关键词： Algebraic Particle Swarm Optimization   Permutation Problems   Permutation Search Space  

摘要： Particle Swarm Optimization (PSO), though originally introduced for continuous search spaces, has been increasingly applied to combinatorial optimization problems. In this paper, we focus on the PSO applications to permutation-based problems. As far as we know, the most popular and general PSO schemes for permutation solutions are those based on random key techniques. After highlighting the main criticalities of the random key approach, we introduce a discrete PSO variant for permutation-based optimization problems. By simulating search moves through a vector space, the proposed algorithm, Algebraic PSO (APSO), allows the original PSO design to be applied to the permutation search space. APSO directly represents both particle positions and velocities as permutations. The APSO search scheme is based on a general algebraic framework for combinatorial optimization based on strong mathematical foundations. However, in order to make this new scheme viable, some challenges have to be overcome: the choice of the order of the velocity terms, and the rationale behind the PSO inertial move. Design solutions have been proposed for both the issues. Furthermore, an alternative geometric interpretation of classical PSO dynamics allows to introduce a major APSO variant based on a novel concept of convex combination between permutation objects. In total, four APSO schemes have been introduced. Experiments have been held to compare the performances of the APSO schemes with respect to the random key based PSO schemes in literature. Widely adopted benchmark instances of four popular permutation problems have been considered. The experimental results clearly show that, with high statistical evidence, APSO outperforms its competitors and it reaches results comparable with state-of-the-art on most of the instances considered.

关键词： 小学数学   数的运算   计算   算理  

摘要： "数"在我们生活中无处不在,"数的运算"更是人们生活中应用最多的数学知识,因此"数的运算"是小学数学教学的重要内容之一。在新课标中提出,运算能力已成为了小学生数学能力的核心要素,而它是在正确计算的基础上提出的更高要求,所以在计算教学时,教师需要在算法和算理之间架起一座桥梁,使学生明晰各个知识点之间的联系,从而真正理解算理。

关键词： 小学数学   算理与算法   融合策略  

摘要： "数与代数"知识是小学数学学科的基本内容,而数的运算活动也必将伴随着小学生的数学学习过程。其中,算理反映的是数的运算规律,解决的是"为什么这样算"的问题,而算法则是计算方法与准则,解决的是"如何运算"这一问题。因此,小学数学教师要积极整合算理与算法,全面优化小学生的数感与计算能力,促使小学生利用数的运算知识来迁移数学知识,把握数量关系的运算规律。本文将从丰富动手操作活动,显化算理,引出算法;组织迁移活动,引导学生掌握算理与算法;突出算理内涵,以算法验证算理三个角度来分析小学数学教师应该如何整合算理与算法。

关键词： 无网格法   数值传热   拉氏粒子模型   SPH  

摘要： 随着我国经济的快速发展,煤炭、石油等能源资源日益紧缺,对工业生产提出了更高的要求。作为节约资源的有效途径之一,热量的高效利用已经得到了全社会的广泛关注。如何高效精确地模拟数值传热问题,把握热量的传导量、传导速度、传导范围等规律以及温度分布场状况,对于节约能源资源和指导工业生产具有重大意义。目前,各种数值分析与计算方法已经被广泛应用于数值传热学研究中,宏观上可以分为网格方法与无网格方法两类。其中,无网格方法不依赖于网格的预先设定,避免了因网格重构或网格畸变所带来的精度损失,在处理瞬态及较大形变问题时具有明显的优势。因此,本文重点研究无网格方法的典型代表——光滑粒子流体动力学方法(smoothed particle hydrodynamics,SPH)及其改进算法——对称光滑粒子流体动力学方法(symmetric smoothed particle hydrodynamics,SSPH),新方法成功应用于模拟数值传热中。本文提出了二阶SSPH(SO-SSPH)方法,并利用一阶SSPH(FO-SSPH)和二阶SSPH(SO-SSPH)方法对间断分布热源传导问题进行模拟,同时对两种方法的截断误差、精度、稳定性条件以及收敛性进行了理论分析。实验结果表明,SO-SSPH方法能够有效消除FO-SSPH方法在模拟间断分布热源传导问题时出现的非物理振荡现象,并且是二阶收敛的。其次,考虑到数值传热的对流影响,本文模拟了二维情形下的热对流传导问题。为了充分说明无网格方法SPH的优势,文中选用对流占优问题,并对传热系统施加横向均匀、斜向均匀、匀速旋转等不同类型的速度场。实验结果表明,SPH方法是处理对流占优问题的有效数值工具。最后,进一步考虑不同物质之间反应所产生的影响,本文提出了热对流反应问题的拉氏粒子数学模型,并对反应系统中各个物质的浓度进行了计算。实验结果表明,拉氏粒子数学模型能够避免网格方法模拟结果中的数值振荡,尤其是在涉及多种物质之间反应的时候。

关键词： 老年   慢性肾脏病   血清肌酐   血清胱抑素C   全年龄段公式   老年   血清肌酐   血清胱抑素   肾功能   数学算法   估算公式   慢性肾脏病   血清肌酐   血清胱抑素C   支持向量回归算法  

摘要： 背景:肾小球滤过率（GFR）是诊断慢性肾脏病（CKD）并对其危险分层的关键指标,是药物调整和术前准备的重要参考。GFR估算公式已经在临床广泛应用,且不断更新,准确性日渐提高,适用性逐渐普遍,并开始细分适用人群,分别出现了儿童公式和成人公式。然而,在我们前期的研究中,发现这些成人公式并不适合我国老年人。2016年,欧洲Pottel H等学者发起,欧洲多家医疗中心参与,新建了全年龄段（FAS）系列公式。该公式是否可用于我国的老年人,尚未得到验证。为此,我们开展了FAS系列公式在我国老年人中适用性评价。 方法:本研究以99mTc-DTPA肾动态显像法测定GFR作为GFR参考值（r GFR）,使用颗粒增强免疫比浊法检测血清胱抑素C（Scys）,氧化酶法测定血清肌酐 （Scr）,验证CKD-EPI公式与FAS公式的准确性。以60岁为界,将入选受试者分为非老年组和老年组。以偏差、偏倚度、P30、均方根误差等评价FAS系列公式的准确性。 结果:来自南京医科大学第一附属医院（江苏省人民医院）、中山大学第三附属医院、南京医科大学附属无锡第二医院（无锡市第二人民医院）和吉林大学第四医院四个中心的1329名受试者入组本研究。老年组平均年龄70岁,肾功能较非老年组组明显下降,r GFR中位数是51.79ml/min/1.73m2。由CKD-EPI系列公式和FAS系列公式估算的GFR值与标准方法（核素肾动态显像法）测定的GFR在相关性比较中,均较为相近,大部分R值大于0.8。老年组的相关性略高于非老年组,联合指标组的相关性高于单纯胱抑素组。由这两类公式估算的GFR值与参考GFR值均存在一定的离散度,在老年人群中更加突出。与单纯胱抑素公式相比,CKD-EPIScr-Scys和FASScr Scys公式的离散度相对降低,P30和均方根误差均提示联合公式优于单纯胱抑素公式。而在比较CKD-EPIScr-Scys和FASScr-Scys公式之间的准确性,可以看到二者相近。 结论:FAS系列公式评估我国老年人的GFR的准确性与CKD-EPI公式相近,并无显著优势,考虑FAS系列公式仍存在种族、GFR参考方法及人群种族的自身特点。因此,建立适合本地区人群的GFR估算模型显得非常必要。

关键词： Accounting   Artificial intelligence  

摘要： Fraud is everywhere. Sometimes it is minuscule, and other times, it is massive, but make no mistake it is everywhere in every industry, no business or industry is immune. The difference between ignorance, errors, and fraud is simply intent. Furthermore, the devastation that it can cause has been felt for many years after the fact. However, the problem that exists is that auditors and accountants are needed to keep businesses in line and the public safe, but in reality, they do not have the tools for that to be possible. Auditors are not aware of the latest uses for existing technology, mathematical algorithms, and Artificial Intelligence. The qualitative case study design of the research delivers a trail to follow of what, why, where, and how fraud exists, the history, the research, the findings, and the possibilities for the future. The themes that developed were similar to the findings from other researchers; auditors are unaware of the uses of mathematical algorithms and artificial intelligence during financial statement audits. They also do not have any knowledge of the capabilities of the technology. Both of these items can be useful during financial statement audits to discover immaterial fraud that when aggregate is material. In the future these tools need to be evaluated and a packet of tools developed that can run through the entire list of financial transactions looking for areas that need further research for possible fraud.

关键词： 高中数学   学习   算法思想  

摘要： 在高中数学知识的学习中,算法可以说是其中非常重要的一项内容,对实际数学问题的求解具有积极的意义.本文将就高中数学学习中的算法思想进行一定的研究.

关键词： 数学   算法教学  

摘要： 数学课涉及知识广,逻辑性强,对技校学生而言,数学课是一门比较头痛的学科,学习难度大。本文以高教版数学(职业模块)教材的算法知识点教学为例,从课前准备到课堂教学,多个方面入手,点燃学生的学习激情,找回学习的自信心,提高学习效率,达到预期教学目标。

关键词： Hub-and-spoke network (H-SN)   container shipping   backup port   alternative routes   genetic algorithm (GA)   reliable hub location problem  

摘要： In container shipping, the carrier may suffer substantial economic losses arising from hub failures and reactive disruption management. To solve the problem, this paper proposes a new mathematical model for the reliable hub-and-spoke network (H-SN) design, which allows multiple calls on hub-level routes and involves multiple allocation modes under multiple hub failures. The integrated model considers hub location, backup ports configuration and vessel rerouting at the same time. Next, a genetic algorithm (GA)-based method was designed to find the optimal solutions to the 0-1 nonlinear programming model in an efficient manner. After that, several computational experiments were conducted using real data. The results show that the proposed formulations and algorithm were feasible, and the integrated model could save operating cost and enhance service quality. The research findings shed new light on the network design for container shipping in maritime transport.

关键词： 高中数学   课堂教学   范例教学   算法案例  

摘要： 在高中数学课堂教学中,应用范例教学的前提是根据教学内容及其特性精选示范材料,突出范例中的方法,在此基础上,设计范例教学的课堂应用,让学生通过汲取成功经验、借鉴成功方法,提高学习的有效性。本文以"算法案例"一课为例,探讨了范例教学的课堂设计。