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出土《算数书》初探 被引量:36
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作者 邹大海 《自然科学史研究》 CSSCI CSCD 北大核心 2001年第3期193-205,共13页
通过分析《算数书》的体例和结构,对照《算数书》 与《九章算术》,并结合其他文献和社会背景进行考察,得出以下结论:《算数书》是至少 有两个来源的撮编之书,它与《九章算术》没有直接的文本影响关系,它们在先秦可以追溯 到共同... 通过分析《算数书》的体例和结构,对照《算数书》 与《九章算术》,并结合其他文献和社会背景进行考察,得出以下结论:《算数书》是至少 有两个来源的撮编之书,它与《九章算术》没有直接的文本影响关系,它们在先秦可以追溯 到共同的来源,《九章算术》的主要方法产生于先秦,《算数书》是利用某种后来演变为《 九 章算术》主要来源的先秦数学著作或其衍生本的数学方法并结合下层官吏管理的实际而编成 的作品。《算数书》有助于确立先秦至秦汉实用算法式数学发展演变的历史。 展开更多
关键词 《算数书》 《九章算术》 先秦 秦朝 汉代 数学发展史
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从《算数书》和秦简看上古粮米的比率 被引量:7
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作者 邹大海 《自然科学史研究》 CSSCI CSCD 北大核心 2003年第4期318-328,共11页
《九章算术》、《说文解字》中关于几种粮米的记载互有异同 ,清代段玉裁等以前者校改后者 ,并认为在上古时稻和粟都可以舂出粝、、、御等一系列不同精度的米。现代学者则利用湖北云梦睡虎地出土的秦简和湖北江陵张家山出土的《算数... 《九章算术》、《说文解字》中关于几种粮米的记载互有异同 ,清代段玉裁等以前者校改后者 ,并认为在上古时稻和粟都可以舂出粝、、、御等一系列不同精度的米。现代学者则利用湖北云梦睡虎地出土的秦简和湖北江陵张家山出土的《算数书》对两者都有校订 ,但在后一问题上仍沿袭清儒的见解。文章在前人的基础上 ,对这些有关文献进行了新的审视 ,提出了新的校勘意见 ,指出《九章算术》和《说文解字》这两种传世文献中的错误比原来认为的要少 ,《说文解字》只有以为是后起的 ,《九章算术》只有米和饭之率是错误的 ,上古由粟、稻舂出的米分属两个不同的系列 ,不能混为一谈。《说文解字》和《九章算术》的作者都没有直接参考过《算数书》 ,后者也没有直接参考过秦简关于粮米比率的材料。 展开更多
关键词 上古粮米比率 《算数书》 睡虎地秦简 《九章算术》 《说文解字》 校勘
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从《算数书》盈不足问题看上古时代的盈不足方法 被引量:8
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作者 邹大海 《自然科学史研究》 CSCD 北大核心 2007年第3期312-323,共12页
盈不足方法是古代数学中一项具有一般性的重要方法。通过将《算数书》和《九章算术》及其他文献结合起来,探讨它在中国上古时代的形成与流传。认为:先秦时期实际工作中经常出现某种东西过多或过少的情况,为了得到合适的数量,人们通过运... 盈不足方法是古代数学中一项具有一般性的重要方法。通过将《算数书》和《九章算术》及其他文献结合起来,探讨它在中国上古时代的形成与流传。认为:先秦时期实际工作中经常出现某种东西过多或过少的情况,为了得到合适的数量,人们通过运用比、比例和分数的知识,找到了解决问题的盈不足方法。这种方法及其应用形成了先秦数学的一个科目——盈不足,并记载于《九章算术》在先秦的祖本中。受它直接或间接的影响,先秦到汉代的学者们根据需要设置了很多盈不足问题。《算数书》中的盈不足问题即由此而来。 展开更多
关键词 盈不足方法 《算数书》 《九章算术》 上古数学
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《算数书》“少广”“大广”二问的释读与校勘 被引量:4
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作者 纪志刚 《自然科学史研究》 CSCD 北大核心 2005年第3期229-235,共7页
对《算数书》“少广”术文进行释读与算法分析,同时与《九章算术》“少广”术进行对比,认为《算数书》的“少广”术正确地选用了“最小公倍数”进行分数通分。这一算法是在对“最小公倍数”的正确认识指导下完成的,表明在《算数书》的时... 对《算数书》“少广”术文进行释读与算法分析,同时与《九章算术》“少广”术进行对比,认为《算数书》的“少广”术正确地选用了“最小公倍数”进行分数通分。这一算法是在对“最小公倍数”的正确认识指导下完成的,表明在《算数书》的时代,中国古代数学的“最小公倍数算法”已经十分纯熟。《算数书》“大广”问中缺失的数字,一直为研究者所关注。在假定残文数字和文字无误的前提下,借助计算机的帮助,可以获得11种成立的可能;通过对《算数书》用语习惯和算法合理性的分析,确定其中2种是最可能的结果,从而为解决《算数书》“大广”问的校勘困难提出一种新的思路。 展开更多
关键词 《算数书》 少广术 最小公倍数 大广术
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《算数书》中的记数方法 被引量:1
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作者 王青建 张新立 《自然科学史研究》 CSCD 北大核心 2005年第3期222-228,共7页
《算数书》以竹简的原始形态验证了中国古代数学发展中的一些关键环节,记数方法就是一例。其中正整数、负数、分数的记载和表述方法与后世算书及其他国家和地区的记数法比较独具特色,其形式在一定程度上反映了先秦数学发展的某些特点。
关键词 《算数书》 记数法 整数 分数
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《算数书》“以睘材方”、“以方材睘”两问校证
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作者 段耀勇 邹大海 《自然科学史研究》 CSSCI CSCD 北大核心 2003年第2期168-172,共5页
张家山汉墓出土《算数书》中“以睘材方”、“以方材睘”两问是《算数书》校勘工作的难点之一。文章在分析前人校勘得失的基础上,采其所长,根据古人误认二问互逆、脱简等方面的情况,对二问文字进行了新的校勘。
关键词 “以方材Yuan” “以Yuan材方“ 《算数书》 校正 中国 古代数学
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张家山汉简《算数书》校证三题
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作者 吴朝阳 晋文 《自然科学史研究》 CSCD 北大核心 2013年第1期48-54,共7页
张家山汉简《算数书》中的"传马"、"缯幅"、"挈脂"三个算题虽然多位研究者已各有考论,但仍然存在错误及疑问。诸专家将"传马"题中"传马日二匹"中的"二匹"校改为"三匹... 张家山汉简《算数书》中的"传马"、"缯幅"、"挈脂"三个算题虽然多位研究者已各有考论,但仍然存在错误及疑问。诸专家将"传马"题中"传马日二匹"中的"二匹"校改为"三匹"是非常错误的,对"缯幅"题中"从利广"的校释也需要再作深入的讨论,而对"挈脂"题中"(?)"、"(?)"的考释则至今不尽如人意。文章据算题的行文逻辑、《九章算术》中相似算题,以及秦、汉法令,证明"传马"题中的"二匹"不误;据秦、汉易代的现实及文字训诂对"缯幅"题之"从利广"给出全新而可信的诠释;据甲骨文、金文及战国楚文字对"挈脂"题中的"(?)"、"(?)"二字做出合理的释读。 展开更多
关键词 张家山汉简 《算数书》 传马 缯幅 挐脂
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Deformations and extensions of modified λ-differential Lie-Yamaguti algebras
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作者 TENG Wen PAN Yuewei 《中山大学学报(自然科学版)(中英文)》 北大核心 2025年第4期115-127,共13页
The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce t... The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group. 展开更多
关键词 Lie-Yamaguti algebra modifiedλ-differential operator representation and cohomology one-parameter formal deformation Abelian extension
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Design Method for Optimizing the Interactive Interface of Live Broadcasting Platform for the Elderly Users 被引量:1
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作者 WEI Bi-ze FAN Wei DUAN Ying-ke 《印刷与数字媒体技术研究》 CAS 北大核心 2024年第4期167-178,共12页
In the era of network live broadcasting for everyone,the development of live broadcasting platforms is also more intelligent and diversified.However,in the face of a large group of elderly users,the interface interact... In the era of network live broadcasting for everyone,the development of live broadcasting platforms is also more intelligent and diversified.However,in the face of a large group of elderly users,the interface interaction design mode used is still mainly based on the interaction mode for young groups,and is not designed for elderly users.Therefore,a design method for optimizing the interaction interface of live broadcasting platform for elderly users was proposed in this study.Firstly,the case study method and Delphi expert survey method were used to determine the design needs of elderly users and the design mode was analysed.Secondly,the orthogonal design principle was used to design a test sample of the interactive interface of live broadcasting platform applicable for the elderly users,and then a user evaluation system was established to calculate the weights of the design elements using hierarchical analysis,and then the predictive relationship between the design mode of the interactive interface of live broadcasting platform and the elderly users was established by Quantitative Theory I.Finally,Genetic Algorithm was applied to generate the optimized design scheme.The results showed that the design method based on the Genetic Algorithm and the combination of Quantitative Theory can scientifically and effectively optimize the design of the interactive interface of the live broadcasting platform for the elderly users,and improve the experience of the elderly users. 展开更多
关键词 Live broadcasting platform Interaction design Elderly users Genetic Algorithm Quantitative Theory I
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日本新编小学数学教材的特点 被引量:1
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作者 李淑文 《外国教育研究》 CSSCI 北大核心 2004年第3期26-28,共3页
日本新编小学数学教材《算数》根据新的小学算数学习指导要领精简了教学内容。在内容编排上,各领域内容齐头并进、相互融合,各部分内容由易到难、分散安排。在教材编写上,重视通过操作、实验等活动抽象概括出数学知识,重视启发学生思考... 日本新编小学数学教材《算数》根据新的小学算数学习指导要领精简了教学内容。在内容编排上,各领域内容齐头并进、相互融合,各部分内容由易到难、分散安排。在教材编写上,重视通过操作、实验等活动抽象概括出数学知识,重视启发学生思考,重视问题解决,内容编写尽量符合学生的认知特点。 展开更多
关键词 日本 小学 数学教材 教材特点 《算数》 内容编排 教材编写 教学内容
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Second-Order Side-Channel Attacks on Kyber: Targeting the Masked Hash Function
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作者 WANG Ya-Qi HUANG Fan +1 位作者 DUAN Xiao-Lin HU Hong-Gang 《密码学报(中英文)》 CSCD 北大核心 2024年第6期1415-1436,共22页
Recently,several PC oracle based side-channel attacks have been proposed against Kyber.However,most of them focus on unprotected implementations and masking is considered as a counter-measure.In this study,we extend P... Recently,several PC oracle based side-channel attacks have been proposed against Kyber.However,most of them focus on unprotected implementations and masking is considered as a counter-measure.In this study,we extend PC oracle based side-channel attacks to the second-order scenario and successfully conduct key-recovery attacks on the first-order masked Kyber.Firstly,we analyze the potential joint information leakage.Inspired by the binary PC oracle based attack proposed by Qin et al.at Asiacrypt 2021,we identify the 1-bit leakage scenario in the masked Keccak implementation.Moreover,we modify the ciphertexts construction described by Tanaka et al.at CHES 2023,extending the leakage scenario from 1-bit to 32-bit.With the assistance of TVLA,we validate these leakages through experiments.Secondly,for these two scenarios,we construct a binary PC oracle based on t-test and a multiple-valued PC oracle based on neural networks.Furthermore,we conduct practical side-channel attacks on masked Kyber by utilizing our oracles,with the implementation running on an ARM Cortex-M4 microcontroller.The demonstrated attacks require a minimum of 15788 and 648 traces to fully recover the key of Kyber768 in the 1-bit leakage scenario and the 32-bit leakage scenario,respectively.Our analysis may also be extended to attack other post-quantum schemes that use the same masked hash function.Finally,we apply the shuffling strategy to the first-order masked imple-mentation of the Kyber and perform leakage tests.Experimental results show that the combination strategy of shuffling and masking can effectively resist our proposed attacks. 展开更多
关键词 side-channel attack plaintext-checking oracle post-quantum cryptography masked Kyber masked hash function
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从出土竹简看中国早期委输算题及其社会背景 被引量:5
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作者 邹大海 《湖南大学学报(社会科学版)》 CSSCI 北大核心 2010年第4期5-10,共6页
考察了睡虎地汉简《算术》和《九章算术》、《张丘建算经》中的委输算题的特点,利用刘徽的《九章算术注》、岳麓书院秦简《数》、张家山汉简《算数书》等材料提出推导其术文的复原方案。并用睡虎地秦律和张家山汉简《二年律令》,探讨了... 考察了睡虎地汉简《算术》和《九章算术》、《张丘建算经》中的委输算题的特点,利用刘徽的《九章算术注》、岳麓书院秦简《数》、张家山汉简《算数书》等材料提出推导其术文的复原方案。并用睡虎地秦律和张家山汉简《二年律令》,探讨了这类算题的社会背景,特别是律令中的程。 展开更多
关键词 委输问题及其社会背景 《算术》 《九章算术》 《数》 《算数书》 律程
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中国上古时代数学门类均输新探 被引量:3
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作者 邹大海 《自然科学史研究》 CSSCI CSCD 北大核心 2020年第4期395-424,共30页
均输是中国古代数学的一个重要门类,数学经典《九章算术》专设第6章讨论它。前人对其渊源和它与作为经济政策的均输之关系,都多有未及或存在若干问题。文章利用更为丰富的考古文献和传世文献,对中国上古时代均输的发展进行较为系统深入... 均输是中国古代数学的一个重要门类,数学经典《九章算术》专设第6章讨论它。前人对其渊源和它与作为经济政策的均输之关系,都多有未及或存在若干问题。文章利用更为丰富的考古文献和传世文献,对中国上古时代均输的发展进行较为系统深入的研究。文章对《九章算术》“均输”章算题的特征进行了新的概括,指出“均输”的含义比前人理解的公平负担要宽泛,“均输”章的构成具有高度的一致性,算题的列入是编者刻意为之,而非随意安排。文章证明,不论是数学上的两类均输算题还是经济上的两种均输都有先秦及秦代的渊源,现存《九章算术》“均输”章的5个均输算题和睡虎地汉简《算术》中的一个均输算题虽然都定型于西汉,但在先秦及秦代应该已有其蓝本。岳麓书院藏秦简《数》和张家山汉简《算数书》证明,“均输”章后24题中有一部分在战国到西汉初期就很可能存在,不必等到公元前1世纪由耿寿昌补入。 展开更多
关键词 均输 《九章算术》 秦汉法律简牍 《盐铁论》 岳麓书院藏秦 简《数》 张家山汉简《算数书》 睡虎地汉简《算术》
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再论《九章算术》通分术 被引量:4
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作者 朱一文 《自然科学史研究》 CSCD 北大核心 2009年第3期290-301,共12页
前人把《九章算术》通分术理解为分子、分母扩大相同倍数而分数值保持不变的算法,实际上等价于现今的算法。其实《九章算术》中的通分是指用一个正整数乘以分数以化分数为整数的算法;前人对此理解有误,因此导致了前人对于《九章算术》... 前人把《九章算术》通分术理解为分子、分母扩大相同倍数而分数值保持不变的算法,实际上等价于现今的算法。其实《九章算术》中的通分是指用一个正整数乘以分数以化分数为整数的算法;前人对此理解有误,因此导致了前人对于《九章算术》经分术"同而通之"和少广术"通而同之"的错误理解,以及对于《九章算术》环田题密率术的校勘争论。依据对通分术新的理解,对以上问题进行了辨析,进而认为:古今通分术计算结果殊途同归是产生对通分术普遍误解的算理基础;忽视古代数学术语和算法的统一性,忽视古代数学筹算的表达形式带来的实用性、经济性的要求,以及大量的以今释古是对通分术产生误解的原因。事实上,《九章算术》通分术,在现今数学中并无与之精确对应的算法;前人对通分的误解实际上抹杀了通分术演进的历史——从《九章算术》少广术总术和分术的不一致,可以看出从先秦《算数书》到西汉《九章算术》编撰,通分术历史演进的痕迹。 展开更多
关键词 《算数书》《九章算术》通分术
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Inverse procedure for determining model parameter of soils using real-coded genetic algorithm 被引量:3
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作者 李守巨 邵龙潭 +1 位作者 王吉喆 刘迎曦 《Journal of Central South University》 SCIE EI CAS 2012年第6期1764-1770,共7页
The hybrid genetic algorithm is utilized to facilitate model parameter estimation.The tri-dimensional compression tests of soil are performed to supply experimental data for identifying nonlinear constitutive model of... The hybrid genetic algorithm is utilized to facilitate model parameter estimation.The tri-dimensional compression tests of soil are performed to supply experimental data for identifying nonlinear constitutive model of soil.In order to save computing time during parameter inversion,a new procedure to compute the calculated strains is presented by multi-linear simplification approach instead of finite element method(FEM).The real-coded hybrid genetic algorithm is developed by combining normal genetic algorithm with gradient-based optimization algorithm.The numerical and experimental results for conditioned soil are compared.The forecast strains based on identified nonlinear constitutive model of soil agree well with observed ones.The effectiveness and accuracy of proposed parameter estimation approach are validated. 展开更多
关键词 parameter estimation real-coded genetic algorithm tri-dimensional compression test gradient-based optimization
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Multi-line code: A low complexity revocable fingerprint template for cancelable biometrics 被引量:1
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作者 WONG Wei-jing WONG Mou-ling Dennis KHO Yau-hee 《Journal of Central South University》 SCIE EI CAS 2013年第5期1292-1297,共6页
A low computational cost cancelable fingerprint template, namely the multi-line codes was proposed. The formulation of a single-line code involves the inspection of minutiae distribution along a straight line construc... A low computational cost cancelable fingerprint template, namely the multi-line codes was proposed. The formulation of a single-line code involves the inspection of minutiae distribution along a straight line constructed based on the reference minutia. Multi-line code is introduced to elevate the performance by combining several single-line codes. Experiments were carried out on a few FVC databases. It has been proven that the proposed method yields relatively low computational complexity as compared to existing minutiae distribution-based methods, while preserving the performance. The equal error rate obtained for FVC2002 DB1 is 4.69% in stolen-key case, and the total arithmetic operations utilized are 14 520 additions and zero multiplication. 展开更多
关键词 cancelable fingerprint template multi-line code single-line code stolen-key case
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Optimized algorithm in mine production planning, mined material destination, and ultimate pit limit 被引量:1
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作者 Rahimi ESMAEIL Moosavi EHSAN +1 位作者 Shirinabadi REZA Gholinejad MEHRAN 《Journal of Central South University》 SCIE EI CAS CSCD 2018年第6期1475-1488,共14页
An integral connection exists among the mine production planning, the mined material destination, and the ultimate pit limit (UPL) in the mining engineering economy. This relation is reinforced by real information a... An integral connection exists among the mine production planning, the mined material destination, and the ultimate pit limit (UPL) in the mining engineering economy. This relation is reinforced by real information and the benefits it engenders in the mining economy. Hence, it is important to create optimizing algorithms to reduce the errors of economic calculations. In this work, a logical mathematical algorithm that considers the important designing parameters and the mining economy is proposed. This algorithm creates an optimizing repetitive process among different designing constituents and directs them into the maximum amount of the mine economical parameters. This process will produce the highest amount of ores and the highest degree of safety. The modeling produces a new relation between the concept of the cutoff grade, mine designing, and mine planning, and it provides the maximum benefit by calculating the destination of the ores. The proposed algorithm is evaluated in a real case study. The results show that the net present value of the mine production is increased by 3% compared to previous methods of production design and UPL. 展开更多
关键词 mined material destination ultimate pit limit net present value production planning
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A new clustering algorithm for large datasets 被引量:1
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作者 李清峰 彭文峰 《Journal of Central South University》 SCIE EI CAS 2011年第3期823-829,共7页
The Circle algorithm was proposed for large datasets.The idea of the algorithm is to find a set of vertices that are close to each other and far from other vertices.This algorithm makes use of the connection between c... The Circle algorithm was proposed for large datasets.The idea of the algorithm is to find a set of vertices that are close to each other and far from other vertices.This algorithm makes use of the connection between clustering aggregation and the problem of correlation clustering.The best deterministic approximation algorithm was provided for the variation of the correlation of clustering problem,and showed how sampling can be used to scale the algorithms for large datasets.An extensive empirical evaluation was given for the usefulness of the problem and the solutions.The results show that this method achieves more than 50% reduction in the running time without sacrificing the quality of the clustering. 展开更多
关键词 data mining Circle algorithm clustering categorical data clustering aggregation
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Calculation of maximum surface settlement induced by EPB shield tunnelling and introducing most effective parameter 被引量:6
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作者 Sayed Rahim Moeinossadat Kaveh Ahangari Kourosh Shahriar 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第12期3273-3283,共11页
This study aims to predict ground surface settlement due to shallow tunneling and introduce the most affecting parameters on this phenomenon.Based on data collected from Shanghai LRT Line 2 project undertaken by TBM-E... This study aims to predict ground surface settlement due to shallow tunneling and introduce the most affecting parameters on this phenomenon.Based on data collected from Shanghai LRT Line 2 project undertaken by TBM-EPB method,this research has considered the tunnel's geometric,strength,and operational factors as the dependent variables.At first,multiple regression(MR) method was used to propose equations based on various parameters.The results indicated the dependency of surface settlement on many parameters so that the interactions among different parameters make it impossible to use MR method as it leads to equations of poor accuracy.As such,adaptive neuro-fuzzy inference system(ANFIS),was used to evaluate its capabilities in terms of predicting surface settlement.Among generated ANFIS models,the model with all input parameters considered produced the best prediction,so as its associated R^2 in the test phase was obtained to be 0.957.The equations and models in which operational factors were taken into consideration gave better prediction results indicating larger relative effect of such factors.For sensitivity analysis of ANFIS model,cosine amplitude method(CAM) was employed; among other dependent variables,fill factor of grouting(n) and grouting pressure(P) were identified as the most affecting parameters. 展开更多
关键词 surface settlement shallow tunnel tunnel boring machine (TBM) multiple regression (MR) adaptive neuro-fuzzyinference system (ANFIS) cosine amplitude method (CAM)
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Similarity measure design and similarity computation for discrete fuzzy data 被引量:7
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作者 LEE Sang-Hyuk PARK Wook-Je JUNG Dong-yean 《Journal of Central South University》 SCIE EI CAS 2011年第5期1602-1608,共7页
The similarity computations for fuzzy membership function pairs were carried out.Fuzzy number related knowledge was introduced,and conventional similarity was compared with distance based similarity measure.The useful... The similarity computations for fuzzy membership function pairs were carried out.Fuzzy number related knowledge was introduced,and conventional similarity was compared with distance based similarity measure.The usefulness of the proposed similarity measure was verified.The results show that the proposed similarity measure could be applied to ordinary fuzzy membership functions,though it was not easy to design.Through conventional results on the calculation of similarity for fuzzy membership pair,fuzzy membership-crisp pair and crisp-crisp pair were carried out.The proposed distance based similarity measure represented rational performance with the heuristic point of view.Furthermore,troublesome in fuzzy number based similarity measure for abnormal universe of discourse case was discussed.Finally,the similarity measure computation for various membership function pairs was discussed with other conventional results. 展开更多
关键词 similarity measure fuzzy number DISTANCE similarity evaluation fuzzy membership function
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