Game Theory Based Model for Predictive Analytics Using Distributed Position Function

This paper presents a game theory-based method for predicting the outcomes of negotiation and group decision-making problems. We propose an extension to the BDM model to address problems where actors’ positions are distributed over a position spectrum. We generalize the concept of position in the model to incorporate continuous positions for the actors, enabling them to have more flexibility in defining their targets. We explore different possible functions to study the role of the position function and discuss appropriate distance measures for computing the distance between the positions of actors. To validate the proposed extension, we demonstrate the trustworthiness of our model’s performance and interpretation by replicating the results based on data used in earlier studies.

Existence of Positive Solutions for A Fourth-order Boundary Value Problems with p-Laplacian Operators

This paper investigates the existence of positive solutions for a fourth-order p-Laplacian nonlinear equation. We show that, under suitable conditions, there exists a positive number λ~*such that the above problem has at least two positive solutions for 0 < λ < λ~* , at least one positive solution for λ = λ~* and no solution forλ > λ~* by using the upper and lower solutions method and fixed point theory.

Existence of Positive Solutions to a Fractional-Kirchhoff System

LetΩbe a bounded smooth domain in RN(N≥3).Assuming that 0<s<1,1<p,q≤N+2s/N-2s with(p,q)≠(N+2s/N-2s,N+2s/N-2s),and a,b>0 are constants,we consider the existence results for positive solutions of a class of fractional elliptic system below,{(a+b[u]^(2)_(s))(-Δ)^(s)u=vp+h_(1)(x,u,v,▽u,▽v),x∈Ω,(-Δ)^(s)v=u^(q)+h_(2)(x,u,▽,▽u,▽v),x∈Q,u,v>0,x∈Ω,u=v=0,x∈RN\Ω.Under some assumptions of hi(x,u,v,▽u,▽v)(i=1,2),we get a priori bounds of the positive solutions to the problem(1.1)by the blow-up methods and rescaling argument.Based on these estimates and degree theory,we establish the existence of positive solutions to problem(1.1).

一种新型3-RRPU并联机构的运动学及鲁棒控制研究

针对现有的三平移并联机构大多正解不唯一、较难实现精确稳定运动控制的问题,提出了一种新的3-RRPU型三平移并联机构,同时研究了机构的运动学、动力学及轨迹跟踪控制方法。首先,运用螺旋理论分析了该机构三平移的原理,进行了驱动输入的选取与论证,对机构平台奇异性、驱动奇异性和支链奇异性进行了分析;其次,运用运动学理论建立了运动学模型,推导了位置正、逆解析解;再次,运用拉格朗日动力学理论建立了机构操作空间的刚体动力学模型;最后,提出了一种基于非线性反馈解耦的自适应滑模轨迹跟踪控制方法,以证明其控制稳定性,并基于动力学模型对空间轨迹跟踪精度和控制力矩进行了仿真分析。研究结果表明:3-RRPU并联机构的位置正解在一般位形下具有唯一性,机构的平台奇异位形和驱动奇异位形少且无支链奇异。该轨迹控制方法可使机构在载荷20 kg、速度0.18 m/s、加速度0.12 m/s 2下,实现0.002 m以内的高精度复杂轨迹跟踪;基于Sigmoid函数的轨迹控制方法还能有效削弱控制力矩的抖振,为实现工业领域高速、高精度、高性能的三平移运动提供了新方法。

关于丢番图方程(1023n)^(x)+(64n)^(y)=(1025n)^(z)

设a,b,c是两两互素的正整数且满足商高数条件,即当a,b,c为本原商高数时,方程(an)^(x)+(bn)^(y)=(cn)^(z)仅有正整数解(x,y,z)=(2,2,2).而现有的丢番图方程形式并没有将b的具体形式与初等数论紧密结合,利用奇偶分析法、简单同余理论、将b取为26并与初等数论相结合,还运用了分类讨论、反证法的思想,具体为先采用反证法进行假设,根据所化简的等式选取合适的模数进行推算得出与假设相悖的结论,即证明了:若n为正整数,当(a,b,c)=(1023,64,1025)时,丢番图方程(1023n)x+(64n)y=(1025n)z仅有正整数解(x,y,z)=(2,2,2),以此验证Jesmanowicz猜想成立,这个证明结果使Jesmanowicz猜想更加充实.

基于新图模糊距离的EDAS决策方法及其应用

研究决策信息为图模糊集的多属性决策问题。首先,针对现有图模糊距离的不足,定义了含参数的弃权度的分配,同时结合一致性概念提出了反映决策者风险偏好的图模糊距离,通过数值算例将新图模糊距离与现有图模糊距离进行比较分析,验证其优越性。其次,针对属性权重,采用博弈论组合赋权法对熵权法确定的客观权重和决策者给出的主观权重进行组合优化。在此基础上,将新图模糊距离拓展到一种离平均方案距离的决策方法(EDAS),并运用新图模糊距离计算各方案与平均方案的正、负距离加权和,进而得到综合得分。最后,通过算例来验证所提决策方法的适用性和有效性。灵敏度与对比分析结果表明:决策者可以依据自身风险偏好调整参数的取值来满足不同的决策需求;所提方法相较于其他现有决策方法更具一般性与灵活性,所得排序结果更加合理。

Pythagorean模糊环境下的三支多属性决策方法

将后悔理论与逼近理想解排序(TOPSIS)法相结合,提出了一种新的三支多属性决策方法,旨在减少决策者的后悔情绪,提高决策满意度.首先,通过评价信息表确定各属性下备选方案的状态集,计算各方案的条件概率.其次,结合TOPSIS和后悔理论,计算相对损失函数,进而确定期望损失,并建立三支决策规则,对方案进行排序并划分为接受域、延迟决策域或拒绝域.最后,以城市轨道交通站点选择为例,进行案例对比分析,验证了该方法的可行性和有效性;接着进行参数分析,以验证该方法的稳定性.

Positive solutions for a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-Ⅱ functional response

We consider a Lotka-Volterra prey-predator model with cross-diffusion and Holling type-II functional response.The main concern is the existence of positive solutions under the combined effect of cross-diffusion and Holling type-II functional response.Here,a positive solution corresponds to a coexistence state of the model.Firstly,we study the sufficient conditions to ensure the existence of positive solutions by using degree theory and analyze the coexistence region in parameter plane.In addition,we present the uniqueness of positive solutions in one dimension case.Secondly,we study the stability of the trivial and semi-trivial solutions by analyzing the principal eigenvalue of the corresponding linearized system,and then we characterize the stable/unstable regions of semi-trivial solutions in parameter plane.

Multiple positive periodic solutions for a generalized delayed population model with an exploited term

In this paper, the existence of two positive periodic solutions for a generalized delayed population model with an exploited term is established by using the continuation theorem of the coincidence degree theory.

EXISTENCE OF POSITIVE SOLUTIONS TO SUBLINEAR SECOND-ORDER PERIODIC BOUNDARY VALUE PROBLEM

In this paper, we consider a second-order periodic boundary value problem. By the topological degree theory and fixed point index theory, we prove the existence of positive solutions which gives the relationship between the first positive eigenvalue of the associated eigenvalue problem and the behavior of the nonlinear term of the system.

POSITIVE SOLUTIONS OF HIGHER DIMENSIONAL DISCRETE BOUNDARY VALUE PROBLEM

By means of the critical point theory, we prove the existence of positive solutions for a higher dimensional discrete boundary value problem. Our results generalize one of Agarwal in [2].

EXISTENCE OF POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEM OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

In this paper, using the property of the corresponding Green’s function and fixed point index theory, some sufficient conditions for the multiplicity and nonexistence of positive solutions to a class of nonlinear fractional boundary value problem are obtained. Three examples are given to show the effectiveness of our results.

THREE POSITIVE SOLUTIONS TO BVP FOR p-LAPLACIAN IMPULSIVE FUNCTIONAL DYNAMIC EQUATIONS ON A TIME SCALE

In this paper, we axe interested in the existence of three positive solutions to a BVP for p-Laplacian impulsive functional dynamic equations on a time scale. Using the five-functional fixed theory, we establish a Banach space and an appropriate operator. In this paper, we combine the delta-nabla p-Laplacian BVP with impulsive functional dynamic equations, and obtain some new sufficient conditions for the existence of three positive solutions to the BVP, and our result here generalizes the previous related results.

ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR SINGULAR NEUMANN BOUNDARY VALUE PROBLEMS

By using fixed point index theory, we consider the existence of positive solutions for singular nonlinear Neumann boundary value problems. Our main results extend and improve many known results even for non-singular cases.

POSITIVE SOLUTIONS TO A CLASS OF SECOND-ORDER SINGULAR SEMIPOSITIVE NEUMANN BOUNDARY VALUE PROBLEM WITH GENERAL FORM

By constructing an explicit Green function and using the fixed point index theory on a cone, we present some existence results of positive solutions to a class of second-order singular semipositive Neumann boundary value problem, where the nonlinear term is allowed to be nonnegative and unbounded.

EXISTENCE OF POSITIVE SOLUTIONS TO SINGULAR SUBLINEAR SEMIPOSITONE NEUMANN BOUNDARY VALUE PROBLEM

The existence of positive solutions to a singular sublinear semipositone Neumann boundary value problem is considered. In this paper,the nonlinearity term is not necessary to be bounded from below and the function q(t) is allowed to be singular at t = 0 and t = 1.

一类数论函数方程φ(φ(n))=2^(■(n))(■)(n)的可解性研究

φ(n)是欧拉函数,其中n是任意大于零的正整数,(■)(n)是n的约束函数,文章另辟蹊径,运用初等数论及不等式放缩法研究方程φ(φ(n))=2^(■)(n)(■)(n)的可解性,并给出了该方程的所有正整数解,对传统研究方法及研究结果作了相应的补充,扩大了研究视野,也为计算机科学及密码学研究提供了理论基础及方法支持.

一类二阶非齐次边值问题正解的存在性与多解性

研究了二阶非齐次边值问题{-u″(t)+k^(2)u(t)=f(u(t)),t∈[0,],正解的存在性与多解性,其中k,b>0为常数,f∈C([0,∞),[0,∞)),f_(0):=lim_(u→0^(+))f(u)/u=0,f_(∞):=lim_(u→∞)f(u)/u=∞.运用上下解方法和拓扑度理论,证明了存在常数b^(*)>0,使得当0<b<b^(*)时,该问题不存在2个正解;当b=b^(*)时,该问题存在1个正解。

人工智能时代高校思想政治理论课创新难点及突破路径

人工智能时代高校思想政治理论课具备科学的思想政治理论课创新决策系统,能够实现全面精细的思想政治理论课创新实施过程,拥有准确高效的思想政治理论课创新评估体系。然而,当前高校在推进人工智能与思想政治理论课建设深度融合方面仍面临智能干预弱化思政理论课教师的主导地位,流量效应削弱思想政治理论课的价值理性,信息过载对学习者学习主体性和互动性产生消解,赋能不足导致思想政治理论课技术应用浅层化等问题。人工智能时代高校思想政治理论课创新应强化思想政治理论课教师的主导性地位、彰显和重塑思想政治理论课的价值理性、激发学习者的学习主体性与教学互动性、推动人工智能技术深度赋能思想政治理论课实践。

基于证据理论的传动方案决策系统设计

针对大型拖拉机变速箱智能化设计过程中难以在多个近似变速箱传动方案中决策出最佳方案的问题,基于证据理论构建了一个大型拖拉机变速箱传动方案智能决策系统。依据变速箱传动方案中各属性的特点,采用了模糊数、区间数与语言评价集等理论构建了各属性的基础概率分配模块;采用层次分析法与博弈论思想构建了属性权重分配模块;对基础概率加权平均之后,采用证据理论组合规则构建了融合决策模块。通过综合决策者的偏好与待决策方案之间的相互关系实现传动方案的快速决策。测试结果表明:该系统能够准确地依据决策偏好实现传动方案的快速决策,具有一定的应用价值。