Dynamical distribution of continuous service time model involving non-Maxwellian collision kernel and value functions

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.

BSDES IN GAMES,COUPLED WITH THE VALUE FUNCTIONS.ASSOCIATED NONLOCAL BELLMAN-ISAACS EQUATIONS

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.

Multiagent reinforcement learning through merging individually learned value functions

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.

AN INEQUALITY ON THE ZEROS AND POLES OF VECTOR VALUED MEROMORPHIC FUNCTIONS

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.

Resolution of Grandi’s Paradox as Extended to Complex Valued Functions

Grandi’s paradox, which was posed for a real function of the form 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 1/(1+ ex ) . Grandi-type complex valued functions such as 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 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.

Sub-Differential Characterizations of Non-Smooth Lower Semi-Continuous Pseudo-Convex Functions on Real Banach Spaces

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.

Deep reinforcement learning using least-squares truncated temporal-difference

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.

Research on the Coupled and Coordinated Development of Tourism and Transport in Chongqing Municipality

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.

Value Evaluation of Water Ecosystem Services——A Case Study of Changshu City

[ 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.

Another Approach to Multiobjective Programming Problems with V-invex Functions

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.

Lipschitz continuity of the optimal value function and KKT solution set in indefinite quadratic programs

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.

Continuity of the optimal value function and optimal solutions of parametric mixed-integer quadratic programs

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.

Saddle Point Optimality Criteria of Interval Valued Non-Linear Programming Problem

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.

ON MULTIPLE WIENER INTEGRAL EXPANSIONS FOR D'-VALUED NONLINEAR RANDOM FUNCTIONALS

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.

ON VECTOR VALUED FUNCTION APPROXIMATION USING A PEAK NORM

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.

Uniqueness of meromorphic functions concerning differential polynomials

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.

DIFFERENTIAL POLYNOMIALS SHARING ONE VALUE

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.

The Expanding Analysis of Enterprise＇s Human Capital Investment Value

Value is the scale that appraises whether the comparison between a certain thing and its realization which we need to consume is rational. The paper appraises the investment value and incomes of human capital by applying value engineering method. It elaborates the investment structure and contents of human capital first, and then analyzes and summarizes various functions of enterprise＇s human capital. It educes the production function and the optimum equilibrium solution of human capital on this basis. Finally, it appraises the investment value of human capital by applying VE method. Thus we will apply a new method in the human capital field.

Estimation of Relative Ecological Value of Returning Farmland to Forest & Mountain Enclosure for Grazing Prohibition——A case study in Yongxing Township of Jingyuan County,Gansu Province

[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.

A kinetic description of the impact of agent competence and psychological factors on investment decision-making

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.