The solvability of some kinds of singular integral equations of convolution type with variable integral limits

In this paper, we discuss several classes of convolution type singular integral equations with variable integral limits in class $ H^*_1 $. By means of the theory of complex analysis, Fourier analysis and integral transforms, we can transform singular integral equations with variable integral limits into the Riemann boundary value problems with discontinuous coefficients. Under the solvability conditions, the existence and uniqueness of the general solutions can be obtained. Further, we analyze the asymptotic properties of the solutions at the nodes. Our work improves the Noether theory of singular integral equations and boundary value problems, and develops the knowledge architecture of complex analysis.     

The Shapley value,the Proper Shapley value,and sharing rules for cooperative ventures

In this note, we discuss two solutions for cooperative transferable utility games, namely the Shapley value and the Proper Shapley value. We characterize positive Proper Shapley values by affine invariance and by an axiom that requires proportional allocation of the surplus according to the individual singleton worths in generalized joint venture games. As a counterpart, we show that affine invariance and an axiom that requires equal allocation of the surplus in generalized joint venture games characterize the Shapley value.     

Modelling life tables with advanced ages: An extreme value theory approach

We propose a new model – we call it a smoothed threshold life table (STLT) model – to generate life tables incorporating information on advanced ages. Our method allows a smooth mortality transition from non-extreme to extreme ages, and provides objectively determined highest attained ages with which to close the life table.We proceed by modifying the threshold life table (TLT) model developed by Li et al. (2008). In the TLT model, extreme value theory (EVT) is used to make optimal use of the relatively small number of observations at high ages, while the traditional Gompertz distribution is assumed for earlier ages. Our novel contribution is to constrain the hazard function of the two-part lifetime distribution to be continuous at the changeover point between the Gompertz and EVT models. This simple but far-reaching modification not only guarantees a smooth transition from non-extreme to extreme ages, but also provides a better and more robust fit than the TLT model when applied to a high quality Netherlands dataset. We show that the STLT model also compares favourably with other existing methods, including the Gompertz–Makeham model, logistic models, Heligman–Pollard model and Coale–Kisker method, and that a further generalisation, a time-dependent dynamic smooth threshold life table (DSTLT) model, generally has superior in-sample fitting as well as better out-of-sample forecasting performance, compared, for example, with the Cairns et al. (2006) model.     

Trigonometric fitted modification of RADAU5

Implicit Runge-Kutta (RK) methods are in common use when addressing stiff initial value problems (IVP). They usually share the property of A-stability that is of crucial importance in solving the latter type of IVP. Radau IIA family of implicit RK methods is among the preferred ones. Especially its fifth-order representative named RADAU5 has received a lot of attention for use with lax accuracies. Here, we try the lesser possible perturbation of its coefficients. Then, we derive a trigonometric fitted modification that is intended to be applied in periodic IVPs. Numerical tests over a variety of problems with oscillatory solutions justify our effort.     

Compact block boundary value methods for semi-linear delay-reaction–diffusion equations with algebraic constraints

In the present paper, we study a class of linear approximation methods for solving semi-linear delay-reaction–diffusion equations with algebraic constraint (SDEACs). By combining a fourth-order compact difference scheme with block boundary value methods (BBVMs), a class of compact block boundary value methods (CBBVMs) for SDEACs are suggested. It is proved under some suitable conditions that the CBBVMs are convergent of order 4 in space and order p in time, where p is the local order of the used BBVMs, and are globally stable. With several numerical experiments for Fisher equation with delay and algebraic constraint, the computational effectiveness and theoretical results of CBBVMs are further illustrated.     

灰色关联度法在工业企业去库存中的应用

工业企业为了赢得市场竞争地位,必须向市场提供质量好、人民满意的产品,这就需要处理企业库存中市场过剩的、不对路的产品,也就是开展“去库存”工作。论文通过设置与库存相关的指标,计算临界值来判断工业企业产品是否“过剩”,再通过灰色关联度法进行优化排序,确定整个工业行业“去库存”的主要抓手。研究结果表明,工业企业去库存的主要抓手有三个:一要加速库存商品资金周转;二要提高产品销售率;三要降低库存商品占流动资产的比例。论文将研究结论用于徐工集团工程机械股份有限公司,得到有效的验证。     

具有脉冲的分数阶Bagley-Torvik 模型边值问题

将具有脉冲的分数阶Bagley-Torvik微分方程边值问题巧妙地转化为积分方程,定义加权Banach空间及全连续算子,运用不动点定理获得该边值问题解的存在性定理.举例说明了定理的应用.最后提出有趣的研究问题.     

考虑患者回诊情况下的门诊科室调度优化

目前国内大型三甲医院最突出的问题就是资源稀缺,这些稀缺资源主要包括手术室、大型检查设备以及门诊科室等,造成患者严重的排队现象,从而导致患者等待时间过长,满意度下降。通过对哈尔滨市某大型医院进行调研,收集相关数据,研究在考虑患者回诊(即患者当天做完各项检查后又回到初次检查的门诊科室)情况下,对医生门诊科室的数量进行调度优化。利用排队论中的动态优先级对排队规则进行限定,同时引入前景理论中的价值函数,确立以最小化患者时间感知不满意度为主要目标,最小化医院运营成本为次要目标的多目标优化问题。并且分析了两个目标的权重参数变化对总体满意度的影响。建立相应的数学模型,利用模拟植物生长算法( plant growth simulation algorithm,简称PGSA)进行算法设计,通过MATLAB进行仿真,得出在有限度优先的排队规则下,能够更大程度的降低患者不满意度,同时保证较低的运营成本,证明了此研究的有效性和可行性。     

基于区间与模糊Shapley值的合作收益分配策略

将经典Shapley值三条公理进行拓广,提出具有模糊支付合作对策的Shapley值公理体系。研究一种特殊的模糊支付合作对策,即具有区间支付的合作对策,并且给出了该区间Shapley值形式。根据模糊数和区间数的对应关系,提出模糊支付合作对策的Shapley值,指出该模糊Shapley值是区间支付模糊合作对策的自然模糊延拓。结果表明:对于任意给定置信水平α,若α=1,则模糊Shapley值对应经典合作对策的Shapley值,否则对应具有区间支付合作对策的区间Shapley值。通过模糊数的排序,给出了最优的分配策略。由于对具有模糊支付的合作对策进行比较系统的研究,从而为如何求解局中人参与联盟程度模糊化、支付函数模糊化的合作对策,奠定了一定的基础。     

顾客参与研发过程的价值共创机理与策略研究

顾客参与企业研发是产品价值创造的最初始过程,不仅提高产品接受度、满足顾客需求,而且为企业增加收入,但同时也产生相应成本。文章探究顾客参与研发的系统中,顾客、企业和产品的价值共创行为以及企业决策如何影响三者价值;立足多目标视角,充分考虑企业与顾客的收益、成本,采用系统动力学方法建立顾客参与研发过程的动态价值共创模型,全面探究系统内部共创机理。在模型基础上,重点就企业产品价格、交互次数以及激励资金比例等策略进行仿真,使企业、顾客及产品实现价值共创。结论如下:(1)随着顾客、企业交互次数的增多,顾客参与研发过程同样具备一般产品生命周期导入期、成长期、成熟期以及衰退期的特点。(2)系统存在最优交互次数;且最优交互次数随着研发投入比例减少而增加。(3)在不考虑参与顾客获取激励资金的情况下,企业针对不同顾客群(参与研发顾客与普通购买顾客)进行定价,在最优交互次数状态下,统一定价模式优于差别定价模式,将为企业带来更大的收益。