基于灰作用量优化的分数阶灰色预测模型研究

针对小样本振荡型数据序列的灰建模预测问题,提出基于灰作用量优化的分数阶GM(1,1|sin+cos)预测模型.在已有经典GM(1,1|sin)的基础上,一方面,将一阶累加灰生成拓展为分数阶累加灰生成,使得构建的模型更加符合新信息优先原理.另一方面,将灰作用量b_1 sin pk+b_2改进为b_1 sin pk+b_2 cos qk+b_3,其作用是通过增加余弦函数项cos qk,使得具有两个不同周期的运动项cos qk与b_1 sin pk+b_2叠加复合之后,能够生成更加贴近于振荡原始序列趋势和特征的时间响应序列,从而得到拟合精度较高的灰色模型.其次,对建模过程的时间响应式、模型参数p和q的最优估计问题进行了研究,构造了最优累加阶数r、参数p和q的粒子群优化算法,得到的优化模型实现了某些类型振荡序列较高精度的预测.实际数据例子结果表明,所建立的模型能够较好地模拟常见振荡型数据序列的波动趋势和特征,具有较强的适用性和拟合性能.     

Slice filtration on motives and the Hodge conjecture (with an appendix by J. Ayoub)

We clarify the expected properties of the slice filtration on triangulated motives from the point of view of the generalized Hodge conjecture. In the appendix, J. Ayoub proves unconditionally that the slice filtration does not respect geometric motives. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal lot size model for deteriorating items with demand rate dependent on displayed stock level (DSL) and partial backordering

In this paper, we consider the problem of determining the lot size of a single deteriorating item with the demand rate dependent on displayed stock level, selling price of an item and frequency of advertisement in the popular electronic and print media, also through the sales representatives. Shortages, if any, are allowed and partially backlogged with a variable rate which depends on the duration of waiting time upto the arrival of next lot. Here, the transportation cost for replenishing the goods is considered explicitly and the storage capacity of the showroom/shop is assumed to be limited (finite). According to the relative size of the stock level dependency demand parameters and the storage capacity of the showroom/shop, different scenarios with sub scenarios have been mentioned and solved with the help of GRG (generalised reduced gradient) method and the computational procedure. The convexity analysis is done by showing the average profit function in each case as pseudo concave. To illustrate the results and its significant features, a numerical example is given. Finally, to study the effect of changes of demand parameters, deterioration, backlogging parameters and mark-up rate on the maximum initial stock level, shortage level, frequency of advertisement per cycle along with the maximum average profit are presented numerically.     

Inventory rationing in an (<Emphasis Type="Italic">s,Q</Emphasis>) inventory model with lost sales and two demand classes

Whenever demand for a single item can be categorised into classes of different priority, an inventory rationing policy should be considered. In this paper we analyse a continuous review (s, Q) model with lost sales and two demand classes. A so-called critical level policy is applied to ration the inventory among the two demand classes. With this policy, low-priority demand is rejected in anticipation of future high-priority demand whenever the inventory level is at or below a prespecified critical level. For Poisson demand and deterministic lead times, we present an exact formulation of the average inventory cost. A simple optimisation procedure is presented, and in a numerical study we compare the optimal rationing policy with a policy where no distinction between the demand classes is made. The benefit of the rationing policy is investigated for various cases and the results show that significant cost reductions can be obtained.     

Comment on “Existence and stability of periodic solution of a Lotka-Volterra predator-prey model with state dependent impulsive effects” [J. Comput. Appl. Math. 224 (2009) 544-555]

In this paper, according to integrated pest management principles, a class of Lotka-Volterra predator-prey model with state dependent impulsive effects is presented. In this model, the control strategies by releasing natural enemies and spraying pesticide at different thresholds are considered. The sufficient conditions for the existence and stability of the positive order-1 periodic solution are given by the Poincaré map and the properties of the LambertW function.     

On Numerically Implementable Explicit Formulas for the Solutions to the 2D and 3D Equations $$operatorname{div}(alpha(w)nabla w)=0$$ and $$operatorname{div}(betanabla w)=0$$ with Cauchy Data on an Analytic Boundary

Functional Analysis and Its Applications - A construction of numerically implementable explicit expressions for the solutions of the two- and three-dimensional equations...     

Biorthogonal exponential sequences with weight function on the real line and an orthogonal sequence of trigonometric functions

Some orthogonal functions can be mapped onto other orthogonal functions by the Fourier transform. In this paper, by using the Fourier transform of Stieltjes-Wigert polynomials, we derive a sequence of exponential functions that are biorthogonal with respect to a complex weight function like on . Then we restrict these introduced biorthogonal functions to a special case to obtain a sequence of trigonometric functions orthogonal with respect to the real weight function on .