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基于改进协方差控制的传感器管理算法 被引量:6
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作者 吕鹏飞 彭冬亮 +1 位作者 左燕 谷雨 《火力与指挥控制》 CSCD 北大核心 2016年第7期28-33,共6页
针对传统的基于协方差控制的传感器管理算法使用全遍历方法所造成的计算量大,以及传感器切换频繁的问题,提出了一种基于改进协方差控制的传感器管理算法。该算法在每一时刻首先判断前一时刻所用传感器组是否能够满足目标跟踪需求,以滤... 针对传统的基于协方差控制的传感器管理算法使用全遍历方法所造成的计算量大,以及传感器切换频繁的问题,提出了一种基于改进协方差控制的传感器管理算法。该算法在每一时刻首先判断前一时刻所用传感器组是否能够满足目标跟踪需求,以滤波协方差与期望协方差的偏差作为参考,结合量纲变换和特征值求取,为协方差偏差矩阵经过量纲变换后得到的量纲一致阵的所有特征值设定一个精度阈值,然后判断滤波协方差是否满足期望,从而决定是否维持当前选择的传感器组。在目标作匀速、匀加速、协同转弯等多种场景下进行了算法性能测试分析,仿真结果表明,该算法不仅在大部分场景下满足目标跟踪精度,而且能够提高传感器管理算法的实时性,同时降低传感器的切换频率。 展开更多
关键词 传感器管理 协方差控制 目标跟踪精度 量纲变换
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Chiral transfer amidst one-dimensional linear polymers and twodimensional network covalent organic frameworks:Striking a fine balance between helicity and crystallinity 被引量:2
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作者 Xinlin Zha Mengjuan Zuo +10 位作者 Guilin Xu Zhong Yan Haining You Yi Xiong Ying Liu Yingying Li Liyan Yang Ke Liu Mufang Li Tao Zhao Dong Wang 《Nano Research》 SCIE EI CSCD 2024年第6期5726-5734,共9页
The current landscape of chiral covalent organic frameworks(COFs)predominantly centered on constructing asymmetric molecular-scale chirality,often introducing an inherent contradiction to the COF symmetry and limiting... The current landscape of chiral covalent organic frameworks(COFs)predominantly centered on constructing asymmetric molecular-scale chirality,often introducing an inherent contradiction to the COF symmetry and limiting diversity.Herein,we overcome these challenges by achieving chiral transfer between one-dimensional(1D)imine linear polymers(LPs)and two-dimensional(2D)networkβ-ketoenamine COFs composed of achiral monomers.We successfully synthesize several 1D imine LPs with mesoscopic helical chirality,comprising achiral C2-symmetric terephthalaldehyde and diamine linkers in a chiral supramolecular transcription system.Leveraging the irreversible tautomerism mechanism within the linker replacement approach,terephthalaldehyde(TPA)units in these helical 1D LPs are substituted with C3-symmetric 1,3,5-triformylphloroglucinol(TP),yielding the corresponding 2D networkβ-ketoenamine COFs.Crystallinity and helicity of the resultantβ-ketoenamine COFs intimately hinge on reaction conditions,including the aldehyde stoichiometry of Tp and TPA,as well as the quantity and concentration of the catalyst employed.Under optimized conditions,the nucleation and growth were precisely governed,achieving a harmonious equilibrium of crystallinity and helicity within the generated 2D networkβ-ketoenamine COFs,even with covalent bond rupture,recombination,and topological transition(from[C2+C2]to[C3+C2]).Impressively,the ground state chirality inherent to helical 1D LPs seamlessly transfers to helical 2D networkβ-ketoenamine COFs.This study not only offers new perspectives on the development of chiral functional COFs,but also provides fresh insights into the precise control of COFs'microscopic morphology. 展开更多
关键词 chiral covalent organic frameworks chiral transfer dimensional transformation HELICITY
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Integrability and solutions of a nonsymmetric discrete Korteweg-de Vries equation 被引量:1
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作者 Maebel Mesfun Da-jun Zhang Song-lin Zhao 《Communications in Theoretical Physics》 SCIE CAS CSCD 2024年第2期45-50,共6页
In this paper,we present Lax pairs and solutions for a nonsymmetric lattice equation,which is a torqued version of the lattice potential Korteweg-de Vries equation.This nonsymmetric equation is special in the sense th... In this paper,we present Lax pairs and solutions for a nonsymmetric lattice equation,which is a torqued version of the lattice potential Korteweg-de Vries equation.This nonsymmetric equation is special in the sense that it contains only one spacing parameter but consists of two consistent cubes with other integrable lattice equations.Using such a multidimensionally consistent property we are able to derive its two Lax pairs and also construct solutions using B?cklund transformations. 展开更多
关键词 discrete Korteweg-de Vries equation NONSYMMETRIC multi-dimensional consistency Backlund transformation solution
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三维虚拟环境中二维平面动态实时渲染方法 被引量:5
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作者 杨扬 肖飞 +1 位作者 孟坤 赵晓永 《计算机科学》 CSCD 北大核心 2011年第6期279-282,共4页
为实现三维虚拟世界中二维平面动态实时渲染,提出一种有效的方法并通过实验验证了其可行性。通过在三维虚拟环境中加载该方法,不仅可以实现用户与三维环境中图像交互,而且可以在该系统上集成传统的二维图像业务,弥补了当前三维虚拟世界... 为实现三维虚拟世界中二维平面动态实时渲染,提出一种有效的方法并通过实验验证了其可行性。通过在三维虚拟环境中加载该方法,不仅可以实现用户与三维环境中图像交互,而且可以在该系统上集成传统的二维图像业务,弥补了当前三维虚拟世界技术对二维平面业务支持不足的缺点。 展开更多
关键词 三维虚拟现实 平面绘图 纹理映射 坐标变换 实时渲染
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基于卷积神经网络的高效知识表示模型 被引量:5
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作者 李少杰 陈曙东 +2 位作者 郝悦星 欧阳小叶 龚立晨 《高技术通讯》 EI CAS 北大核心 2020年第9期901-907,共7页
为提升知识表示的有效性和可靠性,提出一种基于卷积神经网络(CNN)的知识表示模型(ConvKE)。ConvKE采用维度变换策略来提升卷积滑动窗口在三元组矩阵上的滑动步数以及三元组内实体和关系在更多维度上的信息交互能力。ConvKE还通过2-D卷... 为提升知识表示的有效性和可靠性,提出一种基于卷积神经网络(CNN)的知识表示模型(ConvKE)。ConvKE采用维度变换策略来提升卷积滑动窗口在三元组矩阵上的滑动步数以及三元组内实体和关系在更多维度上的信息交互能力。ConvKE还通过2-D卷积滑动窗口提升感受野来捕获三元组更多维度上的整体信息。通过采用知识补全任务来评估ConvKE模型的效果,实验结果证明了ConvKE在2个基准数据集WN18RR、FB15K-237的平均排名(MR)指标上取得了较好的结果。 展开更多
关键词 知识图谱 知识表示 卷积神经网络(CNN) 知识补全 维度变换 信息交互
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A Study of English Translation Strategies of Subtitles of the Domestic Animated Film Chang’an from the Perspective of Eco-translatology
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作者 LIU Ya-ru 《Journal of Literature and Art Studies》 2024年第3期220-225,共6页
This article conducts an analysis and exploration of the English subtitles translation of the domestic animated film Chang’an from the perspective of eco-translatology.Taking three-dimensional transformation as the e... This article conducts an analysis and exploration of the English subtitles translation of the domestic animated film Chang’an from the perspective of eco-translatology.Taking three-dimensional transformation as the entry point,it analyzes the adaptation and selection of subtitle translators in the translation process from the dimensions of language,culture,and communication in Chang’an,aiming to enrich the practical analysis of eco-translatology and provide valuable insights and references for the theoretical construction and practical application of eco-translatology.This article enriches the practical analysis of eco-translatology and also validates to a certain extent the applicability of“three-dimensional”transformation. 展开更多
关键词 subtitle translation ECO-TRANSLATOLOGY Chang’an three-dimensional transformation translation as adaptation and selection
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环境约束视角下集合住宅邻里交往空间在垂直维度的重构与进化
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作者 丁炜 《华中建筑》 2024年第8期53-56,共4页
目前国内大规模建设的集合住宅与传统住宅比较,普遍存在邻里关系活跃度较低及邻里交往空间有效性不足的问题。因为环境约束条件的变化,传统邻里交往行为的多样性、有机性、心理自由等积极特征在集合住宅中遭到极大的削弱。通过重新建构... 目前国内大规模建设的集合住宅与传统住宅比较,普遍存在邻里关系活跃度较低及邻里交往空间有效性不足的问题。因为环境约束条件的变化,传统邻里交往行为的多样性、有机性、心理自由等积极特征在集合住宅中遭到极大的削弱。通过重新建构集合住宅的环境约束条件,在垂直维度上实现多线程交通、开放边界、增加空间冗余度与节点自由度,可以提升邻里交往空间设计的自由度,形成邻里交往空间的自然进化,实现恢复住区内良好邻里关系的目标。 展开更多
关键词 集合住宅 维度转变 邻里交往 环境约束 设计改进
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An improved bearing fault detection strategy based on artificial bee colony algorithm 被引量:3
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作者 Haiquan Wang Wenxuan Yue +6 位作者 Shengjun Wen Xiaobin Xu Hans-Dietrich Haasis Menghao Su Ping liu Shanshan Zhang Panpan Du 《CAAI Transactions on Intelligence Technology》 SCIE EI 2022年第4期570-581,共12页
The operating state of bearing affects the performance of rotating machinery;thus,how to accurately extract features from the original vibration signals and recognise the faulty parts as early as possible is very crit... The operating state of bearing affects the performance of rotating machinery;thus,how to accurately extract features from the original vibration signals and recognise the faulty parts as early as possible is very critical.In this study,the one‐dimensional ternary model which has been proved to be an effective statistical method in feature selection is introduced and shapelet transformation is proposed to calculate the parameter of one‐dimensional ternary model that is usually selected by trial and error.Then XGBoost is used to recognise the faults from the obtained features,and artificial bee colony algorithm(ABC)is introduced to optimise the parameters of XGBoost.Moreover,for improving the performance of intelligent algorithm,an improved strategy where the evolution is guided by the probability that the optimal solution appears in certain solution space is proposed.The experimental results based on the failure vibration signal samples show that the average accuracy of fault signal recognition can reach 97%,which is much higher than the ones corresponding to traditional extraction strategies.And with the help of improved ABC algorithm,the performance of XGBoost classifier could be optimised;the accuracy could be improved from 97.02%to 98.60%compared with the traditional classification strategy. 展开更多
关键词 fault diagnosis feature extraction improved artificial bee colony algorithm improved one-dimensional ternary pattern method shapelet transformation
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Two-dimensional nanomaterials confined single atoms: New opportunities for environmental remediation 被引量:2
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作者 Yu Yin Lei Shi +4 位作者 Shu Zhang Xiaoguang Duan Jinqiang Zhang Hongqi Sun Shaobin Wang 《Nano Materials Science》 EI CAS CSCD 2023年第1期15-38,共24页
Two-dimensional(2D)supports confined single-atom catalysts(2D SACs)with unique geometric and electronic structures have been attractive candidates in different catalytic applications,such as energy conversion and stor... Two-dimensional(2D)supports confined single-atom catalysts(2D SACs)with unique geometric and electronic structures have been attractive candidates in different catalytic applications,such as energy conversion and storage,value-added chemical synthesis and environmental remediation.However,their environmental appli-cations lack of a comprehensive summary and in-depth discussion.In this review,recent progresses in synthesis routes and advanced characterization techniques for 2D SACs are introduced,and a comprehensive discussion on their applications in environmental remediation is presented.Generally,2D SACs can be effective in catalytic elimination of aqueous and gaseous pollutants via radical or non-radical routes and transformation of toxic pollutants into less poisonous species or highly value-added products,opening a new horizon for the contami-nant treatment.In addition,in-depth reaction mechanisms and potential pathways are systematically discussed,and the relationship between the structure-performance is highlighted.Finally,several critical challenges within this field are presented,and possible directions for further explorations of 2D SACs in environmental remediation are suggested.Although the research of 2D SACs in the environmental application is still in its infancy,this review will provide a timely summary on the emerging field,and would stimulate tremendous interest for designing more attractive 2D SACs and promoting their wide applications. 展开更多
关键词 Single-atom catalysis Two-dimensional material Advanced oxidation process Degradation transformation Industrial wastewater
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基于同源机构构造的一类自运动机构综合及其比例尺度特征 被引量:2
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作者 沈铖玮 杭鲁滨 《机械工程学报》 EI CAS CSCD 北大核心 2018年第19期41-48,共8页
以一类动静平台均为等边三角形的6-SS型自运动机构为研究对象,从同源机构构造的视角探究该类机构的综合以及尺度特征。根据末端构件存在的转动、移动特征,建立空间单环SSC机构的共形几何代数模型,分析其运动参数与尺寸参数之间的映射关... 以一类动静平台均为等边三角形的6-SS型自运动机构为研究对象,从同源机构构造的视角探究该类机构的综合以及尺度特征。根据末端构件存在的转动、移动特征,建立空间单环SSC机构的共形几何代数模型,分析其运动参数与尺寸参数之间的映射关系;基于该机构在最高位置处的垂直投影,构造了具有相同映射关系的一簇3-SS/C机构,揭示了等边三角形平台的6-SS型自运动机构的同源构成本质以及所需满足的位形条件。根据机构簇存在的尺寸转换关系,设计给定的3-SS/C机构的同源机构,分析并得出平台设计点满足的几何规律,提出了6-SS型自运动机构综合的几何化方法;进一步基于所得出的几何规律,揭示了该类机构的比例尺度特征,Griffis-Duffy平台为该类机构的特例。该项研究在丰富同源机构种类的同时,也为包含比例尺度特征的机器人机构拓扑结构设计提供了一个崭新视角。 展开更多
关键词 自运动机构 同源机构 尺寸转换 机构综合 比例
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材料特性与工艺参数对PIM产品尺寸稳定性之影响 被引量:1
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作者 殳国俊 黄坤祥 《粉末冶金技术》 EI CAS CSCD 北大核心 2005年第2期134-139,共6页
由于粉末注射成形(PowderInjectionMolding,PIM)产品具有很高的形状复杂度,故此工艺目前在工业界被广泛应用。其中铁系合金与不锈钢由于其性质优良,因此在近年来被广泛的使用在PIM工艺上。不过,由于粉末注射成形的粉末固体含量低,从生... 由于粉末注射成形(PowderInjectionMolding,PIM)产品具有很高的形状复杂度,故此工艺目前在工业界被广泛应用。其中铁系合金与不锈钢由于其性质优良,因此在近年来被广泛的使用在PIM工艺上。不过,由于粉末注射成形的粉末固体含量低,从生坯到最后的烧结工件,常伴随很大收缩(>12%)。使得此工艺之尺寸稳定性相对于其他工艺而言,是较差的。为了改善尺寸稳定性的问题,本研究针对升温速率、烧结温度以及相变态行为分别做探讨。试验结果显示,在全部步骤中,烧结过程有最大的收缩量,所以在此阶段中之尺寸稳定性最不容易控制,而较快的升温速率以及相变态的产生更造成此问题之恶化。本试验结果显示,使用较慢的升温速率,在烧结过程中避免相变态的发生,以及调整合金成分可大幅改善PIM件的尺寸稳定性。 展开更多
关键词 尺寸稳定性 PIM 工艺参数 材料特性 产品 粉末注射成形 升温速率 试验结果 烧结过程 铁系合金 固体含量 烧结温度 合金成分 复杂度 工业界 不锈钢 变态 收缩量 显示 生坯
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3D Geology Modeling from 2D Prospecting Line Profile Map
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作者 Qing-Yuan Li Yang Cui +2 位作者 Chun-Mei Chen Qian-Lin Dong Zi-Xiang Ma 《International Journal of Geosciences》 2015年第2期180-189,共10页
Using prospecting line profile map in combination with drilling and other information for 3D reconstruction of geological model is an important method of 3D geological modeling.?This paper?discusses the theory and imp... Using prospecting line profile map in combination with drilling and other information for 3D reconstruction of geological model is an important method of 3D geological modeling.?This paper?discusses the theory and implementation method of 2D prospecting line map into 3D prospecting line map and then into 3D model. The authors propose that it needs twice upgrading dimension to reconstruction 3D geology model from prospecting line profile map. The first upgrading dimension is to convert profile from 2D into 3D profile,?i.e.?the 2D points in the 2D profile map upgrading dimensional transformation to 3D points in a 3D profile. The second upgrading dimension is that transform 0D point 1D curve and 2D polygon feature into 1D curve, 2D surface and 3D solid feature. The paper reexamines contents and forms in prospecting line map from the two different viewpoints of geology and geographic information science. The process of 3D geology modeling from 2D prospecting map is summarized as follows. Firstly, profile is divided into several sections by beginning, end and drill point of the prospecting line. Next, a 3D folded upright profile frame is built by 2D folded prospecting line on the plan map. Then, 2D points of features on 2D profile are converted into 3D points on 3D profile section by section. And then, adding switch control points for the long line crossover two segments. Lastly, 1D curve features are upgraded to 2D surface. 展开更多
关键词 PROSPECTING LINE PROFILE 3D GEOLOGY Modeling UPGRADING dimensional Coordinate transformation PROFILE Framework Segmented CONVERT
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A Computational Investigation of the Lid-Driven Cavity Flow
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作者 Nawal Odah Al-Atawi Daoud Suleiman Mashat 《American Journal of Computational Mathematics》 2022年第2期283-296,共14页
The lid-driven cavity is an important fluid mechanical system that serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. These flows are ... The lid-driven cavity is an important fluid mechanical system that serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. These flows are driven by the tangential motion of a bounding wall. The lid-driven cavity serves as a benchmark for testing numerical methods and for studying fundamental aspects of incompressible flows in confined volumes. This article presents a complete study of lid-driven cavity flows, with the primary focus being placed on the development of the flow when the Reynolds number was increased. In order to fully comprehend the physics of flow, it is necessary to take into consideration not only pure two-dimensional flows but also flows that are periodic in one space direction and the whole three-dimensional flow. 展开更多
关键词 STEADY Two dimensional Navier Stokes Similarity transformation Finite Difference Scheme
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求解三维装配几何约束闭环系统的约束变换方法 被引量:1
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作者 黄学良 李娜 陈立平 《机械科学与技术》 CSCD 北大核心 2014年第1期57-64,共8页
采用等价性分析方法消除三维几何约束系统中的伪约束闭环,并将几何约束图分解为单边子图、独立闭环子图和耦合闭环子图;采用螺旋理论识别出装配几何约束组合对应的运动副约束,将约束闭环子图映射为运动副约束图;通过分析运动副约束图的... 采用等价性分析方法消除三维几何约束系统中的伪约束闭环,并将几何约束图分解为单边子图、独立闭环子图和耦合闭环子图;采用螺旋理论识别出装配几何约束组合对应的运动副约束,将约束闭环子图映射为运动副约束图;通过分析运动副约束图的拓扑结构选择切除约束,建立装配几何约束闭环系统的相对坐标表达,将约束闭环系统的整体迭代求解转换为切除部分约束与相对坐标的迭代求解。该方法降低了数值迭代求解的规模,考虑了约束方向对求解结果的影响,既提高了约束求解的效率和稳定性,又保证了约束求解结果的正确性。 展开更多
关键词 几何约束 约束闭环 等价性分析 约束变换 相对坐标
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高校思想政治理论课教材体系向教学体系转化的三个维度 被引量:1
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作者 李德芝 张万连 李丹 《山西高等学校社会科学学报》 2015年第2期35-38,共4页
实现高校思想政治理论课教材体系向教学体系的转化,实质上是把思想政治理论的知识结构体系转化为思想政治理论课的教学结构体系。为此,一是正确把握思想政治理论课教学过程的"整体优化规律",着力促进教材体系向教学体系的全... 实现高校思想政治理论课教材体系向教学体系的转化,实质上是把思想政治理论的知识结构体系转化为思想政治理论课的教学结构体系。为此,一是正确把握思想政治理论课教学过程的"整体优化规律",着力促进教材体系向教学体系的全面转化;二是正确把握思想政治理论课教学过程的"要素协同规律",着力促进教材体系向教学体系的结构转化;三是正确把握思想政治理论课教学的"过程充足规律",着力促进教材体系向教学体系的层次转化。 展开更多
关键词 思想政治理论课 教材体系 教学体系 转化维度
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Numerical Simulation of Retrofit Scheme of a Boiler Tail Flue 被引量:1
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作者 Yukun Lv Jiaxi Yang +3 位作者 Jiawen Wang Runcheng Zhang Shuang Yang Wentao Li 《Fluid Dynamics & Materials Processing》 EI 2020年第6期137-151,共15页
Aiming at the problem that the total pressure loss of the flue of the electric precipitator of the 350 MW unit of a power plant to the inlet of the draft fan is too large,the numerical simulation software Fluent and t... Aiming at the problem that the total pressure loss of the flue of the electric precipitator of the 350 MW unit of a power plant to the inlet of the draft fan is too large,the numerical simulation software Fluent and the standard k-εmodel was used to simulate the flue,the results show that the main part of the flue mean total pressure loss is derived from the confluence header and elbow.In order to reduce the loss and consider the cost of transformation,the concept of twodimensional feature surface is established,gradually proposed three sets of flue transformation program and analysis of the flue transformation program drag reduction effect,the results show that the total reduction of the flue can be reduced from 486 Pa to 89 Pa and the reduction rate is 81.7%,which is the best solution;The concept of two-dimensional feature plane is helpful for quick condensing of flue;Double V-type structure of the convergence of the box has a better drag reduction effect. 展开更多
关键词 FLUE numerical simulation total pressure loss two-dimensional feature surface transformation program
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Research on Translation Strategies of Political Texts for International Publicity from the Perspective of Eco-Translatology
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作者 Jia Yang Chengjing Li 《Journal of Contemporary Educational Research》 2023年第12期64-70,共7页
Eco-translatology provides a new perspective and methodology for the international publicity translation of political texts.This paper applies the viewpoint and methodology of eco-translatology,focuses on the three-di... Eco-translatology provides a new perspective and methodology for the international publicity translation of political texts.This paper applies the viewpoint and methodology of eco-translatology,focuses on the three-dimensional transformation of language,culture,and communication,and discusses how translators can adapt to the eco-environment of political texts through the specific example of the keynote speech of China’s president at the opening ceremony of the Third Belt and Road Forum for International Cooperation and select suitable translation strategies and techniques to achieve an ecological balance of the target text in multiple dimensions. 展开更多
关键词 ECO-TRANSLATOLOGY Three-dimensional transformation Political texts International publicity translation
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“兴会”的多维阐释 被引量:1
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作者 吕颖 《西北第二民族学院学报(哲学社会科学版)》 2007年第3期106-109,共4页
“兴会”是中国古代诗学中内涵最丰富、歧义最纷纭的诗学范畴之一。本文从创作心理角度,阐释由“兴会”引起的审美主客体的互动;从文本构成维面,审视“兴会”多向度运动与文本形态的关系;从阅读鉴赏角度,兼及接受主客体及接受主体之间... “兴会”是中国古代诗学中内涵最丰富、歧义最纷纭的诗学范畴之一。本文从创作心理角度,阐释由“兴会”引起的审美主客体的互动;从文本构成维面,审视“兴会”多向度运动与文本形态的关系;从阅读鉴赏角度,兼及接受主客体及接受主体之间的心理互动;从中西诗学比较视阈,展示灵感与“兴会”相生共融的关系。旨在彰显中国古代诗学精神,强调当代语境下古代文论的现代转换意义。 展开更多
关键词 兴会 多维 中西比较 现代转换
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Painlevé Property and Exact Solutions to a (2+1) Dimensional KdV-mKdV Equation 被引量:1
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作者 Yuqing Liu Fang Duan Chao Hu 《Journal of Applied Mathematics and Physics》 2015年第6期697-706,共10页
A (2 + 1) dimensional KdV-mKdV equation is proposed and integrability in the sense of Painlevé and some exact solutions are discussed. The B?cklund transformation and bilinear equations are obtained through Painl... A (2 + 1) dimensional KdV-mKdV equation is proposed and integrability in the sense of Painlevé and some exact solutions are discussed. The B?cklund transformation and bilinear equations are obtained through Painlevé analysis. Some exact solutions are deduced by Hirota method and generalized Wronskian method. 展开更多
关键词 (2+1) dimensional KdV-mKdV Equation Painlevé Property Backlund transformation Bilinear Equation Wronskian Method
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Forward Expansiveness and Entropies for Subsystems of Z^(k)_(+)-actions
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作者 Yao Jia GUO Xin Sheng WANG Yu Jun ZHU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2023年第4期633-662,共30页
In this paper,forward expansiveness and entropies of"subsystems"2)of Z^(k)_(+)-actions are investigated.Letαbe a Z^(k)_(+)-action on a compact metric space.For each 1≤j≤k-1,denote G^(j)_(+)={V+:=V∩R^(k)_... In this paper,forward expansiveness and entropies of"subsystems"2)of Z^(k)_(+)-actions are investigated.Letαbe a Z^(k)_(+)-action on a compact metric space.For each 1≤j≤k-1,denote G^(j)_(+)={V+:=V∩R^(k)_(+):V is a j-dimensional subspace of R^(k)}.We consider the forward expansiveness and entropies forαalong V+∈G^(j)_(+).Adapting the technique of"coding",which was introduced by M.Boyle and D.Lind to investigate expansive subdynamics of Z^(k)-actions,to the Z^(k)_(+)cases,we show that the set E^(j)_(+)(α)of forward expansive j-dimensional V_(+)is open in G^(j)_(+).The topological entropy and measure-theoretic entropy of j-dimensional subsystems ofαare both continuous in E^(j)_(+)(α),and moreover,a variational principle relating them is obtained.For a 1-dimensional ray L∈G^(+)_(1),we relate the 1-dimensional subsystem ofαalong L to an i.i.d.random transformation.Applying the techniques of random dynamical systems we investigate the entropy theory of 1-dimensional subsystems.In particular,we propose the notion of preimage entropy(including topological and measure-theoretical versions)via the preimage structure ofαalong L.We show that the preimage entropy coincides with the classical entropy along any L∈E1+(α)for topological and measure-theoretical versions respectively.Meanwhile,a formula relating the measure-theoretical directional preimage entropy and the folding entropy of the generators is obtained. 展开更多
关键词 Z^(k)_(+)-action forward expansiveness j-dimensional subsystems ENTROPY preimage entropy folding entropy variational principle random transformation
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