基于Nie-Tan算法的区间二型模糊集质心计算:改变主变量采样个数

计算区间二型模糊集的质心(也称降型)是区间二型模糊逻辑系统中的一个重要模块。Karnik-Mendel(KM)迭代算法通常被认为是计算区间二型模糊集质心的标准算法。尽管如此,KM算法涉及复杂的计算过程,不利于实时应用。在各种改进类算法中,非迭代的Nie-Tan(NT)算法可节省计算消耗。此外,连续版本NT(CNT,continuous version of NT)算法被证明是计算质心的准确算法。本文比较了离散版本NT算法中求和运算和连续版本NT算法中求积分运算,通过四个计算机仿真例子证实了当适度增加区间二型模糊集主变量采样个数时,NT算法的计算结果可以精确地逼近CNT算法。     

一类正交空间填充设计的构造

空间填充设计在计算机试验中应用十分广泛,当拟合回归模型时,正交的空间填充设计保证了因子效应估计的独立性.基于广义正交设计,文章给出了构造二阶正交拉丁超立方体设计和列正交设计的方法,新构造的设计不仅满足任意两列之间相互正交,还能保证每一列与任一列元素平方组成的列以及任两列元素相乘组成的列都正交.当某些正交的空间填充设计不存在时,具有较小相关系数的近似正交设计可作为替代设计使用.设计构造的灵活性为计算机试验在实践中的广泛应用提供了必要的支持.     

Fast computation of generic bivariate resultants

We prove that the resultant of two “sufficiently generic” bivariate polynomials over a finite field can be computed in quasi-linear expected time, using a randomized algorithm of Las Vegas type. A similar complexity bound is proved for the computation of the lexicographical Gröbner basis for the ideal generated by the two polynomials.     

Fast amortized multi-point evaluation

The efficient evaluation of multivariate polynomials at many points is an important operation for polynomial system solving. Kedlaya and Umans have recently devised a theoretically efficient algorithm for this task when the coefficients are integers or when they lie in a finite field. In this paper, we assume that the set of points where we need to evaluate is fixed and “sufficiently generic”. Under these restrictions, we present a quasi-optimal algorithm for multi-point evaluation over general fields. We also present a quasi-optimal algorithm for the opposite interpolation task.     

Students’ Reasoning About One-Object Stochastic Phenomena in an ICT-Environment

This paper focuses on the different ways in which students in lower secondary school (14–16 year olds) experience compound random events, presented to them in the form of combined junctions. A carefully designed ICT environment was developed enabling the students to interact with different representations of such structures. Data for the analysis was gathered from two interview sessions. The analysis of the interaction is based on constructivist principles on learning; i.e. we adopted a student-oriented perspective, taking into consideration the different ways students try to make sense of chance encounters. Our results show how some students give priority to geometrical and physical concerns, and we discuss how seeking causal explanations of random phenomena may have encouraged this. With respect to numerically oriented models a division strategy appears to stand out as the preferred one.     

Batching deteriorating items with applications in computer communication and reverse logistics

We study two deterministic scheduling problems that combine batching and deterioration features. In both problems, there is a certain demand for identical good quality items to be produced in batches. In the first problem, each batch is assigned an individual machine that requires a cost and a time to be activated. All the machines are identical, work in parallel, and always produce good quality items. All the items are available at time zero and they deteriorate while waiting for production. Deterioration results in a linear increase of time and cost of production. In the second problem, there is a single machine that produces good quality as well as defective items in batches. Each batch is preceded by a setup time and requires a setup cost. Defective items have to be reworked on the same machine. They deteriorate while waiting for rework. At a time to be decided, the machine switches from production to rework defective items of the current batch. After rework, every defective item has the required good quality. In both problems, the objective is to find batch partitioning such that a linear combination of the production cost and production completion time is minimized. The two problems are observed at computer service providers and also reverse logistics. In computer service providers, machines and items correspond to communication service channels and information transfer tasks, respectively. We reduce both problems to minimizing a function of one variable representing the number of batches. In an optimal solution of either problem, there are at most two different batch sizes. Linear time algorithms are proposed for both problems.     

Error estimation in measuring strain fields with DIC on planar sheet metal specimens with a non-perpendicular camera alignment

The determination of strain fields based on displacement components obtained via 2D-DIC is subject to several errors that originate from various sources. In this contribution, we study the impact of a non-perpendicular camera alignment to a planar sheet metal specimen's surface. The errors are estimated in a numerical experiment. To this purpose, deformed images - that were obtained by imposing finite element (FE) displacement fields on an undeformed image - are numerically rotated for various Euler angles. It is shown that a 3D-DIC stereo configuration induces a substantial compensation for the introduced image-plane displacement gradients. However, higher strain accuracy and precision are obtained - up to the level of a perfect perpendicular alignment - in a proposed “rectified” 2D-DIC setup. This compensating technique gains benefit from both 2D-DIC (single camera view, basic amount of correlation runs, no cross-camera matching nor triangulation) and 3D-DIC (oblique angle compensation). Our conclusions are validated in a real experiment on SS304.     

基于标准互相关函数的图像分辨率自动标定方法

理想规则图像特征经标准互相关函数匹配后,相似函数C*(x)可用确定的解析式Z(x)表达.但是对于含噪声图像,相似函数C(x)较之C*(x)发生了变化,但存在"零相似不变性".将此原理应与于显微视觉中图像物面分辨率的在线标定,推导了矩形图像特征的一维相似函数解析式Z(x);求解C(x)=0作为Z(x)的近似,并给出了具体标定算法;通过仿真图像实验,给出标定算法的正确度在0.1～0.2 pixel;最后,将标定算法应用于可连续变焦的微对准装配系统,实测算法的精密度可达为0.08 pixel.实验结果表明,基于"零相似不变性"的标定算法是具有实用性的亚像素标定方法.～290nm波长激发下,310～390nm范围内产生荧光光谱,峰位波长在350nm,最佳激励波长为250nm;采用垂直偏振片(起偏角为0°)起偏照射样品,发现偏振荧光峰位不变,荧光峰强度随检偏角的增大而呈明显的线性递减关系.由实验数据计算得到荧光偏振度为0.783,表明分子具有一定确定取向;另外,分析认为酸性橙Ⅱ产生荧光,是由于分子中含有苯环和萘环结构吸收紫外光能量,以及氮键在光子作用下形成顺式异构体的激发单线态后,两者发射的光子所致.整个结果对酸性橙Ⅱ在食品中的违禁使用检测、特性表征、以及分子规律的更深入研究,有一定的参考价值.     

An improved broad-spectrum room acoustics model including diffuse reflections

More and more literature has paid attention to the diffuse reflections in enclosed space during the past few years. In this paper, the current computer models including diffuse reflections have been reviewed briefly at first. Then, to realize the broad-spectrum simulation for enclosed sound fields including diffuse reflections, an improved ray-tracing algorithm, which combines the splitting coefficient diffusion model and a dynamic sound ray receiving method, has been given. The algorithm can deal with broad frequency bands simultaneously by using the frequency independent splitting coefficient. To test the algorithm and also to investigate the significance of the diffuse reflections in enclosed sound fields, experiments have been made in three spaces including a virtual room and two real rooms. The results and discussions have validated the applicability of the improved algorithm and they have also shown that diffuse reflections can improve room acoustic prediction, although it not always promote a sound field to be more diffused.     

Teacher and students’ joint production of a reversible fraction conception

Within a constructivist perspective, I conducted a teaching experiment with two fourth graders to study how a teacher and students can jointly produce the reversible fraction conception. Ongoing and retrospective analysis of the data revealed the non-trivial process by which students can abstract multiplicative reasoning about fractions. The study articulates a conception in a developmental sequence of iteration-based fraction conceptions and the teacher’s role in fostering such a conception in students.