A multiple imputation method for incomplete correlated ordinal data using multivariate probit models

The multiple imputation technique has proven to be a useful tool in missing data analysis. We propose a Markov chain Monte Carlo method to conduct multiple imputation for incomplete correlated ordinal data using the multivariate probit model. We conduct a thorough simulation study to compare the performance of our proposed method with two available imputation methods – multivariate normal-based and chain equation methods for various missing data scenarios. For illustration, we present an application using the data from the smoking cessation treatment study for low-income community corrections smokers.     

Total shift during the first passages of Markov-modulated Brownian motion with bilateral ph-type jumps: Formulas driven by the minimal solution matrix of a Riccati equation

This article describes our study of the total shift during the first passages (one-sided and two-sided exit times) of Markov-modulated Brownian motion with bilateral ph-type jumps, which is referred to as MMBM. The total shift is defined as the value of a so-called shift process at the first passage epochs of the MMBM. The shift process, introduced by Bean and O’Reilly, behaves like a continuous Markovian fluid process; that is, it increases or decreases linearly with slopes regulated by the underlying Markov process that determines the path of the MMBM. Hence, the notion of total shift, which includes the first passage times of the MMBM as special cases, is useful for describing various performance measures of systems modeled by the MMBM. In this article, we present formulas for the Laplace–Stieltjes transform matrices of the total shift during various first passages of the MMBM. In particular, a Riccati equation is derived so that a matrix associated with the Laplace–Stieltjes transform of the total shift during the first return time of the MMBM is its minimal non-negative solution matrix. With this solution matrix, the Laplace–Stieltjes transform matrices can be obtained without much additional work. Furthermore, it is shown that the Riccati equation satisfies the conditions for the Newton scheme to have quadratic convergence, which enables us to use algorithms with quadratic convergence, such as Newton’s method and the Stochastic Doubling Algorithm, to compute the presented matrix-driven formulas. For the analyses, we take an approach based on approximating the MMBM with a sequence of scaled Markov-modulated fluid flows with bilateral ph-type jumps, referred to as MMFF, that weakly converge to the MMBM. Another contribution of this article is that duality results are derived in relation to the MMBM, which is an extension of the duality theorems developed by Ahn and Ramaswami for an MMFF without a jump.     

混合碳政策下两产品供应链的协同研究

本文在碳税-碳交易并行的混合碳政策下，面对存在低碳偏好的市场，以单一制造商和零售商组成的二级供应链为研究对像，考虑其生产和销售存在一定竞争关系或替代关系的两种不同产品时，供应链企业的最优定价和减排决策，并改进收益共享契约，提出通过构造同解方程进行契约设计的新思路。研究发现，制造商和零售商采用改进的收益共享契约可以使得自身利益实现帕累托改进，并确保供应链的整体利润达到帕累托最优，而契约中的收益共享金额主要取决于双方的溢价能力和其在供应链中的地位，只要它在特定范围内波动，供应链就可以实现协同。最后，利用数值例子验证了上述结论。     

Study on Multi-Trip Vehicle Routing Problem with Stochastic Simultaneous Pickup-Delivery Demand

Characterized by high service efficiency and low vehicle cost, multi-trip distribution allows the vehicle to travel multiple times between the distribution center and customers in order to complete the delivery task. Dynamic and uncertain customer demand is common during delivery. Combined pickup-delivery integration pattern with stochastic customer demand, an optimization model for multi-trip vehicle routing problem is set up with stochastic simultaneous pickup-delivery demand. Due to the sudden and simultaneous pickup-delivery of dynamic demand, the original distribution scheme needs to be optimized and adjusted, and the multi-trip routing adjustment strategy of "real-time flexible point" is proposed. According to the stochastic characteristics of the optimization model, a stochastic chance-constrained programming transformation model is introduced. A hybrid algorithm with nested stochastic simulation and variable neighborhood tabu search algorithm is designed to find the optimal distribution path. Finally, an example shows that the optimization model and algorithm are feasible and effective.     

关于丢番图方程x~3±5~3=3py~2的整数解

设p为奇素数,运用同余式、平方剩余等初等方法得出了丢番图方程x3±53=3py2无正整数解的两个充分条件.     

On Transition and First Hitting Time Densities and Moments of the Ornstein–Uhlenbeck Process

This paper derives transition and first hitting time densities and moments for the Ornstein–Uhlenbeck Process (OUP) between exponential thresholds. The densities are obtained by simplifying the process via Doob’s representation into Brownian motion between affine thresholds. The densities in this paper also offer easy-to-use and fast small-time approximations for the densities of OUP between constant thresholds given that exponential thresholds are virtually constant for a small time. This is of interest for estimation with high-frequency data given that extant approaches for constant thresholds impose a large demand on computing power. The moments of the transition distribution up to order n are derived within a closed-form recursive formula that offers valuable information for management. Expressions for the moments of the first hitting time distribution are also obtained in closed form by simplifying integrals via series expansions.     

关于线性二次型调节器次最优控制模型和方法的研究

讨论了解决线性二次型调节器系统的次最优方案，目的是要确定一个相对易改进的线性反馈规律，它可导出接近的最优系统指标用这种方法，次最优线性调节器问题被精确公式化，并导出了其解的必要条件     

具有整体单极黑洞的Hawking辐射

利用零标架,采用Tortoise 坐标,在具有整体单极时空中,将Dirac 方程在事件视界附近化为波动方程,并得到了出射波和入射波,导出了Hawking 温度和Dirac 粒子的热谱公式.结果表明Hawking 温度不仅依赖于黑洞的质量,而且还依赖了对称自发破缺标度.     

基于结构方程的知识型服务质量的评价方法

本文论述了结合知识型服务业的特点，构建知识型服务业的服务质量评价体系的问题。通过对现有服务质量评价方法的比较分析，在SERVQUAL模式基础上，提出了基于结构方程模型的知识型服务质量评价方法，且从数据处理技术与测评平台建设等方面探讨了测评体系的实施。     

破解绘画色彩选择的两个障碍

在色彩写生中，能够引起人们审美愉悦、满足人们生理、心理需求的真实绘画色彩的道路上存在着许多障碍，其中“固有色观念”和“局部观察习惯”是经常碰到的易犯病。