Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ x), has been resolved and extended to complex valued functions. Resolution of this approximate...Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ x), 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>x </sup>) . Grandi-type complex valued functions such as <span style="white-space:nowrap;">1/(i + x) 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
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
Amphibious vehicles are more prone to attitude instability compared to ships,making it crucial to develop effective methods for monitoring instability risks.However,large inclination events,which can lead to instabili...Amphibious vehicles are more prone to attitude instability compared to ships,making it crucial to develop effective methods for monitoring instability risks.However,large inclination events,which can lead to instability,occur frequently in both experimental and operational data.This infrequency causes events to be overlooked by existing prediction models,which lack the precision to accurately predict inclination attitudes in amphibious vehicles.To address this gap in predicting attitudes near extreme inclination points,this study introduces a novel loss function,termed generalized extreme value loss.Subsequently,a deep learning model for improved waterborne attitude prediction,termed iInformer,was developed using a Transformer-based approach.During the embedding phase,a text prototype is created based on the vehicle’s operation log data is constructed to help the model better understand the vehicle’s operating environment.Data segmentation techniques are used to highlight local data variation features.Furthermore,to mitigate issues related to poor convergence and slow training speeds caused by the extreme value loss function,a teacher forcing mechanism is integrated into the model,enhancing its convergence capabilities.Experimental results validate the effectiveness of the proposed method,demonstrating its ability to handle data imbalance challenges.Specifically,the model achieves over a 60%improvement in root mean square error under extreme value conditions,with significant improvements observed across additional metrics.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.
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 ...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
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
The ecological concept of Plant Functional Types（PFTs）, which refers to the assemblage of plants with certain functional traits, has been introduced for the study of plant responses to the environment change and hum...The ecological concept of Plant Functional Types（PFTs）, which refers to the assemblage of plants with certain functional traits, has been introduced for the study of plant responses to the environment change and human disturbance. Taking the alpine meadow community in the Zoigê Plateau as a study case, this paper classified PFTs in terms of plant nutrition traits. The sequential results are as follows.（1） The main herbages in the Zoigê Plateau included 16 species in 5 families. Among the five families, Cyperaceae vegetation accounted for 81.37%of herbage area in total, while the remaining 4families occupied less than 20%. As for the species,Kobresia setchwanensis Hand.-Maizz. was dominant,accounting for 48.74% of the total area; while the remaining 51.26% was comprised of Polygonum viviparum L., Anaphalis fiavescens Hand.-Mazz.,Stipa aliena Keng and other species.（2） By using the Principal Component Analysis（PCA）, the assessment of herbages nutrition was carried out based on the comprehensive multi-index evaluation model.Polygonum viviparum L. had the highest nutritional value score（1.43）, and Stipa aliena Keng had the lowest（-1.40）. Nutritional value of herbage species had a significantly positive correlation with altitude（P＆lt;0.01） in the Zoigê Plateau.（3） Based on the nutritional values, herbages in the Zoigê Plateau could be grouped into 3 nutrition PFTs（high, medium and low） by using the Natural Breaks（Jenks） method.展开更多
In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modif...In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.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
The distribution of continuous service time in call centers is investigated.A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of conti...The distribution of continuous service time in call centers is investigated.A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of continuous service time,respectively.Using the statistical mechanical and asymptotic limit methods,Fokker–Planck equations are derived from the corresponding Boltzmann-type equations with non-Maxwellian collision kernels.The steady-state solutions of the Fokker–Planck equation are obtained in exact form.Numerical experiments are provided to support our results under different parameters.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
In cooperative multiagent systems, to learn the optimal policies of multiagents is very difficult. As the numbers of states and actions increase exponentially with the number of agents, their action policies become mo...In cooperative multiagent systems, to learn the optimal policies of multiagents is very difficult. As the numbers of states and actions increase exponentially with the number of agents, their action policies become more intractable. By learning these value functions, an agent can learn its optimal action policies for a task. If a task can be decomposed into several subtasks and the agents have learned the optimal value functions for each subtask, this knowledge can be helpful for the agents in learning the optimal action policies for the whole task when they are acting simultaneously. When merging the agents’ independently learned optimal value functions, a novel multiagent online reinforcement learning algorithm LU-Q is proposed. By applying a transformation to the individually learned value functions, the constraints on the optimal value functions of each subtask are loosened. In each learning iteration process in algorithm LU-Q, the agents’ joint action set in a state is processed. Some actions of that state are pruned from the available action set according to the defined multiagent value function in LU-Q. As the items of the available action set of each state are reduced gradually in the iteration process of LU-Q, the convergence of the value functions is accelerated. LU-Q’s effectiveness, soundness and convergence are analyzed, and the experimental results show that the learning performance of LU-Q is better than the performance of standard Q learning.展开更多
Based on a unicity theorem for entire funcitions concerning differential polynomials proposed by M. L. Fang and W. Hong, we studied the uniqueness problem of two meromorphic functions whose differential polynomials sh...Based on a unicity theorem for entire funcitions concerning differential polynomials proposed by M. L. Fang and W. Hong, we studied the uniqueness problem of two meromorphic functions whose differential polynomials share the same 1- point by proving two theorems and their related lemmas. The results extend and improve given by Fang and Hong’s theorem.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
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-ty...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
The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle ...The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).展开更多
We introduce a total order and an absolute value function for dual numbers.The absolute value function of dual numbers takes dual number values,and has properties similar to those of the absolute value function of rea...We introduce a total order and an absolute value function for dual numbers.The absolute value function of dual numbers takes dual number values,and has properties similar to those of the absolute value function of real numbers.We define the magnitude of a dual quaternion,as a dual number.Based upon these,we extend 1-norm,co-norm,and 2-norm to dual quaternion vectors.展开更多
This paper discussed the keystone species concept and introduced the typical characteristics of keystone species and their identification in communities or ecosystems. Based on the research of the keystone species, th...This paper discussed the keystone species concept and introduced the typical characteristics of keystone species and their identification in communities or ecosystems. Based on the research of the keystone species, the concept of species importance (SI) was first advanced in this paper. The species importance can be simply understood as the important value of species in the ecosystem, which consists of three indexes: species structural important value (SIV), functional important value (FIV) and dynamical important value (DIV). With the indexes, the evaluation was also made on species importance of arbor trees in the Three-Hardwood forests (Fraxinus mandshurica, Juglans mandshurica, and Phellodendron amurense) ecosystem.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
文摘Grandi’s paradox, which was posed for a real function of the form <span style="white-space:nowrap;">1/(1+ x), 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>x </sup>) . Grandi-type complex valued functions such as <span style="white-space:nowrap;">1/(i + x) 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.
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 National Defense Basic Scientific Research Program of China.
文摘Amphibious vehicles are more prone to attitude instability compared to ships,making it crucial to develop effective methods for monitoring instability risks.However,large inclination events,which can lead to instability,occur frequently in both experimental and operational data.This infrequency causes events to be overlooked by existing prediction models,which lack the precision to accurately predict inclination attitudes in amphibious vehicles.To address this gap in predicting attitudes near extreme inclination points,this study introduces a novel loss function,termed generalized extreme value loss.Subsequently,a deep learning model for improved waterborne attitude prediction,termed iInformer,was developed using a Transformer-based approach.During the embedding phase,a text prototype is created based on the vehicle’s operation log data is constructed to help the model better understand the vehicle’s operating environment.Data segmentation techniques are used to highlight local data variation features.Furthermore,to mitigate issues related to poor convergence and slow training speeds caused by the extreme value loss function,a teacher forcing mechanism is integrated into the model,enhancing its convergence capabilities.Experimental results validate the effectiveness of the proposed method,demonstrating its ability to handle data imbalance challenges.Specifically,the model achieves over a 60%improvement in root mean square error under extreme value conditions,with significant improvements observed across additional metrics.
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.
基金supported by the sub topics of National Key Technology R&D Program (Grant No. 2015BAC05B05-01)
文摘The ecological concept of Plant Functional Types（PFTs）, which refers to the assemblage of plants with certain functional traits, has been introduced for the study of plant responses to the environment change and human disturbance. Taking the alpine meadow community in the Zoigê Plateau as a study case, this paper classified PFTs in terms of plant nutrition traits. The sequential results are as follows.（1） The main herbages in the Zoigê Plateau included 16 species in 5 families. Among the five families, Cyperaceae vegetation accounted for 81.37%of herbage area in total, while the remaining 4families occupied less than 20%. As for the species,Kobresia setchwanensis Hand.-Maizz. was dominant,accounting for 48.74% of the total area; while the remaining 51.26% was comprised of Polygonum viviparum L., Anaphalis fiavescens Hand.-Mazz.,Stipa aliena Keng and other species.（2） By using the Principal Component Analysis（PCA）, the assessment of herbages nutrition was carried out based on the comprehensive multi-index evaluation model.Polygonum viviparum L. had the highest nutritional value score（1.43）, and Stipa aliena Keng had the lowest（-1.40）. Nutritional value of herbage species had a significantly positive correlation with altitude（P＆lt;0.01） in the Zoigê Plateau.（3） Based on the nutritional values, herbages in the Zoigê Plateau could be grouped into 3 nutrition PFTs（high, medium and low） by using the Natural Breaks（Jenks） method.
基金Supported by the National Natural Science Foundation of China(19871009)
文摘In this paper, optimality conditions for multiobjective programming problems having V-invex objective and constraint functions are considered. An equivalent multiobjective programming problem is constructed by a modification of the objective function.Furthermore, a (α, η)-Lagrange function is introduced for a constructed multiobjective programming problem, and a new type of saddle point is introduced. Some results for the new type of saddle point are given.
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the Special Project of Yili Normal University(to improve comprehensive strength of disciplines)(Grant No.22XKZZ18)Yili Normal University Scientific Research Innovation Team Plan Project(Grant No.CXZK2021015)Yili Science and Technology Planning Project(Grant No.YZ2022B036).
文摘The distribution of continuous service time in call centers is investigated.A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of continuous service time,respectively.Using the statistical mechanical and asymptotic limit methods,Fokker–Planck equations are derived from the corresponding Boltzmann-type equations with non-Maxwellian collision kernels.The steady-state solutions of the Fokker–Planck equation are obtained in exact form.Numerical experiments are provided to support our results under different parameters.
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.
文摘In cooperative multiagent systems, to learn the optimal policies of multiagents is very difficult. As the numbers of states and actions increase exponentially with the number of agents, their action policies become more intractable. By learning these value functions, an agent can learn its optimal action policies for a task. If a task can be decomposed into several subtasks and the agents have learned the optimal value functions for each subtask, this knowledge can be helpful for the agents in learning the optimal action policies for the whole task when they are acting simultaneously. When merging the agents’ independently learned optimal value functions, a novel multiagent online reinforcement learning algorithm LU-Q is proposed. By applying a transformation to the individually learned value functions, the constraints on the optimal value functions of each subtask are loosened. In each learning iteration process in algorithm LU-Q, the agents’ joint action set in a state is processed. Some actions of that state are pruned from the available action set according to the defined multiagent value function in LU-Q. As the items of the available action set of each state are reduced gradually in the iteration process of LU-Q, the convergence of the value functions is accelerated. LU-Q’s effectiveness, soundness and convergence are analyzed, and the experimental results show that the learning performance of LU-Q is better than the performance of standard Q learning.
文摘Based on a unicity theorem for entire funcitions concerning differential polynomials proposed by M. L. Fang and W. Hong, we studied the uniqueness problem of two meromorphic functions whose differential polynomials share the same 1- point by proving two theorems and their related lemmas. The results extend and improve given by Fang and Hong’s theorem.
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 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 Innovation Research for the Postgrad-uates of Guangzhou University(2020GDJC-D06)supported by the National Natural Science Foundation of China(12071229)。
文摘The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).
基金supported by Hong Kong Innovation and Technology Commission(InnoHK Project CIMDA)supported by the National Natural Science Foundation of China(No.11971138)+3 种基金the Natural Science Foundation of Zhejiang Province of China(Nos.LY19A010019,LD19A010002)supported by Hong Kong Research Grants Council(Project 11204821)Hong Kong Innovation and Technology Commission(InnoHK Project CIMDA)City University of Hong Kong(Project 9610034).
文摘We introduce a total order and an absolute value function for dual numbers.The absolute value function of dual numbers takes dual number values,and has properties similar to those of the absolute value function of real numbers.We define the magnitude of a dual quaternion,as a dual number.Based upon these,we extend 1-norm,co-norm,and 2-norm to dual quaternion vectors.
基金The paper was supported by science foundation of Changbai Mountain Open Research Station Chinese Academy of Sci-ences and Heilongjiang Natural Science Foundation (C00-01).
文摘This paper discussed the keystone species concept and introduced the typical characteristics of keystone species and their identification in communities or ecosystems. Based on the research of the keystone species, the concept of species importance (SI) was first advanced in this paper. The species importance can be simply understood as the important value of species in the ecosystem, which consists of three indexes: species structural important value (SIV), functional important value (FIV) and dynamical important value (DIV). With the indexes, the evaluation was also made on species importance of arbor trees in the Three-Hardwood forests (Fraxinus mandshurica, Juglans mandshurica, and Phellodendron amurense) ecosystem.
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.
