The rnemmorphic functions of positive order(both finite positive order and infinite order) are discussed.First,the precise order and type function are given by using the characteristic function.Then some singular dire...The rnemmorphic functions of positive order(both finite positive order and infinite order) are discussed.First,the precise order and type function are given by using the characteristic function.Then some singular directions are defined and their existence is proved.展开更多
Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scalin...Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.展开更多
This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projectiv...This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.展开更多
According to the necessary condition of the functional taking the extremum, that is its first variation is equal to zero, the variational problems of the functionals for the undetermined boundary in the calculus of va...According to the necessary condition of the functional taking the extremum, that is its first variation is equal to zero, the variational problems of the functionals for the undetermined boundary in the calculus of variations are researched, the functionals depend on single argument, arbitrary unknown functions and their derivatives of higher orders. A new view point is posed and demonstrated, i.e. when the first variation of the functional is equal to zero, all the variational terms are not independent to each other, and at least one of them is equal to zero. Some theorems and corollaries of the variational problems of the functionals are obtained.展开更多
Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition fo...Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.展开更多
In this article,we discuss,by Nevanlinna theory,the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions.We get several uniqueness theorems of algebroid functions which includ...In this article,we discuss,by Nevanlinna theory,the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions.We get several uniqueness theorems of algebroid functions which include an at most 3v-valued theorem.These results extend the existing achievements of some scholars.展开更多
In this paper,we obtain the fractal dimension of the graph of the Weierstrass function, its derivative of the fractional order and the relation between the dimension and the order of the fractional derivative.
In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k...In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k＋1t/（tlogt）k-（t-1）^k（k=1,2…）,gk（t）=t^klog^k＋1t/（t-1）^k-log^kt（k=1,2…）defined onWe find that they are all operator monotone functions with respect to the strictly chaoticorder and some ordinary orders among positive invertible operators. Indeed, we extend theresults of the operator monotone function tlogt-t＋1/log^2t which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1].展开更多
To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive t...To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.展开更多
In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation functi...In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation function, Filippov solution of the neural network is defined. Based on Brouwer's fixed point theorem and definition of Mittag–Leffler stability, sufficient criteria are established to ensure the existence of (2k + 3)~n (k ≥ 1) equilibrium points, among which (k + 2)~n equilibrium points are locally Mittag–Leffler stable. Compared with the existing results, the derived results cover local Mittag–Leffler stability of both fractional-order and integral-order recurrent neural networks. Meanwhile discontinuous networks might have higher storage capacity than the continuous ones. Two numerical examples are elaborated to substantiate the effective of the theoretical results.展开更多
This paper obtains some solutions of the 5th-order mKdV equation by using the exponential-fraction trial function method, such as solitary wave solutions, shock wave solutions and the hopping wave solutions. It succes...This paper obtains some solutions of the 5th-order mKdV equation by using the exponential-fraction trial function method, such as solitary wave solutions, shock wave solutions and the hopping wave solutions. It successfully shows that this method may be valid for solving other nonlinear partial differential equations.展开更多
针对武器装备体系能力需求分析问题,提出基于犹豫模糊环境下的决策实验室分析法(Decision-making Trial and Evaluation Laboratory,DEMATEL)和逼近理想解排序法改进质量功能展开(Quality Function Deployment,QFD)的新方法。利用基于...针对武器装备体系能力需求分析问题,提出基于犹豫模糊环境下的决策实验室分析法(Decision-making Trial and Evaluation Laboratory,DEMATEL)和逼近理想解排序法改进质量功能展开(Quality Function Deployment,QFD)的新方法。利用基于犹豫模糊理论的DEMATEL方法分析装备体系任务需求之间的影响关系,以确定任务需求重要度;根据装备体系任务需求重要度,建立基于犹豫模糊TOPSIS的装备能力需求优选模型,并通过改进的加权汉明距离计算装备能力需求的相对重要性,以智能城市作战装备体系为例,对比传统方法验证了改进QFD方法的有效性。研究结果表明,改进方法较好地解决了传统QFD在处理犹豫模糊信息时的缺陷,可为装备体系能力需求分析提供新的工具支持。展开更多
文摘The rnemmorphic functions of positive order(both finite positive order and infinite order) are discussed.First,the precise order and type function are given by using the characteristic function.Then some singular directions are defined and their existence is proved.
基金Project supported by the National Natural Science Foundation of China(Grant No.11371049)the Science Foundation of Beijing Jiaotong University(Grant Nos.2011JBM130 and 2011YJS076)
文摘Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.
文摘This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.
文摘According to the necessary condition of the functional taking the extremum, that is its first variation is equal to zero, the variational problems of the functionals for the undetermined boundary in the calculus of variations are researched, the functionals depend on single argument, arbitrary unknown functions and their derivatives of higher orders. A new view point is posed and demonstrated, i.e. when the first variation of the functional is equal to zero, all the variational terms are not independent to each other, and at least one of them is equal to zero. Some theorems and corollaries of the variational problems of the functionals are obtained.
基金Supported by the National Natural Science Foundation of China（11271293）
文摘Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.
基金supported by the Natural Science Foundation of China(11871108)Teacher Research Capacity Promotion Program of Beijing Normal University Zhuhai+2 种基金Guangdong Natural Science Foundation(2018A030313954)Guangdong Universities(Basic Research and Applied Research)Major Project(2017KZDXM038)Guangdong Provincical Anti-monopoly Law Enforcement and Big Data Analysis Research Center Project(2019D04)。
文摘In this article,we discuss,by Nevanlinna theory,the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions.We get several uniqueness theorems of algebroid functions which include an at most 3v-valued theorem.These results extend the existing achievements of some scholars.
基金Project supported by National Natural Science Foundation of China.
文摘In this paper,we obtain the fractal dimension of the graph of the Weierstrass function, its derivative of the fractional order and the relation between the dimension and the order of the fractional derivative.
文摘In this paper we introduce two sequences of operator functions and their dualfunctions： fk（t） = （flogt）k-（t-1）k/log^k＋2t （k = 1,2,...）, gk（t） = （t-1）k-logkt /log^k＋1t （k = 1,2,...） and fk（t）tklog^k＋1t/（tlogt）k-（t-1）^k（k=1,2…）,gk（t）=t^klog^k＋1t/（t-1）^k-log^kt（k=1,2…）defined onWe find that they are all operator monotone functions with respect to the strictly chaoticorder and some ordinary orders among positive invertible operators. Indeed, we extend theresults of the operator monotone function tlogt-t＋1/log^2t which is widely used in the theory of heat transfer of the heat engineering and fluid mechanics[1].
基金Project supported by the Foundation for Young Talents in College of Anhui Province, China (Grant Nos. gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions, China (Grant Nos. 2022AH051580 and 2022AH051586)。
文摘To conveniently calculate the Wigner function of the optical cumulant operator and its dissipation evolution in a thermal environment, in this paper, the thermo-entangled state representation is introduced to derive the general evolution formula of the Wigner function, and its relation to Weyl correspondence is also discussed. The method of integration within the ordered product of operators is essential to our discussion.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China(Grant Nos.LY18F030023,LY17F030016,and LY18F020028)the National Natural Science Foundation of China(Grant Nos.61503338,61502422,and 61773348)
文摘In this paper, coexistence and local Mittag–Leffler stability of fractional-order recurrent neural networks with discontinuous activation functions are addressed. Because of the discontinuity of the activation function, Filippov solution of the neural network is defined. Based on Brouwer's fixed point theorem and definition of Mittag–Leffler stability, sufficient criteria are established to ensure the existence of (2k + 3)~n (k ≥ 1) equilibrium points, among which (k + 2)~n equilibrium points are locally Mittag–Leffler stable. Compared with the existing results, the derived results cover local Mittag–Leffler stability of both fractional-order and integral-order recurrent neural networks. Meanwhile discontinuous networks might have higher storage capacity than the continuous ones. Two numerical examples are elaborated to substantiate the effective of the theoretical results.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10575082 and 10247008）.
文摘This paper obtains some solutions of the 5th-order mKdV equation by using the exponential-fraction trial function method, such as solitary wave solutions, shock wave solutions and the hopping wave solutions. It successfully shows that this method may be valid for solving other nonlinear partial differential equations.
文摘针对武器装备体系能力需求分析问题,提出基于犹豫模糊环境下的决策实验室分析法(Decision-making Trial and Evaluation Laboratory,DEMATEL)和逼近理想解排序法改进质量功能展开(Quality Function Deployment,QFD)的新方法。利用基于犹豫模糊理论的DEMATEL方法分析装备体系任务需求之间的影响关系,以确定任务需求重要度;根据装备体系任务需求重要度,建立基于犹豫模糊TOPSIS的装备能力需求优选模型,并通过改进的加权汉明距离计算装备能力需求的相对重要性,以智能城市作战装备体系为例,对比传统方法验证了改进QFD方法的有效性。研究结果表明,改进方法较好地解决了传统QFD在处理犹豫模糊信息时的缺陷,可为装备体系能力需求分析提供新的工具支持。
