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浅析哈佛微积分教材对导数概念解释的特点及启示 预览
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作者 孔宪芬 《曲阜师范大学学报:自然科学版》 CAS 2019年第2期126-128,共3页
作为20世纪80年代美国微积分教学改革运动的重要成果,哈佛微积分教材对导数概念的解释独具匠心.用导数的单位给出了导数的一种数值解释,即导数是自变量再增加1个单位后因变量相应的变化量.为介绍导数概念而设计的相应例题和习题特色鲜明... 作为20世纪80年代美国微积分教学改革运动的重要成果,哈佛微积分教材对导数概念的解释独具匠心.用导数的单位给出了导数的一种数值解释,即导数是自变量再增加1个单位后因变量相应的变化量.为介绍导数概念而设计的相应例题和习题特色鲜明.题目知识点考察单一,只关注导数概念.其来源广泛,贴近生活.还另辟蹊跷用导数在生活中的这些应用来解释导数概念.这些编写设计特点对我国微积分教材编撰和教学都提供了有价值的参考. 展开更多
关键词 微积分教材 导数 导数概念 微积分改革
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Lineament characteristics using gravity data in the Garoua Zone,North Cameroon:Natural risks implications 预览
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作者 Kokea Ariane Darolle Fofie Fidèle Koumetio +1 位作者 Jean Victor Kenfack David Yemele 《地球与行星物理:英文版》 CSCD 2019年第1期33-44,共12页
The Garoua Zone in North Cameroon,the subject of this study,is known to have undergone tectonic movements during the Cretaceous,but the zone’s structural data remain poorly known.This study exploits the Bouguer anoma... The Garoua Zone in North Cameroon,the subject of this study,is known to have undergone tectonic movements during the Cretaceous,but the zone’s structural data remain poorly known.This study exploits the Bouguer anomaly to improve knowledge of Garoua tectonics structures.In order to characterize these structures,two methods are used:Euler’s deconvolution method and the method of the horizontal gradient of the vertical derivative.Superposition of the Euler’s solutions map for index N=1 with the map from the horizontal gradient of the vertical derivative method allows determination of gravimetric lineaments,interpreted as faults or as linear contacts,from which we deduce a structural map of the study area.Based on this map,we identify sixteen lineaments,of which we count eight as linear contacts and eight as faults.Among the faults,we denote one of depth between 4 and 8 km,five faults of depth ranging between 8 and 13 km,and two faults of depths between 13 and 36 km.Analysis of these faults shows that the seven deepest faults might present a natural risk in our study area.For purposes of civil protection,such deep faults should be monitored and taken into consideration in the implementation of large public works.The structural map,established herein from data on the in-depth extension of each fault,thus increases scientific knowledge in the area that can be used to site public works in ways that reduce risk. 展开更多
关键词 Bouguer ANOMALY horizontal DERIVATIVE vertical DERIVATIVE EULER DECONVOLUTION natural RISKS
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槲皮素衍生物的合成及其生物活性研究
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作者 冯亚莉 刘金海 +1 位作者 谢新年 翟广玉 《化学与粘合》 CAS 2019年第5期344-349,共6页
槲皮素是一种优良的天然抗氧化剂。以槲皮素为先导物,选择性对C环3位羟基进行修饰。以廉价的芦丁为原料,经苄基选择性保护、Williamson成醚反应,再经Pd/C催化加氢脱苄基得到5个槲皮素酰胺类衍生物,均未见文献报道,目标产物结构经IR、1H ... 槲皮素是一种优良的天然抗氧化剂。以槲皮素为先导物,选择性对C环3位羟基进行修饰。以廉价的芦丁为原料,经苄基选择性保护、Williamson成醚反应,再经Pd/C催化加氢脱苄基得到5个槲皮素酰胺类衍生物,均未见文献报道,目标产物结构经IR、1H NMR、13C NMR、ESI-MS确证。采用DPPH法考察了5个目标化合物的抗氧化活性,结果显示,大部分目标化合物的SC50小于槲皮素或与槲皮素相当,这表明3-OH不是槲皮素抗氧化活性的必需基团。采用MTT法考察了5个槲皮素酰胺类衍生物对人食管鳞癌细胞EC109、人食管鳞癌细胞EC9706、人胃癌细胞SGC7901及小鼠黑色素瘤细胞B16-F10的增殖抑制作用。结果显示,通过化学方法对槲皮素进行结构修饰后,其体外抗肿瘤活性增强。其中,化合物7-1对SGC7901的抑制作用(IC50=67.228μmol/L)明显优于母药槲皮素(IC50=91.115μmol/L)和5-FU(IC50=78.236μmol/L),是一个很有潜力的新型抗肿瘤候选化合物。 展开更多
关键词 黄酮 槲皮素 酰胺 衍生物 合成 抗氧化 抗肿瘤
西藏六种野生石斛的红外光谱鉴别研究 预览
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作者 徐元江 刘江 +2 位作者 彭诗原 郑维列 兰小中 《高原农业》 2019年第6期664-669,共6页
本研究为了能够有效区分金耳石斛、金钗石斛、齿瓣石斛、束花石斛、大苞鞘石斛、密花石斛6种西藏野生石斛。采用傅立叶变换红外光谱法结合聚类分析方鉴别。结果表明,该方法可以有效、快速、简便鉴别不同石斛,主要特征谱带的相对强度的... 本研究为了能够有效区分金耳石斛、金钗石斛、齿瓣石斛、束花石斛、大苞鞘石斛、密花石斛6种西藏野生石斛。采用傅立叶变换红外光谱法结合聚类分析方鉴别。结果表明,该方法可以有效、快速、简便鉴别不同石斛,主要特征谱带的相对强度的比值可以作为石斛不同品种一维红外光谱差异特征,用二阶导数光谱数据来进行系统聚类分析,发现距离小于25时金钗石斛为一类,说明金钗石斛与其他这种类的石斛差异较大。 展开更多
关键词 傅立叶变换红外光谱法 石斛 聚类分析
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博物馆艺术衍生品的数字化创新发展研究 预览
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作者 丁耀 《邵阳学院学报:社会科学版》 2019年第2期113-116,共4页
数字技术是艺术衍生品创新发展的推动力,只有将互动与体验要素引入衍生品的设计和推广中,才能顺利完成数字经济时代下的新一轮转型。文章从产品分层理论视角,提出衍生品的差异化创新策略——形式创新、功能创新和服务创新,在此基础上充... 数字技术是艺术衍生品创新发展的推动力,只有将互动与体验要素引入衍生品的设计和推广中,才能顺利完成数字经济时代下的新一轮转型。文章从产品分层理论视角,提出衍生品的差异化创新策略——形式创新、功能创新和服务创新,在此基础上充分利用多种新媒体平台,打造全方位立体化创新路径。 展开更多
关键词 衍生品 数字技术 博物馆 文化创意
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熊果酸及其衍生物抗肿瘤作用的研究进展 预览
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作者 向润清 范源 《药学研究》 CAS 2019年第2期63-69,共7页
熊果酸(ursolic acid,UA)是一种五环三萜类化合物,广泛存在于夏枯草、女贞子等多种药用植物中,具有多种生物活性。体内外研究表明,熊果酸抗瘤谱广,且对正常细胞毒性低,是一种理想的天然抗肿瘤候选药物,进行结构改造后具有更广泛的抗肿... 熊果酸(ursolic acid,UA)是一种五环三萜类化合物,广泛存在于夏枯草、女贞子等多种药用植物中,具有多种生物活性。体内外研究表明,熊果酸抗瘤谱广,且对正常细胞毒性低,是一种理想的天然抗肿瘤候选药物,进行结构改造后具有更广泛的抗肿瘤活性。现综合国内外文献报道,对熊果酸及其衍生物抗肿瘤的作用进行综述。 展开更多
关键词 熊果酸 衍生物 抗肿瘤
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关于一元函数导数定义的注记 预览
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作者 马昌秀 《新疆师范大学学报:自然科学版》 2019年第1期50-52,共3页
导数是数学分析中微积分的核心内容之一,也是近代数学的重要基础。在许多数学之外的其他自然科学领域中,导数都扮演着重要的角色,起着至关重要的作用。文章就函数在一点处的导数定义进行深入分析,引出了几点注记。
关键词 函数 导数 极限 可导
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A new asymmetric anthracene derivative with high mobility
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作者 Xixia Yu Lei Zheng +5 位作者 Jinfeng Li Lu Wang Jiangli Han Huayi Chen Xiaotao Zhang Wenping Hu 《中国科学:化学英文版》 SCIE EI CAS CSCD 2019年第2期251-255,共5页
An asymmetric anthracene derivative(4-HDPA) was designed and synthesized. With the optimization of proper scenario of fabrication process, top-contact thin film devices based on 4-HDPA exhibit mobility as high as 3.59... An asymmetric anthracene derivative(4-HDPA) was designed and synthesized. With the optimization of proper scenario of fabrication process, top-contact thin film devices based on 4-HDPA exhibit mobility as high as 3.59 cm2 V^–1 s^–1, while its singlecrystal devices exhibit mobility as high as 5.12 cm2 V^–1 s^–1, which is higher than the symmetrical counterpart of 4-HDPA in both single-crystal and thin film devices. 展开更多
关键词 organic FIELD-EFFECT TRANSISTOR (OFET) ASYMMETRIC anthracene DERIVATIVE MOBILITY
藤黄酸衍生物的合成及其抗肿瘤活性 预览
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作者 姜毅 易春蝶 +3 位作者 张丹妮 尹俊林 曾广智 樊保敏 《云南民族大学学报:自然科学版》 CAS 2019年第6期546-552,共7页
以藤黄酸为原料分别与氨基酸反应,合成了一系列新型的藤黄酸衍生物,其结构经MS、1H NMR、13 C NMR确证.采用磺酰罗丹明B(sulfurhodamine B)法测试目标化合物对人肺癌A549、人黑色素瘤A375、人肝癌HepG2和人胃癌BGC823细胞的体外抗肿瘤活... 以藤黄酸为原料分别与氨基酸反应,合成了一系列新型的藤黄酸衍生物,其结构经MS、1H NMR、13 C NMR确证.采用磺酰罗丹明B(sulfurhodamine B)法测试目标化合物对人肺癌A549、人黑色素瘤A375、人肝癌HepG2和人胃癌BGC823细胞的体外抗肿瘤活性.结果显示,大多数化合物表现出较强的抗肿瘤活性.其中含非极性小基团侧链的氨基酸衍生物的活性普遍较高,化合物3和4的活性明显高于藤黄酸对照品;部分含极性氨基酸的衍生物的活性下降并且针对不同细胞株体现了不同的选择性. 展开更多
关键词 藤黄酸 衍生物 合成 抗肿瘤
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Synthesis and Properties of High Performance Functional Polyimides Containing Rigid Nonplanar Conjugated Fluorene Moieties
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作者 Yi-Wu Liu Li-Shuang Tang +4 位作者 Lun-Jun Qu Si-Wei Liu Zhen-Guo Chi Yi Zhang Jia-Rui Xu 《高分子科学:英文版》 SCIE CAS CSCD 2019年第4期416-427,I0008共13页
A diamine(WuFDA)containing vertical rigid non-planar conjugated fluorene moiety and low polarizability group(C—F)was designcd and synthesized through three steps of reactions(halogenated reaction,Suzuki coupling reac... A diamine(WuFDA)containing vertical rigid non-planar conjugated fluorene moiety and low polarizability group(C—F)was designcd and synthesized through three steps of reactions(halogenated reaction,Suzuki coupling reaction,and reduction reaction).Four kinds of high performance functional polyimides(WuFPI-6F,WuFPI-BP,WuFPI-BT,and WuFPI-PM)were thus prepared by the condensation polymerization of WuFDA with four commercial dianhydride 6FDA,BPDA,BTDA,and PMDA,respectively.The polyimides exhibited low dielectric constant,excellent thermal stability,outstanding solubility,good film-fonning property,and mechanical properties.The dielectric constants of the polyimides were in the range of 2.28-2.88(f=10^4 Hz).The 5%weight-loss temperatures(Td5%)in nitrogen were in the range of 555-584°C,and the glass transition temperatures(Tg)were in the range of 408-448°C.The weight loss of WuFPI-BP maintaining at 450 and 500°C for half an hour was only 0.33%and 1.26%,respectively.All the WuFPIs could be dissolved in almost all organic solvents,even chloroform.The tensile strength and tensile modulus of these films were in the ranges of 78.6-85.7 MPa and 3.1一3.2 GPa,respectively.In addition,the polyimides displayed light color with special fluorescent and resistive switching(ON-OFF)characteristics;the maximum fluorescence emission was observed at 422-424 nm in NMP solution and at 470-548 nm in film state.The memory devices with the configuration of indium tin oxideAVuFPIs/aluminum(ITO/WuFPIs/Al)exhibited distinct volatile memory characteristics of static random access memory(SRAM),with an ON/OFF current ratio of 105-106.These functional polyimides showed attractive potential applications in the field of high performance flexible polymer photoelectronic devices or polymer memory devices. 展开更多
关键词 FUNCTIONAL POLYIMIDE FLUORENE derivative MOIETIES Fluorescence polymer Low dielectric constant Thermal stability
气相色谱法测定功能饮料中肌醇的含量 预览
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作者 方志青 李婷婷 +1 位作者 王娅 林野 《广州化工》 CAS 2019年第20期103-104,共2页
以市售功能饮料为研究对象,样品经无水乙醇溶解,超声萃取后蒸馏至近干,加入硅烷化试剂衍生后超纯水溶解,正己烷萃取,萃取液用DB-5色谱柱进行分离,气相色谱法测定其肌醇的含量.结果表明:在0~2.0 mg/mL范围内线性关系良好,相关系数为0.99... 以市售功能饮料为研究对象,样品经无水乙醇溶解,超声萃取后蒸馏至近干,加入硅烷化试剂衍生后超纯水溶解,正己烷萃取,萃取液用DB-5色谱柱进行分离,气相色谱法测定其肌醇的含量.结果表明:在0~2.0 mg/mL范围内线性关系良好,相关系数为0.9999,方法检出限为0.5 mg/L,在3个不同浓度标准溶液添加水平下回收率范围为84.0%~107.0%,均值为,相对标准偏差(n=6)为5.56~7.76%,该方法灵敏度高,重现性好,能简便快速的测定功能性饮料中肌醇含量. 展开更多
关键词 肌醇 功能饮料 气相色谱法 衍生
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高职学生对导数概念理解的认知诊断--基于规则空间模型 预览
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作者 陆伟峰 陈强 《常州信息职业技术学院学报》 2019年第3期43-46,共4页
在认知诊断理论的指导下,对高职学生导数概念理解情况进行认知诊断。分析了导数概念各个属性之间的层次关系,使用规则空间模型确定了学生对导数概念理解的难点在于:从静态到动态的转变和在实际背景下理解导数概念,并获得每个学生的掌握... 在认知诊断理论的指导下,对高职学生导数概念理解情况进行认知诊断。分析了导数概念各个属性之间的层次关系,使用规则空间模型确定了学生对导数概念理解的难点在于:从静态到动态的转变和在实际背景下理解导数概念,并获得每个学生的掌握模式。与访谈法和APOS理论的分析方法相比,该方法可以兼顾宏观和微观两个方面,并能更细致地从微观方面了解学生的认知特点,便于因材施教。 展开更多
关键词 导数 概念理解 认知诊断 规则空间模型
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微积分学概念溯源例谈 预览
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作者 王继强 范甜 《中国科技术语》 2019年第4期76-78,共3页
微积分学中有许多概念看似寻常,但其背后往往都有着或有趣或厚重的渊源。作者在长期教学和科研经验的基础上,从历史和现实两个角度对微积分学中一些典型概念的来源进行了追溯,以求达到解疑释惑、正本清源之目的。
关键词 函数 极限 导数 微分 积分
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A study of boundary vorticity dynamics and identification of large-scale structures in flow field based on two-dimensional flow around a bluff body 预览
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作者 Da-peng Zhang Yu-zhu Chen Xi-lin Xie 《水动力学研究与进展:英文版》 SCIE EI CSCD 2019年第2期231-248,共18页
A method based on decomposition of acceleration field and Lie derivative is introduced to identify shearing and rotational domains.This method is validated on two typical kinds of model flows.Vorticity dynamics of flo... A method based on decomposition of acceleration field and Lie derivative is introduced to identify shearing and rotational domains.This method is validated on two typical kinds of model flows.Vorticity dynamics of flow around bluff body is studied,illustrated by numerical examples of flow around an elliptic cylinder,a slanted elliptic cylinder and an elliptic cylinder with a pair of bumps on the front side.To explain the generation of vortical structures and how they evolve into inner flow field,boundary vorticity dynamics analysis is performed.Boundary vorticity flux as well as the enstrophy diffusion flux creates vorticity sources and vorticity sinks,which generate or consume boundary vorticity,then shearing layers are generated and interact with each other finally create vortices.The results provide potential in accurate flow control by boundary deformation,and show that relevant theoretical conclusions can be effectively applied in revealing the flow mechanisms. 展开更多
关键词 BOUNDARY VORTICITY dynamics LARGE-SCALE structures LIE DERIVATIVE
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Thermal Diffusivity of Lherzolite at High Pressures and High Temperatures Using Pulse Method
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作者 Sheqiang Miao Yongsheng Zhou Heping Li 《地球科学学刊:英文版》 SCIE CAS CSCD 2019年第1期218-222,共5页
Lherzolite is one of the most important components of the subcontinental mantle lithosphere, and the study of its heat transfer properties aids in understanding the thermal structure of the continental mantle lithosph... Lherzolite is one of the most important components of the subcontinental mantle lithosphere, and the study of its heat transfer properties aids in understanding the thermal structure of the continental mantle lithosphere. Currently, few studies have examined the heat transfer properties of lherzolite, and the experimental results remain controversial. This experiment utilized a pulse method to measure the thermal diffusivity of lherzolite at pressures ranging from 1.0 to 4.0 GPa and temperatures from 300 to 1 073 K on a cubic press apparatus. We obtained a thermal diffusivity for lherzolite of approximately 2.10 mm2s-1 at ambient condition. The experimental pressure derivative of the thermal conductivity of lherzolite decreased with temperature, reaching approximately 10% at high temperature, a value higher than the previously reported 4%, which indicates that the temperature gradient of the upper mantle lithosphere is smaller than previously thought. Therefore, concerning calculation of the lithosphere thickness using the thermal conductivity of the lherzolite, the previous calculation using pressure derivative of the thermal conductivity of 4% may cause an underestimation of the upper mantle lithosphere thickness by approximately 6% in a first approximation. 展开更多
关键词 THERMAL DIFFUSIVITY LHERZOLITE PULSE method PRESSURE DERIVATIVE
槲皮素酰胺类衍生物的合成及其生物活性研究
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作者 刘秋伟 冯亚莉 +1 位作者 渠文涛 翟广玉 《中国药学杂志》 CAS CSCD 北大核心 2019年第19期1565-1574,共10页
目的合成槲皮素酰胺类衍生物并测定其生物活性。方法以槲皮素为先导物,选择性对C环3位羟基进行修饰。以芦丁为原料,经苄基选择性保护、Williamson成醚反应,酰胺化反应,再经Pd/C催化加氢脱苄基得到13个槲皮素酰胺类衍生物。采用DPPH法考... 目的合成槲皮素酰胺类衍生物并测定其生物活性。方法以槲皮素为先导物,选择性对C环3位羟基进行修饰。以芦丁为原料,经苄基选择性保护、Williamson成醚反应,酰胺化反应,再经Pd/C催化加氢脱苄基得到13个槲皮素酰胺类衍生物。采用DPPH法考察了13个目标化合物的抗氧化活性;MTT法考察了13个槲皮素酰胺类衍生物对人食管鳞癌细胞EC109、人食管鳞癌细胞EC9706、人胃癌细胞SGC7901及小鼠黑色素瘤细胞B16-F10的增殖抑制作用。结果目标产物结构经IR、1H NMR、13C NMR、ESI-MS确证。抗氧化实验显示,大部分目标化合物的SC50小于槲皮素或与槲皮素相当,这提示,3-OH不是槲皮素抗氧化活性的必需基团。抗肿瘤活性实验显示,槲皮素酰胺类衍生物抗肿瘤活性增强,其中,化合物7~13对EC109的抑制作用(IC50=10. 25μmol·L^-1)明显优于母药槲皮素(IC50=31. 884μmol·L^-1)和5-FU(IC50=41. 738μmol·L^-1),是一个很有潜力的新型抗肿瘤候选化合物。结论通过化学方法对槲皮素进行结构修饰后,抗氧化活性与槲皮素相当,体外抗肿瘤活性显著增强。 展开更多
关键词 黄酮 槲皮素 酰胺 衍生物 合成 抗氧化 抗肿瘤
Converting Thiophene in Simulated Coking Crude Benzene to N,N-Dimethyl-2-thiophenecarboxamide by Dimethylcarbamyl Chloride Under Mild Conditions
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作者 SHEN Xizhou SONG Hao +3 位作者 FANG Liuya DENG Hang GAN Feng SHEN Zhi 《高等学校化学研究:英文版》 SCIE CAS CSCD 2019年第4期674-679,共6页
Since the content of thiophene in coking crude benzene is high, it is necessary to remove it from coking crude benzene for efficient utilization. In this study, an important intermediate, N,N-dimethyl-2-thiophenecarbo... Since the content of thiophene in coking crude benzene is high, it is necessary to remove it from coking crude benzene for efficient utilization. In this study, an important intermediate, N,N-dimethyl-2-thiophenecarboxamide, was synthesized from thiophene and dimethylcarbamyl chloride. The influences of the dosages of dimethylcarbamyl chloride and ZnCl2 catalyst, reaction temperature and time on the removal rate were further explored based on the reaction kinetics.The structure of the target product was characterized by means of MS,NMR and 13C NMR.The removal rate of thiophene was 98.14% after the reaction for 2 h and thiophene was almost removed after the reaction for 3 h under the optimal reaction conditions [a molar ratio of n(thiophene):n(dimethylcarbamyl chioride):w(ZnCl2)=1:12:10,300 r/min, 318 K and 101.325 kPa].The acylation of thiophene with dimethylcarbamyl chloride was approximately in accord with the first order kinetic equation at 303-323K.The activation energy was 53.9850 kJ/mol and the pre-exponential factor was 1.4521×10^9 h^-1. 展开更多
关键词 COKING crude benzene F-C ACYLATION ACYL CHLORIDE THIOPHENE THIOPHENE derivative
Numerical Methods for Solving Space Fractional Partial Differential Equations Using Hadamard Finite-Part Integral Approach 预览
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作者 Yanyong Wang Yubin Yan Ye Hu 《应用数学与计算数学学报(英文)》 2019年第4期505-523,共19页
We introduce a novel numerical method for solving two-sided space fractional partial differential equations in two-dimensional case.The approximation of the space fractional Riemann-Liouville derivative is based on th... We introduce a novel numerical method for solving two-sided space fractional partial differential equations in two-dimensional case.The approximation of the space fractional Riemann-Liouville derivative is based on the approximation of the Hadamard finite-part integral which has the convergence order O(h^3-a),where h is the space step size and α∈(1,2)is the order of Riemann-Liouville fractional derivative.Based on this scheme,we intro・duce a shifted finite difference method for solving space fractional partial differential equations.We obtained the error estimates with the convergence orders O(τ+h^3-a+h^β),where τ is the time step size and β>0 is a parameter which measures the smoothness of the fractional derivatives of the solution of the equation.Unlike the numerical methods for solving space fractional partial differential equations constructed using the standard shifted Griinwald-Letnikov formula or higher order Lubich's methods which require the solution of the equation to satisfy the homogeneous Dirichlet boundary condition to get the firstorder convergence,the numerical method for solving the space fractional partial differential equation constructed using the Hadamard finite-part integral approach does not require the solution of the equation to satisfy the Dirichlet homogeneous boundary condition.Numerical results show that the experimentally determined convergence order obtained using the Hadamard finite-part integral approach for solving the space fractional partial differential equation with non-homogeneous Dirichlet boundary conditions is indeed higher than the convergence order obtained using the numerical methods constructed with the standard shifted Griinwald-Letnikov formula or Lubich's higher order approximation schemes. 展开更多
关键词 Riemann-Liouville fractional derivative Space fractional partial differentialequation Error estimates
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New Wave Solutions of Time-Fractional Coupled Boussinesq–Whitham–Broer–Kaup Equation as A Model of Water Waves 预览
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作者 Emrah ATILGAN Mehmet SENOL +1 位作者 Ali KURT Orkun TASBOZAN 《中国海洋工程:英文版》 SCIE EI CSCD 2019年第4期477-483,共7页
The main purpose of this paper is to obtain the wave solutions of conformable time fractional Boussinesq–Whitham–Broer–Kaup equation arising as a model of shallow water waves. For this aim, the authors employed aux... The main purpose of this paper is to obtain the wave solutions of conformable time fractional Boussinesq–Whitham–Broer–Kaup equation arising as a model of shallow water waves. For this aim, the authors employed auxiliary equation method which is based on a nonlinear ordinary differential equation. By using conformable wave transform and chain rule, a nonlinear fractional partial differential equation is converted to a nonlinear ordinary differential equation. This is a significant impact because neither Caputo definition nor Riemann–Liouville definition satisfies the chain rule. While the exact solutions of the fractional partial derivatives cannot be obtained due to the existing drawbacks of Caputo or Riemann–Liouville definitions, the reliable solutions can be achieved for the equations defined by conformable fractional derivatives. 展开更多
关键词 time FRACTIONAL COUPLED Boussinesq–Whitham–Broer–Kaup EQUATION conformable FRACTIONAL derivative AUXILIARY EQUATION method
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Modeling and Computing of Fractional Convection Equation 预览
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作者 Changpin Li Qian Yi 《应用数学与计算数学学报(英文)》 2019年第4期565-595,共31页
In this paper,we derive the fractional convection(or advection)equations(FCEs)(or FAEs)to model anomalous convection processes.Through using a continuous time random walk(CTRW)with power-law jump length distributions,... In this paper,we derive the fractional convection(or advection)equations(FCEs)(or FAEs)to model anomalous convection processes.Through using a continuous time random walk(CTRW)with power-law jump length distributions,we formulate the FCEs depicted by Riesz derivatives with order in(0,1).The numerical methods for fractional convection operators characterized by Riesz derivatives with order lying in(0,1)are constructed too.Then the numerical approximations to FCEs are studied in detail.By adopting the implicit Crank-Nicolson method and the explicit Lax-WendrofT method in time,and the second・order numerical method to the Riesz derivative in space,we,respectively,obtain the unconditionally stable numerical scheme and the conditionally stable numerical one for the FCE with second-order convergence both in time and in space.The accuracy and efficiency of the derived methods are verified by numerical tests.The transport performance characterized by the derived fractional convection equation is also displayed through numerical simulations. 展开更多
关键词 Continuous time random walk Fractional convection equation Power-lawdistribution Riesz derivative
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