An asymptotically optimal lower bound on the OBDD size of the middle bit of multiplication for the pairwise ascending variable order

We prove that each OBDD (ordered binary decision diagram) for the middle bit of n-bit integer multiplication for one of the variable orders which so far achieve the smallest OBDD sizes with respect to asymptotic order of growth, namely the pairwise ascending order x₀,y₀,…,x_n−1,y_n−1, requires a size of Ω(2^(6/5)n). This is asymptotically optimal due to a bound of the same order by Amano and Maruoka (2007) [1].     

Minimal clones generated by majority operations

The minimal majority functions of the four-element set are determined. Received October 10, 1997; accepted in final form February 8, 2000.     

Flexibility across and flexibility within: The domain of integer addition and subtraction

To better understand the role that flexibility plays in students’ success on integer addition and subtraction problems, we examined students’ flexibility when solving open number sentences. We define flexibility as the degree to which a learner uses more than one strategy to solve a single task when prompted, as well as the degree to which a learner changes strategies when solving a range of tasks to accommodate task differences. We introduce the categorizations of flexibility within and flexibility across to distinguish these two ways of operationalizing flexibility. We examined flexibility and performance within and among three groups of students — 2nd and 4th graders who had negative numbers in their numerical domains, 7th graders, and college-track 11th graders. Profiles of five students are shared to provide insight in relation to the quantitative findings.     

一些双联运算图的规范拉普拉斯谱

研究了基于剖分图、Q-图、R-图和全图的双联运算图的四类变型,给出了它们的规范拉普拉斯谱.所得结果推广了关于图的联运算的一些已有结果.     

基于随机共振的2PSK信号相干接收误码率的研究*

针对在信道环境恶劣的情况下,数字信号接收端的误码率较高的问题,提出一种基于自适应参数调节双稳随机共振系统降低误码率的新方法,得到了输入信噪比小于0db、相干解调接收二进制相移键控信号(binary phase shift keying,简记为2PSK)条件下,系统误码率与输入信噪比的仿真曲线。研究表明：通过非线性双稳系统的2PSK在输入信噪比达到-7.4db时较传统线性解调系统误码率可降低20.1%,这正是对2PSK信号在信道环境恶劣情况下传输的一个补充,对数字带通信号传输具有一定的参考价值。     

双需求集货送货一体化车辆路径问题的数学模型及算法

本文研究了具有总时间和车容量约束的双需求集货送货一体化车辆路径问题,在综合考虑运输费用和车辆出行固定费用的前提下,建立了该问题的整数线性规划模型,并分别给出了求解该模型的精确算法和基于节约准则的启发式算法。最后通过一个具体实例验证了算法的有效性。     

决策模糊集覆盖系数的实用计算方法

研究了经济学中广泛应用的决策模糊理论中模糊集覆盖系数的性质,并据此提出了无须通过繁杂的统计实验就能够计算覆盖系数的实用方法,进而提出了模糊集交并运算算子.用两个算例说明了该方法和算子与实际情形相符,具有可行性.     

Validating vehicle routing zone construction using Monte Carlo simulation

The primary purpose of this paper is to validate a clustering procedure used to construct contiguous vehicle routing zones (VRZs) in metropolitan regions. Given a set of customers with random demand for pickups and deliveries over the day, the goal of the design problem is to cluster the customers into zones that can be serviced by a single vehicle. Monte Carlo simulation is used to determine the feasibility of the zones with respect to package count and tour time. For each replication, a separate probabilistic traveling salesman problem (TSP) is solved for each zone. For the case where deliveries must precede pickups, a heuristic approach to the TSP is developed and evaluated, also using Monte Carlo simulation. In the testing, performance is measured by overall travel costs and the probability of constraint violations. Gaps in tour length, tour time and tour cost are the measure used when comparing exact and heuristic TSP solutions.