Fractional Order Iteration for Gradient Descent Method Based on Event-Triggered Mechanism

In this work, a novel gradient descent method based on event-triggered strategy has been proposed, which involves integer and fractional order iteration. Firstly, the convergence of integer order iterative optimization method and the stability of its associated system with integrator dynamics are linked. Based on this result, a fractional order iteration approach has been developed by modelling the system with fractional order dynamics. Secondly, to reduce the comsumption of computation, a feedb...     

A Mathematical Model of Real-Time Simulation and the Convergence Analysis on Real-Time Runge-Kutta Algorithms

In this paper, a mathematical model of real-time simulation is given, and the problem of convergence on real-time Runge-Kutta algorithms is analysed. At last a theorem on the relation between the order of compensation and the convergent order of real-time algorithm is proved.     

ACCURACY ANALYSIS FOR QUASI-CAREY ELEMENT*

In this paper, a new triangular element （Quasi-Carey element） is constructed by the idea of Specht element. It is shown that this Quasi-Carey element possesses a very special property, i.e., the consistency error is of order O（h^2）, one order higher than its interpolation error when the exact solution belongs to H^3（Ω）. However, the interpolation error and consistency error of Carey element are of order O（h）. It seems that the above special property has never been seen for other triangular elements for the second order problems.     

Stochastic comparisons in a price-quantity setting firm with uncertain demand and emergency procurement

We consider a newsvendor problem with price-dependent demand, in either additive or multiplicative format. The newsvendor has two modes of purchasing： regular ordering at the beginning of the selling season and emergency ordering （if the realized demand exceeds the initial order quantity） at the end of the selling season. By stochastic comparisons, we systematically investigate the effects of demand magnitude and demand randomness on pricing and ordering quantity decisions as well as expected profit of the newsvendor, under both usual stochastic order （first order stochastic dominance） and convex order （less variable）. Our key findings include： （i） in contrary to the case where price is exogenous, a stochastically larger demand shock may even lead to a lower order quantity; （ii） a stochastically larger demand shock leads to a higher price for the additive demand case, but may lead to a lower price for the multiplicative demand case; （iii） a stochastically larger demand shock leads to a higher expected profit for both demand models; （iv） in general, a less variable demand leads to a higher expected profit for both demand models; and furthermore, a less variable demand shock has no effect on price for the additive demand model, but leads to a higher price for the multiplicative demand model. The implications of all these findings for pricing and order quantity are discussed in detail.     

PACKING A TREE OF ORDER p WITH A （p,p＋1）—GRAPH

Let G1 and G2 be two graphs of the same order,If G1 is isomorphic to a spanning subgraph of the complement of G2,then we say that G1 and G2 are packable.A graph G is called a (p,m)-graph if G has p vertices and m edges.The main purpose of this paper is to present a necessary and sufficient condition for a tree of order p and a (p,p 1)-graph to be packable.     

Collaborative supply chain planning under dynamic lot sizing costs with capacity decision

Studies show that supply chain cooperation improves supply chain performance. However, it remains a challenge to develop and implement the realistic supply chain cooperation scheme. We investigate a two-echelon supply chain planning problem with capacity acquisition decision under asymmetric cost and demand information. A simple negotiation-based coordination mechanism is developed to synchronize production/order strategies of a supplier and a buyer. The coordination scheme shows how the supplier and the buyer modify their production and order policy in order to find a joint economic lot sizing plan, which saves the overall supply chain cost. The allocation of the cooperation benefit is determined by negotiation. Due to the complexity of the multiple periods, multiple level supply chain lot sizing with capacity decision, a heuristic algorithm is developed to find coordination solutions. Finally, the results of the numerical study indicate the performance of supply chain coordination scheme.     

MINIMAL INVERSION AND ITS ALGORITHMS OF DISCRETE-TIME NONLINEAR SYSTEMS

The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.     

ON INVENTORY STRATEGIES OF ONLINE RETAILERS

1.Introduction This research focuses on online retailers(etailers,hereafter)who engage in the sale of physical goods.In general,the order fulfillment process of such an etailer can be depicted by Figure1.As presented in Figure1,a customer will place an order at the etailer’s website.Upon receipt of each order,the etailer will confirm whether or not stock is available to fulfill the order.Assuming that inventory is indeed available,the order will be packaged,after which it will be delivered …     

在线订餐生产配送联合调度模型及算法

The delays of online meal ordering delivery are currently serious. How to coordinate the production and distribution to minimize arrival time has become an urgent problem for online meal ordering during the peak period. Considering the fact that the order information are unknown in advance, a parallel machine production and multi-trip vehicle distribution joint optimization model was established to minimize the makespan of total orders. Besides, a three phase heuristic algorithm was proposed. Through a series of experiments where the orders were generated based on Poisson distribution (),the results were compared with those of the traditional algorithm. Several enlightening findings are discovered: when the order arrival rate, the makespan of total orders of the three phase heuristic algorithm is shorter. Meanwhile with the growth of order arrival rate, the improvement amplitude increases gradually. The model and algorithms proposed are conducive to generating efficiently production and distribution joint scheduling solution during the peak period.     

Distributed Solving Linear Algebraic Equations with Switched Fractional Order Dynamics

This paper proposes a novel distributed optimization algorithm with fractional order dynamics to solve linear algebraic equations. Firstly, the authors proposed “Consensus + Projection” flow with fractional order dynamics, which has more design freedom and the potential to obtain a better convergent performance than that of conventional first order algorithms. Moreover, the authors prove that the proposed algorithm is convergent under certain iteration order and step-size. Furthermore,the author...     

STRONG LAWS OF LIFETIME FOR A CONSECUTIVE K-OUT-OF-N: F SYSTEM

ＳＴＲＯＮＧＬＡＷＳＯＦＬＩＦＥＴＩＭＥＦＯＲＡＣＯＮＳＥＣＵＴＩＶＥＫ－ＯＵＴ－ＯＦ－Ｎ：ＦＳＹＳＴＥＭ￥ＱＩＹｏｎｇｃｈｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｇ，Ｂｅｉｊｉ...     

两类随机控制风险秩序的比较分析与应用

首先对比分析两类风险秩序：随机控制秩序与对偶随机控制秩序，得到关于风险本质特征的三个方面的刻画：(1)效用自由秩序等价于随机控制秩序；(2)畸变自由秩序等价于对偶随机控制秩序；(3)第一、第二阶随机控制秩序等价于相应的对偶随机控制秩序，但对高于三阶的情况不一定成立。其次，针对同单调风险给出了两个方面的应用：(1)确定了一类最优再保险合同；(2)给出了均衡净保费的相对不公平性的一个测度方法。     

中国股票市场限价指令等待成交时间的理论研究与实证分析

在中国指令驱动股票市场中,限价指令需要为成交付出等待成本,如何计量限价指令的等待成交时间是金融市场流动性及微观结构理论领域崭新的研究问题.研究表明,指令生存模型能够比较精确地描述限价指令的等待成交时间概率分布,实证检验结果表明,生存模型具有比较高的准确性;同时发现限价指令等待成交时间对委托价格很敏感,而对委托量不敏感;基于委托价格的敏感性分析绘制出了限价指令等待成交时间概率分布的价格全谱图,根据该图可以预测限价指令的等待成交时间,以及为指令提交策略提供定量分析基础.     

New estimates of trends in births by birth order in England and Wales

A greater understanding of past, present and future trends in fertility can be gained from analysing trends in birth order; that is whether a birth is a first, second, third or higher order birth. However, under current legislation, birth order information is not collected at registration for births outside marriage and birth order recorded within marriage is not the true birth order. This article presents revised and updated estimates of true birth order. It discusses the construction of the new estimates and presents analysis relating the births by true birth order to the population of women by parity on both a period (fertility in a particular year) and cohort (fertility of women born in a particular year) basis. The new true birth order figures are also compared to the previous set of estimates.     

∑-△调制器的高阶滑模设计

由于高阶滑模与传统滑模(一阶滑模)相比有更高的控制精度,把高阶滑模控制引入到∑-Δ调制器设计中来。在设计中,把高阶∑-Δ调制器看成一个带反馈的非线性动态系统,并把系统分成被控对象和控制器,然后应用高阶滑模进行控制设计。作为示例,用二阶滑模对三阶∑-Δ调制器进行了设计,仿真结果表明,基于高阶滑模控制设计的调制器信噪比高、量化误差小。     

含Caputo型分数阶导数的灰色预测模型

针对缺乏统计规律的小样本预测系统,如何挖掘其发展规律,一直是学术界的难点.本文依据分数阶微积分理论,将整数阶导数灰色模型推广到分数阶导数灰色模型,并从是否满足新信息优先原理、初值利用情况、还原误差大小和稳定性等方面说明了新模型的优势,以期用Caputo型分数阶导数的记忆性描述小样本预测系统.实例表明含有Caputo型分数阶导数的灰色预测模型的有效性与实用性.     

成比例分数阶系统的仿真研究

成比例分数阶系统是一种特殊的分数阶系统.这里提出将成比例分数阶系统的基本阶次项看作一个整体,成比例分数阶系统就转化成一个常规的整数阶系统.通过对成比例分数阶系统的基本阶次项进行近似化研究,减少了系统的复杂性.并用仿真实例进一步演示了该方法的简洁性,可以有效分析成比例分数阶系统问题.     

隐式两步混合法

本文构造了三类两步混合方法，其中一类为Ａ稳定的四阶隐式方法，一类为接近Ａ稳定的五阶隐式方法，最后一类为四阶预估－校正混合方法，其稳定区域在负实轴上超过了四级四阶Ｒｕｎｇｅ－Ｋｕｔａ方法的稳定区域，而每积分一步其右函数计算只需三次。对于这三类方法文中均作了精度阶、稳定性、收敛性等的分析，并讨论了四阶预估－校正混合方法的并行实现。     

机构投资者指令提交策略的影响因素

采用上海股票市场的数据,通过有序概率单位分析模型对机构投资者指令提交策略的影响因素进行事前分析。结果表明:对于买方投资者来说,指令的进取性与买方深度成正相关,与卖方深度成负相关;对于卖方投资者来说,指令的进取性与卖方深度成正相关,与买方深度成负相关。此外,买卖价差和波动性与指令的进取性成负相关关系。     

Combination Method for Parallel Computation in ODEs

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