetic theory is employed to analyze influence of agent competence and psychological factors on investment decision-making.We assume that the wealth held by agents in the financial market is non-negative,and agents set their own investment strategies.The herding behavior is considered when analyzing the impact of an agent's psychological factors on investment decision-making.A nonlinear Boltzmann model containing herding behavior,agent competence and irrational behavior is employed to investigate investment decision-making.To characterize the agent's irrational behavior,we utilize a value function which includes current and ideal-investment decisions to describe the agent's irrational behavior.Employing the asymptotic procedure,we obtain the Fokker-Planck equation from the Boltzmann equation.Numerical results and the stationary solution of the obtained Fokker-Planck equation illustrate how herding behavior,agent competence,psychological factors,and irrational behavior affect investment decision-making,i.e.,herding behavior has both advantages and disadvantages for investment decision-making,and the agent's competence to invest helps the agent to increase income and to reduce loss.展开更多
This study focuses on investigating the optimal investment strategy for an optimization problem with delay using the uncertainty theory. The financial market is composed of a risk-free asset and a risk asset with an u...This study focuses on investigating the optimal investment strategy for an optimization problem with delay using the uncertainty theory. The financial market is composed of a risk-free asset and a risk asset with an uncertain price process described by an uncertain differential equation. An optimization problem is assumed that its objective is a nonlinear function of decision variable. By deriving the equation of optimality, an analytical solution is obtained for the optimal delay investment strategy, and the optimal delay value function. Finally, an economic analysis and numerical sensitivity analysis are conducted to evaluate the research results.展开更多
In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Su...In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.展开更多
Background:Salt stress significantly inhibits the growth,development,and productivity of cotton because of osmotic,ionic,and oxidative stresses.Therefore,the screening and development of salt tolerant cotton cultivars...Background:Salt stress significantly inhibits the growth,development,and productivity of cotton because of osmotic,ionic,and oxidative stresses.Therefore,the screening and development of salt tolerant cotton cultivars is a key issue towards sustainable agriculture.This study subjected 11 upland cotton genotypes at the seedling growth stage to five different salt concentrations and evaluated their salt tolerance and reliable traits.Results:Several morpho-physiological traits were measured after 10 days of salinity treatment and the salt tolerance performance varied significantly among the tested cotton genotypes.The optimal Na Cl concentration for the evaluation of salt tolerance was 200 mmol·L-1.Membership function value and salt tolerance index were used to identify the most consistent salt tolerance traits.Leaf relative water content and photosynthesis were identified as reliable indicators for salt tolerance at the seedling stage.All considered traits related to salt tolerance indices were significantly and positively correlated with each other except for malondialdehyde.Cluster heat map analysis based on the morpho-physiological salt tolerance-indices clearly discriminated the 11 cotton genotypes into three different salt tolerance clusters.Cluster I represented the salt-tolerant genotypes(Z9807,Z0228,and Z7526)whereas clusters II(Z0710,Z7514,Z1910,and Z7516)and III(Z0102,Z7780,Z9648,and Z9612)represented moderately salttolerant and salt-sensitive genotypes,respectively.Conclusions:A hydroponic screening system was established.Leaf relative water content and photosynthesis were identified as two reliable traits that adequately represented the salt tolerance of cotton genotypes at the seedling growth stage.Furthermore,three salt-tolerant genotypes were identified,which might be used as genetic resources for the salt-tolerance breeding of cotton.展开更多
As the differences of sensor's precision and some random factors are difficult to control,the actual measurement signals are far from the target signals that affect the reliability and precision of rotating machinery...As the differences of sensor's precision and some random factors are difficult to control,the actual measurement signals are far from the target signals that affect the reliability and precision of rotating machinery fault diagnosis.The traditional signal processing methods,such as classical inference and weighted averaging algorithm usually lack dynamic adaptability that is easy for trends to cause the faults to be misjudged or left out.To enhance the measuring veracity and precision of vibration signal in rotary machine multi-sensor vibration signal fault diagnosis,a novel data level fusion approach is presented on the basis of correlation function analysis to fast determine the weighted value of multi-sensor vibration signals.The approach doesn't require knowing the prior information about sensors,and the weighted value of sensors can be confirmed depending on the correlation measure of real-time data tested in the data level fusion process.It gives greater weighted value to the greater correlation measure of sensor signals,and vice versa.The approach can effectively suppress large errors and even can still fuse data in the case of sensor failures because it takes full advantage of sensor's own-information to determine the weighted value.Moreover,it has good performance of anti-jamming due to the correlation measures between noise and effective signals are usually small.Through the simulation of typical signal collected from multi-sensors,the comparative analysis of dynamic adaptability and fault tolerance between the proposed approach and traditional weighted averaging approach is taken.Finally,the rotor dynamics and integrated fault simulator is taken as an example to verify the feasibility and advantages of the proposed approach,it is shown that the multi-sensor data level fusion based on correlation function weighted approach is better than the traditional weighted average approach with respect to fusion precision and dynamic adaptability.Meantime,the approach is adaptable and easy to use,can be applied to other areas of vibration measurement.展开更多
文摘In this paper, the multiple stochastic integral with respect to a Wiener D'-process is defined. And also it is shown that for a D'-valued nonlinear random functional there exists a sequence of multiple integral kernels such that the nonlinear functional can be expanded by series of multiple Wiener integrals of the integral kernels with respect to the Wiener D'-process.
基金The project is supported by Nature Science Foundation of Anhui Province Education Commission!( 98JL 1 2 9)
文摘In this paper,a kind of boundary value problems for Volterra functional differential equation is studied.\$\$εx″(t)=f(t,x(t),\(t),x(t-τ),x′(t),ε),t∈(0,1), x(t)=φ(t,ε),t∈[-τ,0], ax(1)+bx′(1)=A(ε).\$\$\ \ By using the theory of differential inequality,the author proves the existence of the solutions and a uniformly valid asymptotic expansion of the solution is given as well.
基金Joint Funds of the National Natural Science Foundation of China,Grant/Award Number:U21A20518National Natural Science Foundation of China,Grant/Award Numbers:62106279,61903372。
文摘Policy evaluation(PE)is a critical sub-problem in reinforcement learning,which estimates the value function for a given policy and can be used for policy improvement.However,there still exist some limitations in current PE methods,such as low sample efficiency and local convergence,especially on complex tasks.In this study,a novel PE algorithm called Least-Squares Truncated Temporal-Difference learning(LST2D)is proposed.In LST2D,an adaptive truncation mechanism is designed,which effectively takes advantage of the fast convergence property of Least-Squares Temporal Difference learning and the asymptotic convergence property of Temporal Difference learning(TD).Then,two feature pre-training methods are utilised to improve the approximation ability of LST2D.Furthermore,an Actor-Critic algorithm based on LST2D and pre-trained feature representations(ACLPF)is proposed,where LST2D is integrated into the critic network to improve learning-prediction efficiency.Comprehensive simulation studies were conducted on four robotic tasks,and the corresponding results illustrate the effectiveness of LST2D.The proposed ACLPF algorithm outperformed DQN,ACER and PPO in terms of sample efficiency and stability,which demonstrated that LST2D can be applied to online learning control problems by incorporating it into the actor-critic architecture.
基金Chongqing University of Science and Technology 2023 Postgraduate Innovation Project“Intelligent Tourism Based on Genetic Algorithm in the Era of Self-Driving Destination Route Planning Research in Self-driving Era:Taking Chongqing as an Example”(Project No.YKJCX2320901)。
文摘By examining the current status of tourism and transport research both domestically and internationally,and analyzing the development trends of Chongqing’s tourism and transport industry,this study evaluates the weight indices and performs a coupling and coordination analysis of various indicators of Chongqing’s tourism and transport industry from 2011 to 2019.The following conclusions are drawn:(1)The value of the comprehensive evaluation function for tourism is higher than that of the transport industry,indicating that Chongqing’s tourism industry is in a period of vigorous development;(2)The degree of coupling coordination development between Chongqing’s tourism and transportation industries from 2011 to 2019 is rising.As the coupling coordination stage continues to improve,the level of coupling coordination also improves,with the overall trend showing a progression from mild dysfunction to primary coordination.Based on these conclusions,corresponding countermeasures are proposed to promote the coupling coordination between tourism and transport in Chongqing,and suggestions are made for the overall improvement of the transport industry and the sustainable development of the tourism industry.
基金supported by the National Natural Science Foundation of China(11201395)supported by the Science Foundation of Educational Commission of Hubei Province(Q20132801)
文摘The author proves that if f : C → C^n is a transcendental vector valued mero-morphic function of finite order and assume, This result extends the related results for meromorphic function by Singh and Kulkarni.
文摘Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ <em>x</em>)</span>, has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function <span style="white-space:nowrap;">1/(1+ e<sup><em>x</em> </sup>)</span> . Grandi-type complex valued functions such as <span style="white-space:nowrap;">1/(<em>i</em> + <em>x</em>)</span> are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function <img src="Edit_f4efd7cd-6853-4ca4-b4dc-00f0b798c277.png" width="80" height="24" alt="" /> is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.
基金Supported by the Scientific Research Project of Public Welfare Industry of the Ministry of Water Resources,China (201001030)Natural Science Foundation of Hohai University,China (2009423211)Fundamental Research Funds for the Central Universities,China
文摘[ Objective] The study aimed to quantitatively assess the values of water ecosystem services. [ Method] Combining the market value, travel cost and restoration cost method, the ecological services and their economic values of the lake Taodangmian were assessed from aspects of water supply, recreation and tourism, water purification and biodiversity maintenance. [ Resultl For the lake Taodangmian, its freshwater supply and tourism played more positive roles in the society than the others, while the functions of water purification and biodiversity maintenance brought negative effects, which shows that the ecological environment of Taodangmian has become increasingly worse and needs to be controlled and and protected further. [ Conclusion] The research could provide scientific references for the reasonable exploitation and utilization of water resources.
基金Supported by the National Natural Science Foundation of China(10571141,70971109,71371152)supported by the Talents Fund of Xi’an Polytechnic University(BS1320)the Mathematics Discipline Development Fund of Xi’an Ploytechnic University(107090701)
文摘When all the involved data in indefinite quadratic programs change simultaneously, we show the locally Lipschtiz continuity of the KKT set of the quadratic programming problem firstly, then we establish the locally Lipschtiz continuity of the KKT solution set. Finally, the similar conclusion for the corresponding optimal value function is obtained.
基金Supported by the National Natural Science Foundation of China(10571141,70971109)the Key Projectof the National Natural Science Foundation of China(70531030)
文摘To properly describe and solve complex decision problems, research on theoretical properties and solution of mixed-integer quadratic programs is becoming very important. We establish in this paper different Lipschitz-type continuity results about the optimal value function and optimal solutions of mixed-integer parametric quadratic programs with parameters in the linear part of the objective function and in the right-hand sides of the linear constraints. The obtained results extend some existing results for continuous quadratic programs, and, more importantly, lay the foundation for further theoretical study and corresponding algorithm analysis on mixed-integer quadratic programs.
基金supported by the NSF of China(11071144,11171187,11222110 and 71671104)Shandong Province(BS2011SF010,JQ201202)+4 种基金SRF for ROCS(SEM)Program for New Century Excellent Talents in University(NCET-12-0331)111 Project(B12023)the Ministry of Education of Humanities and Social Science Project(16YJA910003)Incubation Group Project of Financial Statistics and Risk Management of SDUFE
文摘We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs’ condition.
基金Taif University Researchers Supporting Project number(TURSP-2020/20),Taif University,Taif,Saudi Arabia。
文摘The present paper aims to develop the Kuhn-Tucker and Fritz John criteria for saddle point optimality of interval-valued nonlinear programming problem.To achieve the study objective,we have proposed the definition of minimizer and maximizer of an interval-valued non-linear programming problem.Also,we have introduced the interval-valued Fritz-John and Kuhn Tucker saddle point problems.After that,we have established both the necessary and sufficient optimality conditions of an interval-valued non-linear minimization problem.Next,we have shown that both the saddle point conditions(Fritz-John and Kuhn-Tucker)are sufficient without any convexity requirements.Then with the convexity requirements,we have established that these saddle point optimality criteria are the necessary conditions for optimality of an interval-valued non-linear programming with real-valued constraints.Here,all the results are derived with the help of interval order relations.Finally,we illustrate all the results with the help of a numerical example.
文摘A peak norm is defined for Lp spaces of E-valued Bochner integrable functions, where E is a Banach space, and best approximations from a sun to elements of the space are characterized. Applications are given to some families of simultaneous best approximation problems.
基金supported by the NNSF(11201014,11171013,11126036,11371225)the YWF-14-SXXY-008,YWF-ZY-302854 of Beihang Universitysupported by the youth talent program of Beijing(29201443)
文摘In this paper, we investigate uniqueness problems of differential polynomials of meromorphic functions. Let a, b be non-zero constants and let n, k be positive integers satisfying n ≥ 3k + 12. If f^n+ af^(k)and g^n+ ag^(k)share b CM and the b-points of f^n+ af^(k)are not the zeros of f and g, then f and g are either equal or closely related.
基金State 973 upfront-"the formation of oasis in hexi corridor in gansu province edge product sand strip and its ecological effect"(2011CB411912)GEF/OP12-return of the land management and policy support
文摘[Objective]Returning farmland to forest and mountain enclosure for grazing prohibition ecological effect and economy rationality were explored.[Methods]A case study of returning farmland to forest and barren hills grazing prohibition in Yongxing Township of Jingyuan County was used to discuss and estimate the relative ecological function and relative ecological value.[Results]1)The ecological value of the forest of returning farmland was far more than the sum of the ecological value of farm crops and the agricultural output,and also more than the national subsidy standard.So the state policy of returning farmland to forests is not only favorable to local eco-environment restoration,but also reasonable in economic development.2)The ecological value of mountain enclosure for grazing prohibition was less than the opportunity cost of prohibiting grazing,also less than the national subsidy standard.The sum of the relative ecological value of prohibiting grazing and the state subsidies was more than the opportunity cost of prohibiting grazing.However,the ecological value of new vegetation through returning farmland to forest project was greater than the China's average ecological value of grassland.[Conclusion]The relative ecological value can be used to solve the problems in the equivalent conversion among various ecological indexes and between ecological indexes and economic indexes.
基金Supported by the NSF of Guangdong Province!( 980 0 1 8) Higher Education Bureau!( 1 99873)
文摘This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t<0), u (j) (0)=u(1)=0,(1≤j≤n-2).Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.An example to illustrate the application of this theorem is given. [FQ(6*2。39,X-W]
基金Project supported by the Fundamental Research Funds for the Central Universities and Southwest Minzu University(Grant No.2022SJQ002)。
文摘The kinetic theory is employed to analyze influence of agent competence and psychological factors on investment decision-making.We assume that the wealth held by agents in the financial market is non-negative,and agents set their own investment strategies.The herding behavior is considered when analyzing the impact of an agent's psychological factors on investment decision-making.A nonlinear Boltzmann model containing herding behavior,agent competence and irrational behavior is employed to investigate investment decision-making.To characterize the agent's irrational behavior,we utilize a value function which includes current and ideal-investment decisions to describe the agent's irrational behavior.Employing the asymptotic procedure,we obtain the Fokker-Planck equation from the Boltzmann equation.Numerical results and the stationary solution of the obtained Fokker-Planck equation illustrate how herding behavior,agent competence,psychological factors,and irrational behavior affect investment decision-making,i.e.,herding behavior has both advantages and disadvantages for investment decision-making,and the agent's competence to invest helps the agent to increase income and to reduce loss.
文摘This study focuses on investigating the optimal investment strategy for an optimization problem with delay using the uncertainty theory. The financial market is composed of a risk-free asset and a risk asset with an uncertain price process described by an uncertain differential equation. An optimization problem is assumed that its objective is a nonlinear function of decision variable. By deriving the equation of optimality, an analytical solution is obtained for the optimal delay investment strategy, and the optimal delay value function. Finally, an economic analysis and numerical sensitivity analysis are conducted to evaluate the research results.
文摘In this paper, we characterize lower semi-continuous pseudo-convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the pseudo-monotonicity of its Clarke-Rockafellar Sub-differential. We extend the results on the characterizations of non-smooth convex functions f : X → R ∪ {+ ∞} on convex subset of real Banach spaces K ⊂ X with respect to the monotonicity of its sub-differentials to the lower semi-continuous pseudo-convex functions on real Banach spaces.
基金supported by National Key R&D Program(2017YFD0101600)State Key Laboratory of Cotton Biology(CB2019C17)。
文摘Background:Salt stress significantly inhibits the growth,development,and productivity of cotton because of osmotic,ionic,and oxidative stresses.Therefore,the screening and development of salt tolerant cotton cultivars is a key issue towards sustainable agriculture.This study subjected 11 upland cotton genotypes at the seedling growth stage to five different salt concentrations and evaluated their salt tolerance and reliable traits.Results:Several morpho-physiological traits were measured after 10 days of salinity treatment and the salt tolerance performance varied significantly among the tested cotton genotypes.The optimal Na Cl concentration for the evaluation of salt tolerance was 200 mmol·L-1.Membership function value and salt tolerance index were used to identify the most consistent salt tolerance traits.Leaf relative water content and photosynthesis were identified as reliable indicators for salt tolerance at the seedling stage.All considered traits related to salt tolerance indices were significantly and positively correlated with each other except for malondialdehyde.Cluster heat map analysis based on the morpho-physiological salt tolerance-indices clearly discriminated the 11 cotton genotypes into three different salt tolerance clusters.Cluster I represented the salt-tolerant genotypes(Z9807,Z0228,and Z7526)whereas clusters II(Z0710,Z7514,Z1910,and Z7516)and III(Z0102,Z7780,Z9648,and Z9612)represented moderately salttolerant and salt-sensitive genotypes,respectively.Conclusions:A hydroponic screening system was established.Leaf relative water content and photosynthesis were identified as two reliable traits that adequately represented the salt tolerance of cotton genotypes at the seedling growth stage.Furthermore,three salt-tolerant genotypes were identified,which might be used as genetic resources for the salt-tolerance breeding of cotton.
基金supported by National Hi-tech Research and Development Program of China (863 Program, Grant No. 2007AA04Z433)Hunan Provincial Natural Science Foundation of China (Grant No. 09JJ8005)Scientific Research Foundation of Graduate School of Beijing University of Chemical and Technology,China (Grant No. 10Me002)
文摘As the differences of sensor's precision and some random factors are difficult to control,the actual measurement signals are far from the target signals that affect the reliability and precision of rotating machinery fault diagnosis.The traditional signal processing methods,such as classical inference and weighted averaging algorithm usually lack dynamic adaptability that is easy for trends to cause the faults to be misjudged or left out.To enhance the measuring veracity and precision of vibration signal in rotary machine multi-sensor vibration signal fault diagnosis,a novel data level fusion approach is presented on the basis of correlation function analysis to fast determine the weighted value of multi-sensor vibration signals.The approach doesn't require knowing the prior information about sensors,and the weighted value of sensors can be confirmed depending on the correlation measure of real-time data tested in the data level fusion process.It gives greater weighted value to the greater correlation measure of sensor signals,and vice versa.The approach can effectively suppress large errors and even can still fuse data in the case of sensor failures because it takes full advantage of sensor's own-information to determine the weighted value.Moreover,it has good performance of anti-jamming due to the correlation measures between noise and effective signals are usually small.Through the simulation of typical signal collected from multi-sensors,the comparative analysis of dynamic adaptability and fault tolerance between the proposed approach and traditional weighted averaging approach is taken.Finally,the rotor dynamics and integrated fault simulator is taken as an example to verify the feasibility and advantages of the proposed approach,it is shown that the multi-sensor data level fusion based on correlation function weighted approach is better than the traditional weighted average approach with respect to fusion precision and dynamic adaptability.Meantime,the approach is adaptable and easy to use,can be applied to other areas of vibration measurement.