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
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 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, 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
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 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
The authors consider generalized statistically self-affine recursive fractals K with random numbers of subsets on each level. They obtain the Hausdorff dimensions of K without considering whether the subsets on each l...The authors consider generalized statistically self-affine recursive fractals K with random numbers of subsets on each level. They obtain the Hausdorff dimensions of K without considering whether the subsets on each level are non-overlapping or not. They also give some examples to show that many important sets are the special cases of their models.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 paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity sol...This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity solution theory we show that the switching lower-value function is a viscosity solution of the appropriate systems of quasi-variational inequalities（the appropriate generalization of the Hamilton-Jacobi equation in this context） and that the minimal such switching-storage function is equal to the continuous switching lower-value for the game. With the lower value function a optimal switching control is designed for minimizing the cost of running the systems.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
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
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.
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.
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.
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This research is partly supported by NNSF of China (60204001) the Youth Chengguang Project of Science and Technology of Wuhan City (20025001002)
文摘The authors consider generalized statistically self-affine recursive fractals K with random numbers of subsets on each level. They obtain the Hausdorff dimensions of K without considering whether the subsets on each level are non-overlapping or not. They also give some examples to show that many important sets are the special cases of their models.
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.
基金Supported by the SRFEB of Henan Province(2003110002)
文摘This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity solution theory we show that the switching lower-value function is a viscosity solution of the appropriate systems of quasi-variational inequalities（the appropriate generalization of the Hamilton-Jacobi equation in this context） and that the minimal such switching-storage function is equal to the continuous switching lower-value for the game. With the lower value function a optimal switching control is designed for minimizing the cost of running the systems.
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 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).
