Geometrical approach to the evaluation of multileg Feynman diagrams
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Geometric ModelingGeometric modeling is a fundamental concept in computer graphics and design, playing a crucial role in various industries such as architecture, engineering, and entertainment. It involves creating digital representations of physical objects or environments using mathematical and computational techniques. Geometric modeling allows designers and engineers to visualize, analyze, and manipulate complex shapes and structures, leading to the development of innovative products and solutions. However, it also presents several challenges and limitations that need to be addressed to ensure its effectiveness and efficiency. One of the key challenges in geometric modeling is the accurate representation of real-world objects and environments. This requires the use of advanced mathematical algorithms and computational methods to capture the intricate details and complexities of physical entities. For example, creating a realistic 3D model of a human face or a natural landscape involves precise measurements, surface calculations, and texture mapping to achieve a lifelike appearance. This level of accuracy is essential in industries such as animation, virtual reality, and simulation, where visual realism is critical for creating immersive experiences. Another challenge in geometric modeling is the efficient manipulation and editing of geometric shapes. Designers and engineers often need to modify existing models or create new ones to meet specific requirements or constraints. This process can be time-consuming and labor-intensive, especially when dealing with large-scale or highly detailed models. As a result, there is a constant demand for more intuitive and user-friendly modeling tools that streamline the design process and enhance productivity. Additionally, the interoperability of geometric models across different software platforms and systems is a persistent issue that hinders seamless collaboration and data exchange. Moreover, geometric modeling also faces challenges in terms of computational resources and performance. Generating and rendering complex 3D models requires significant computing power and memory, which can limit the scalability and accessibility of geometric modeling applications. High-resolution models with intricate geometries may strain hardware capabilities and lead to slow processing times, making it difficult for designers and engineers to work efficiently. This is particularly relevant in industries such as gamingand virtual reality, where real-time rendering and interactive simulations are essential for delivering engaging and immersive experiences. Despite these challenges, geometric modeling continues to evolve and advance through technological innovations and research efforts. The development of advanced modeling techniques such as parametric modeling, procedural modeling, and non-uniform rational B-spline (NURBS) modeling has significantly improved the accuracy and flexibility of geometric representations. These techniques enable designersand engineers to create complex shapes and surfaces with greater precision and control, paving the way for more sophisticated and realistic virtual environments. Furthermore, the integration of geometric modeling with other disciplines such as physics-based simulation, material science, and machine learning has expanded its capabilities and applications. This interdisciplinary approach allows for the creation of interactive and dynamic models that accurately simulate physical behaviors and interactions, leading to more realistic and immersive experiences. For example, in the field of architecture and construction, geometric modeling combined with structural analysis and environmental simulation enables the design and evaluation of sustainable and resilient buildings and infrastructure. In conclusion, while geometric modeling presents several challenges and limitations, it remains an indispensable tool for innovation and creativity in various industries. The ongoing advancements in geometric modeling techniques and technologies continue to push the boundaries of what is possible, enabling designers and engineers to create increasingly realistic and complex digital representations of the physical world. As computational power and software capabilities continue to improve, the future of geometric modeling holds great promise for revolutionizing the way we design, visualize, and interact with the world around us.。
社会科学研究方法与论文写作智慧树知到期末考试答案章节题库2024年北京第二外国语学院1.What are key components of research design? ()答案:Timeframe.###Sampling Strategy.###Data Collection Methods.2.The following aspects of informed consent that are essential in researchethics include ().答案:Researchers explaining potential risks andbenefits.###Participants being allowed to withdraw from the study.3.When should all authors be included in the in-text citation, according to theAPA style? ()答案:When there are two authors.###When there are three to fiveauthors.4.What are some essential tips for writing an effective abstract? ()答案:Use keywords###Emphasize points differently from thepaper.###Use passive verbs5.Which statements are suggested solutions for improving the Methodologysection? ()答案:Eliminate the use of first-person pronouns.###Provide a clearrationale for the chosen methods.6.What's the difference between methodology and method? ()答案:Methodology encompasses the broader theoretical framework and guiding philosophy of the research process.###Methods encompass the specific techniques and procedures employed for data collection andanalysis.###Methodology is presented as a distinct section in aresearch thesis, explaining the overall approach and rationale.7.What are the downsides of mere listing in a literature review? ()答案:It does not present themes or identify trends.###It often indicatesa lack of critical synthesis.8.The common problems to be aware of in thesis writing include().答案:Excessive reliance on qualitative data###Lack of theoreticalsupport###Failure to integrate theory and practice.###Misuse of tense ponents that are typically embedded in the structure of an academicpaper, especially the journal article, include ()答案:Introduction###Results and Discussion10.Which of the following examples are misconducts? ()答案:Facilitating academic dishonesty.###Unauthorizedcollaboration###Misuse of Patients11.What are the three main elements of a definition, as mentioned in the lecture?()答案:Term, Category, and Features.12.In the Methods section, why is it important to detail the tools or materials fordata collection? ()答案:To explain how instruments to be used to answer researchquestions.13.Which is the method suggested to avoid plagiarism when summarizinginformation from sources? ()答案:Summarize immediately after reading without referring back tothe source.14.The purpose of control variables in research is ().答案:To keep certain factors constant and prevent them frominfluencing the dependent variable.15.What is the purpose of using sampling techniques in research? ()答案:To draw conclusions about the population based on data collected from the sample.16.According to Wallwork’s tips for the final check, what is one way to ensureyour paper is as good as possible before submission? ()答案:Anticipate referees’ comments.17.What does external validity assess? ()答案:The extent to which research findings can be applied orgeneralized to other situations and populations.18.Which of the following expressions are correctly used in the Methods Section?()答案:"We conducted the experiment in a controlled environment."19.Which of the following is NOT a recommended guideline for using tables in aresearch paper? ()答案:Using as many tables as possible to provide comprehensiveinformation.20.What does a structured abstract typically include to make it more readable?()答案:Eye-catching font for the title21.What is the main function of the preparation stage in writing a literaturereview? ()答案:To locate relevant literature and prepare for writing.22.The primary focus of academic integrity is ().答案:Fostering honesty and responsible behavior.23.The act of using someone else’s ideas and writings as your own can beconsidered as ().答案:Plagiarism24.Which step is NOT part of the suggested three-step approach for revisingyour paper? ()答案:Rewrite the entire paper.25.Which is not the reason for an overly broad title being problematic? ()答案:It encourages depth in the study.26. A good thesis or dissertation should tell the reader not just “what I havedone,” but “why what I have done matters.” ()答案:对27.Coherence in academic writing refers to the clarity of the thesis statementand the organization of the paper. ()答案:对28.The research methods section helps readers and reviewers gauge thetransparency, validity, and reliability of the research. ()答案:对29.Research papers are published to share new, original results and ideas withthe academic community. ()答案:对30.Relying solely on secondary sources ensures the originality of researchfindings. ()答案:错31.In introduction writing, it is recommended to delve into an exhaustive reviewof the entire field to provide comprehensive context. ()答案:错32.The Background Method in introduction writing kicks off by presenting aproblem and then addressing the solution. ()答案:错33.Multiculturalism seeks to enhance the self-esteem and identities ofmarginalized groups. ()答案:对34. A Doctoral-level literature review is typically less comprehensive than aMaster's-level literature review. ()答案:错35."Hoaxing" involves deliberately publishing false information with theintention of deceiving others. ()答案:对36.Reflecting on the research process at the end is essential for evaluating itsstrengths and limitations. ()答案:对37. A well-crafted title should engage a wide audience effectively. ()答案:对38.In order to avoid plagiarism, it is suggested to avoid citing references. ()答案:错39.Predicting difficulties and providing countermeasures in a research proposalis essential to show the depth of thinking and enlist expected guidance. ()答案:对40.Conducting a literature review is not necessary when selecting a researchtitle. ()答案:错41.What can authors do to ensure a timely publication in a journal that reviewspapers for job hunting purposes?()答案:Submit the manuscript without checking for errors###Seekinformation from editors about review times###Be efficient in making revisions42.When preparing a manuscript for publication, it is crucial to focus on ethicalstandards.()答案:对43.Why do researchers want to publish their papers?()答案:To share new results and ideas44.How can you identify an appropriate journal for publication? ()答案:Look for journals that publish work similar to your research.45.The editor-in-chief makes the final decision on whether a submitted paper isaccepted or rejected in the review process.()答案:对ing cut and paste extensively is recommended during the final check tosave time.()答案:错47.Exchanging texts with another student for proofreading is encouraged to findcareless errors in your own work.()答案:对48.What is the key idea that should be remembered by the audience from yourtalk?()答案:The key idea of your research49.Why is it important to avoid errors that may distort meaning in your writtenwork? ()答案:To enhance the quality of your writing###To ensure clarity ofcommunication50.What is the main purpose of doing a presentation?()答案:To engage, excite, and provoke the audience51.Making academic writing more tentative involves avoiding over-generalizations and using linguistic hedges and tentative phrases.()答案:对52.What is the purpose of the checklist questions provided for paper revision?()答案:To help improve the writing53.Which of the following are strategies for achieving cohesion in academicwriting? ()答案:Organizing the paper logically###Using transitional words andphrases###Employing reference words54.Redundancy and colloquialisms are considered desirable features ofconciseness in academic writing. ()答案:错55.What should you do when revising your paper writing to improve clarity andspecificity? ()答案:Be self-contained56.What are the characteristics of informative abstracts? ()答案:They may replace the need for reading the full paper###Theycommunicate specific information about the paper###They provide aconcise summary of the paper’s content57.Structured abstracts may have clear subheadings to mark different sections.()答案:对58.What is the recommended maximum word limit for a conference abstract?()答案:250 words59.Which tense is often used when writing an abstract? ()答案:Present tense60.The primary purpose of an informative abstract is to indicate the subjectsdealt with in a paper. ()答案:错61.What are some reasons for using citations in academic writing? ()答案:To show you are a member of a particular disciplinarycommunity###To acknowledge the intellectual property rights ofauthors###To avoid plagiarism62.Self-plagiarism is not considered an ethical concern in academic writing.()答案:错63.What is the primary purpose of citation in academic writing? ()答案:To acknowledge the intellectual property rights of authors64.What is self-plagiarism? ()答案:Presenting one's own previously published work as new65.All sources cited in the text must be documented in the References section.()答案:对66.Which type of conclusion is more common in research papers and theses andfocuses on summarizing research outcomes and aligning them with the initial thesis? ()答案:Thesis-oriented Conclusion67.What are the four sections typically found in the Conclusion section of aresearch paper, according to the material? ()答案:Summary of findings, implications, limitations, further studies68.What is one of the purposes of the conclusions chapter? ()答案:To forestall criticisms by identifying limitations of the research69.Which of the following are types of conclusions discussed in the material? ()答案:Summary type###Field-oriented conclusion###Evaluation type of conclusion###Recommendation type of conclusion70.The conclusion section in academic papers typically follows a uniformstructure across all disciplines.()答案:错71.What is one of the purposes of making comparisons with previous studies inacademic writing? ()答案:To justify the methods or procedures followed72.Which of the following is NOT mentioned as a common type of graphicalfigure in the material? ()答案:Map illustrations73.What can we do in demonstrating our research results in paper? ()答案:Use figures and tables to summarize data###Show the results ofstatistical analysis74.In which field are Qualitative Research methods often used?()答案:Liberal Arts and Social Sciences75.What factors should be considered when choosing research methods for athesis? ()答案:Traditional approaches.###Research questions andobjectives.###Nature of the subject matter.76.What does "Research Design" refer to in the research process?()答案:The overall plan guiding the research study.77.All the following moves are included in the method section except ().答案:Describing the commonly used methods in certain field.78.The research methods section in a thesis is often presented as a distinctsection, separate from the literature review.()答案:对79.What are the two core abilities essential for writing an effective literaturereview? ()答案:Information seeking and critical appraisal.80.Where can a literature review be placed in a research paper or thesis? ()答案:In different places depending on research goals and fieldconventions.81.Which type of literature review focuses on organizing literature aroundspecific research questions?()答案:Question-oriented review.82.The purpose of creating a visual representation, such as a literature map, isto replace the need for drafting concise summaries.()答案:错83.What are the recommended tenses to use when discussing the content of thesources in a literature review? ()答案:Simple Past.###Present Perfect.###Simple Present.84.What is the role of the Problem Statement in the Introduction? ()答案:Justify the importance of the research.85.Which is NOT one of the three methods could be used to write anintroduction? ()答案:Reference Method86.The location and structure of the introduction are standardized across alltypes of research theses. ()答案:错87.In Metadiscourse research, what is the recommended way for a researcher torefer to themselves in the introduction?()答案:Refer to themselves as "this thesis" or a specific section.88.What are the key elements included in Move 2 of the "Create a ResearchSpace" (CARS) framework?()答案:Identifying gaps in prior research.###Indicating a gap.89.What role do Research Grant Proposals play?()答案:Both securing financial support and convincing funding agencies.90.What questions does a research proposal eloquently answer? ()答案:How are you going to do it?###What do you plan toaccomplish?###Why do you want to do it?91.The "Aims/Purposes" section in a research proposal outlines the centralissues to be tackled in the study. ()答案:对92.To whom is a research proposal usually submitted for approval and support?()答案:Funding agencies, academic institutions, or research supervisors.93.What is the purpose of predicting difficulties and providing countermeasuresin the research proposal?()答案:To show the depth of thinking and enlist expected guidance.94.The recency of sources is crucial in research, and older sources are alwayspreferred for their depth.()答案:错95.Which database is specifically mentioned for searching Master's and DoctoralDissertations? ()答案:CNKI96.When conducting a critique of a study, what should be considered about themethods used?()答案:The validity for studying the problem.97.What is the primary characteristic of primary sources in research materialcollection? ()答案:They offer synthesized information from various perspectives. 98.What are common approaches to collecting primary source materialsmentioned in the lecture? ()答案:Surveys and questionnaires###Controlled experiments###One-on-one interviews99.What are potential mistakes in the title selection process? ()答案:Having unclear titles that do not convey the subjectmatter.###Using contemporary language to make the title appearoutdated.100.How does the researcher balance the focus of a research title?()答案:By clearly defining the scope of the study.101.What is the purpose of conducting a comprehensive literature review in the title selection process? ()答案:To identify gaps, controversies, or areas requiring furtherexploration.102.An overly narrow title might limit the potential impact and relevance of the research. ()答案:对103.What is the significance of a well-chosen title? ()答案:It significantly enhances the academic value of the work.104.What are key characteristics of deconstruction in literary theory? ()答案:Highlighting textual undecidability and paradoxes.###Challenging traditional assumptions about language and meaning.###Questioning binary oppositions.105.What distinguishes quantitative data from qualitative data in research? ()答案:Quantitative data are numerical, while qualitative data can bedescribed in words.106.What is the primary goal of case studies in applied linguistics? ()答案:To enhance understanding of a phenomenon, process, person, or group.107.Case studies use a single data source, such as interviews, to explore particular phenomena. ()答案:错108.What are the three types of cultural studies? ()答案:New historicism, postcolonialism, American multiculturalism. 109.The dependent variable in a study investigating the effects of different study methods on exam performance is ().答案:Exam performance110.What role does a moderating variable play in a research study? ().答案:It influences the strength or direction of the relationship between independent and dependent variables.111.External validity assesses the extent to which research findings can be applied to populations, settings, or conditions beyond the specific study. ()答案:对112.How does deduction differ from induction in research? ()答案:Deduction is the process of reasoning from general principles tospecific predictions.113.The purposes of research include ()答案:Solving real-world problems###Testing existingtheories###Meeting graduation requirements###Advancingknowledge114.The potential academic consequences for students who engage in academic dishonesty include ().答案:Monetary fines、Academic suspension and Expulsion from theInstitute115.The three key principles that experimental researchers need to carefully consider and implement before, during and after recruiting researchparticipants are ().答案:Anonymity###Informed consent###Confidentiality116.It is unethical to conduct research which is badly planned or poorly executed.()答案:对117.The primary focus of academic integrity in the context of research ethics is ().答案:Fostering responsibility and trustworthiness in academic work 118.The pillars of academic integrity include all the aspects except ()答案:Excellence119.The primary purpose of literature reviews in research articles is ().答案:To evaluate previously published material120.Methodological articles typically present highly technical materials, derivations, proofs, and details of simulations within the main body of thearticle. ()答案:对121.In a research article, many different sections can be found in empirical studies, including ().答案:Method###Literature review###Introduction###Discussion 122.According to the lecture, which step in the procedures of thesis writing involves drafting a title and abstract? ()答案:Step 1: Choice of Topic123.The primary use of case studies is ().答案:To illustrate a problem or shed light on research needs。
《评估指南》的评估方式English Answer:The Guide for the Assessment of Learning Outcomes (ALO) provides detailed guidance on the assessment of student learning outcomes in higher education. It outlines various assessment methods and provides specific criteria for evaluating the quality of assessments.The ALO recognizes that different learning outcomes require different assessment methods. For example, knowledge and understanding can be assessed throughmultiple-choice questions, essays, or presentations. Skills and abilities can be assessed through practical exercises, projects, or simulations. The choice of assessment method should be based on the specific learning outcomes being assessed.The ALO also emphasizes the importance of validity and reliability in assessment. Validity refers to the extent towhich an assessment measures what it is intended to measure. Reliability refers to the consistency of an assessment in measuring the same thing over time. The ALO providesspecific criteria for evaluating the validity andreliability of assessments.In addition to validity and reliability, the ALO also considers the fairness and practicality of assessments. Fairness refers to the extent to which an assessment isfree from bias and provides all students with an equal opportunity to demonstrate their learning. Practicality refers to the ease of administering and scoring an assessment. The ALO provides specific criteria for evaluating the fairness and practicality of assessments.The ALO is a valuable resource for educators who are developing and implementing assessments. It providesdetailed guidance on the assessment of student learning outcomes and helps to ensure that assessments are valid, reliable, fair, and practical.中文回答:《评估指南》为评估高等教育中学习效果提供了详细的指导,指出了评估方法和评估质量的具体标准。
VIRTUAL REALITYJae-Jin Kim Chapter 4Virtual Reality to Simulate Visual Tasks forRobotic Systems4.1IntroductionVirtual reality (VR) can be used as a tool to analyze the interactions between the visual system of a robotic agent and the environment, with the aim of designing the algorithms to solve the visual tasks necessary to properly behave into the 3D world. The novelty of our approach lies in the use of the VR as a tool to simulate the behavior of vision systems. The visual system of a robot (e.g., an autonomous vehicle, an active vision system, or a driving assistance system) and its interplay with the environment can be modeled through the geometrical relationships between the virtual stereo cameras and the virtual 3D world. Differently from conventional applications, where VR is used for the perceptual rendering of the visual information to a human observer, in the proposed approach, a virtual world is rendered to simulate the actual projections on the cameras of a robotic system. In this way, machine vision algorithms can be quantitatively validated by using the ground truth data provided by the knowledge of both the structure of the environment and the vision system.In computer vision (Trucco & Verri, 1998; Forsyth & Ponce, 2002), in particular for motion analysis and depth reconstruction, it is important to quantitatively assess the progress in the field, but too often the researchers reported only qualitative results on the performance of their algorithms due to the lack of calibrated image database. To overcome this problem, recent works in the literature describe test beds for a quantitative evaluation of the vision algorithms by providing both sequences of images and ground truth disparity and optic flowmaps (Scharstein & Szeliski, 2002; Baker et al., 2007). A different approach is to generate image sequences and stereo pairs by using a database of range images collected by a laser range-finder (Yang & Purves, 2003; Liu et al., 2008).In general, the major drawback of the calibrated data sets is the lack of interactivity: it is not possible to change the scene and the camera point of view. In order to face the limits of these approaches, several authors proposed robot simulators equipped with visual sensors and capable to act in virtual environments. Nevertheless, such software tools are capable of accurately simulating the physics of robots, rather than their visual systems. In many works, the stereo vision is intended for future developments (Jørgensen & Petersen, 2008; Awaad et al., 2008), whereas other robot simulators in the literature have a binocular vision system (Okada et al., 2002; Ulusoy et al., 2004), but they work on stereo image pairs where parallel axis cameras are used. More recently, a commercial application (Michel, 2004) and an open source project for cognitive robotics research (Tikhanoff et al., 2008) have been developed both capable to fixate a target, nevertheless the ground truth data are not provided.4.2 The visual system simulatorFigure 4.1a-b shows the real-world images gathered by a binocular robotic head, for different stereo configurations: the visual axes of the cameras are k ept parallel (Figure 4.1a) and convergentfor fixating an object in the scene (the small tin, see Figure 4.1b). It is worth noting that both horizontal and vertical disparities have quite large values in the periphery, while disparities are zero in the fixat ion point. Analogously, if we look at the motion field generated by an agent moving in the environment (see Figure 4.1c), where both still and moving objects are present the resulting optic flow is composed both by ego-motion components, due to motion of the observer, and by the independent movements of the objects in the scene.(a)(b)(c)Figure 4.1 Binocular snapshots obtained by real-world vision systems. (a)-(b): The stereo image pairs are acquired by a binocular active vision system (http://www.searise.eu/) for different stereo configurations: the visual axes of the cameras are (a) kept parallel, (b) convergent for fixating an object in the scene (the small tin). The anaglyphs are obtained with the left image on the red channel and the right image on the green and blue channels. The interocular distance is 30 cm and the camera resolution is 1392 × 1236 pixels with a focal length of 7.3 mm. The distance between the cameras and the objects is between 4 m and 6 m. It is worth noting that both horizontal and vertical dispariti es are present. (c): Optic flow superimposed on a snapshot of the relative image sequence, obtained by a car, equipped with a pair of stereo cameras with parallel visual axes , moving in a complex real environment. The resolution of the cameras is 1392 × 1040 pixels with a focal length of 6.5mm, and the baseline is 33 cm (http://pspc.dibe.unige.it/drivsco/). Different situations are represented: ego-motion (due to the motion of the car) and a translating independent movement of a pedestrian (only the left frame is shown).The aim of the work described in this chapter is to simulate the active vision system of a robot acting and moving in an environment rather than the mechanical movements of the robot itself. In particular, we aim to precisely simulate the movements (e.g. vergence and version) of the two cameras and of the robot in order to provide the binocular views and the related ground truth data (horizontal and vertical disparities and binocular motion filed ). Thus, our VR tool can be used for two different purposes (see Figure 4.2):1. to obtain binocular image sequences with related ground truth, to quantitatively assess the performances of computer vision algorithms;2. to simulate the closed loop interaction between visual perception and action of the robot.The binocular image sequences provided by the VR engine could be processed by computer vision algorithms in order to obtain the visual features necessary to the control strategy of the robot movements. These control signals act as an input to the VR engine, thus simulating the robot movements in the virtual environment, then the updated binocular views are obtained. In the following, a detailed description of the model of a robotic visual system is presented.Figure 4.2 The proposed active vision system simulator. Mutual interactions between a robot and the environment can be emulated to validate the visual processing modules in a closed perception-action loop and to obtain calibrated ground truth data.4.2.1 Tridimensional environmentThe 3D scene is described by using the VRML format. Together with its successor X3D, VRML has been accepted as an international standard for specifying vertices and edges for 3D polygons, along with the surface color, UV mapped textures, shininess and transparency. Though a large number of VRML models are available, e.g. on the web, they usually have not photorealistic textures and they are often characterized by simple 3D structures. To overcome this problem, a dataset of 3D scenes, acquired in controlled but cluttered laboratory conditions, has been created by using a scanner laser. The results presented in Section 6 are obtained by using the dataset obtained in our laboratory.It is worth noting that the complex 3D VRML models can be easily replaced by simple geomet ric figures (cubes, cones, planes) with or without textures at any time, in order to use the simulator as an agile testing platform for the development of complex computer vision algorithms.4.2.2 RenderingThe scene is rendered in an on-screen OpenGL context (see Section 5 for details). Moreover, the SoOffScreenRenderer class is used for rendering scenes in off-screen buffers and to save to disk the sequence of stereo pairs. The renderer can produce stereo images of different resolution and acquired by cameras with different filed of views. In particular, one can set the following parameters :(1)resolution of the cameras (the maximum possible resolution depends on the resolution ofthe textures and on the number of points of the 3D model);(2)horizontal and verti cal field of view (HFOV and VFOV, respectively);(3)distance from camera position to the near clipping plane in the camera’s view volume,also referred to as a viewing frustum, (nearDistance);(4)distance from camera position to the far clipping plane in the came ra’s view volume(farDistance);(5)distance from camera position to the point of focus (focalDistance).4.2.3 Binocular head and eye movementsThe visual system, presented in this Section, is able to generate the sequence of stereo imagepairs of a binocular head moving in the 3D space and fixating a 3D point (X F, Y F, Z F).The geometry of the system and the parameters that can be set are shown in Figure 4.3.Figure 4.3 Schematic representation of the geometry of the binocular active vision system.The head is characterized by the following parameters (each expressed with respect to the world reference frame (X W, Y W, Z W)) :(1)cyclopic position C =(X C, Y C, Z C);(2)nose orientation;(3)fixation point F =(X F, Y F ,Z F ).Once the initial position of the head is fixed, then dif ferent behaviours are possible:(1)to move the eyes by keeping the head (position and orientation) fixed;(2)to change the orientation of the head, thus mimicking the movements of the neck;(3)to change both the orientation and the position of the head, thus generating more complexmotion patterns.These situations imply the study of different perceptual problems, from scene exploration to navigation with ego-motion. Thus, in the following (see Section 6), we will present the results obtained in different situations. For the sake of clarity and simplicity, in the following we will consider the position C = (X C,Y C,Z C) and the orientation of the head fixed, thus only the ocular movements will be considered. In Section 3.3.1 different stereo systems will be described (e.g. pan-tilt, tilt-pan, etc.), the simulator can switch through all these different behaviours. The results presented in the following consider a situation in which the eyes can rotate around an arbitrary axis, chosen in order to obtain the minimum rotation to make the ocular axis rotate from the initial position to the target position (see Section 3.3.1).第二部分中文译文虚拟现实Jae-Jin Kim 第四章虚拟现实机器人的模拟视觉任务4.1引言虚拟现实(VR)可以作为一种工具,用来分析机器人代理的视觉系统和环境之间的相互作用,意在设计算法来解决3D世界中必要的正确行为的视觉任务。
几何量具测量器具术语及英文对照1.刀口型直尺:knife straigjht edge2.刀口尺: knife straigjht edge3.三棱尺three edges straigjht edge4.四棱尺four edges straigjht edge5.条式和框式水平仪 bar form and square levels6.合像水平仪imaging level meter7铸铁平板cast iron surface plate8.岩石平板granite surface plate9.铸铁平尺cast iron straigjht edge10.钢平尺和岩石平尺 steel and granite straigjht edge11.圆度仪roundness measuring instrument12.电子水平仪electronic level meter13.表面粗糙度比较样块铸造表面roughness comparison specimens cast surface14.表面粗糙度比较样块磨、车、铣、插及刨加工表面roughness comparison specimens-ground,turned,bored,milled,shape and planed15.表面粗糙度比较样块电火花加工表面roughness comparison specimens spark-erostion machining surfaces16.表面粗糙度比较样块抛光加工表面roughness comparison specimens pollshed surfaces17.接触式仪器的标称特性18.轮廓profiles19.轨迹轮廓traced profile20.基准轮廓reference profile21.总轮廓total profile22.原始轮廓primary profile23.残余轮廓residual profile24.触针式仪器stylus instrument25.感应位移数字存储触针式量仪displacement sensitive,digitally storing stylus instrument26.触针式仪器的部件stylus instrument components27.测量环measurement loop28.导向基准renfence guide29.驱动器drive unit30.测头(传感器)probe(pick-up)31.拾取单元tracing element32.针尖stylus tip33.转换器transducer34.放大器amplifier35.模/数转换器analog-to-digital converter36.数据输入data input37.数据输出data output38.轮廓滤波和评定profile filtering and evaluation39.轮廓记录器profile recorder40.仪器的计量特性metrological characteristics of the instrument41.静测力的变化change of static measuring force42.静态测力static measuring force43.动态测量力dynamic measuring force44.滞后hysteresis45.测头的测量范围transmission function for the sine waves46.仪器的测量范围measuring range of the instrument47.模数转换器的量化步距quantization step of the ADC48.仪器分辨力instrument resolution49.量程分辨力比range-to-resolution ratio50.测头线性偏差probe linearity deviation51.短波传输界限short-wave transmission limitation52.轮廓垂直成分传输vertical profile component transmission153表面粗糙度比较样块抛丸、喷砂加工表面roughness comparison specimens shot blasted and blasted surfaces54产品结构几何量计术规范(GPS)geometrical product specifications(GPS)55表面结构surface texture56接触式仪器的标称特性nominal characteristics of contact instruments57公法线千分尺micrometer for mearsuring root tangent lenghths of gear teeth58最大允许误差maximum permissible error59圆柱直齿渐开线花键量规gauges for straight cylindrical involute splines60齿厚游标卡尺Gear tooth vernier calipers61齿轮渐开线样板the involute master of gear62齿轮螺旋线样板the helix master of gear63矩形花键量规gauges for straight –sided splines64测量蜗杆master worm65万能测齿仪universal gear measuring instrument66万能渐开线检查仪universal involute measuring instrument67齿轮齿距测量仪gear circular pictch measuring instrument68万能齿轮测量机Universal gear measuring machine69齿轮螺旋线测量仪gear helix measuring instrument70便携式齿轮齿距测量仪manual gear circular pitch measuring instrument71便携式齿轮基节测量仪manual gear base pitch measuring instrument72立式滚刀测量仪vertical hob measuring instrument73齿轮双面啮合综合测量仪Gear dual-flank measuring instrument74齿轮单面啮合整体误差测量仪Gear single-flank meshing integrated error measuring instrument 75梯形螺纹量规gauges for metric trapezoidal screw threads76工作螺纹量规work gauges for metric trapezoidal screw threads77校对螺纹量规check gauges for metric trapezoidal screw threads78.梯形螺纹量规型式与尺寸Types and dimensions of metric trapezoidal screw threads79.普通螺纹量规型式与尺寸Types and dimensions of gauges purpose screw threads80.非螺纹密封的管螺纹量规Gauges for pipe threads prcessure-tight joints are not made on the threads81.螺纹千分尺Screw thread micrometer82.最大允许误差maximum permissible error83.间隙螺纹量规Clearance screw gauge84.量针Bar gauge85.螺纹样板Screw thread template86.用螺纹密封的管螺纹量规Gauges for pipe threads where pressure-tight joints are made on the threads87.刀具预调测量仪精度Accuracy of the presetting instrument88.薄膜式气动量仪Membrane type pneumatic measuring instrument89.光栅线位移测量系统Grating linear displacement measuring system90.光栅角位移测量系统Grating angular displacement measuring system91.磁栅线位移测量系统Magnet-grid linear displacement measuring system92.量块附件Accessories for gauge blocks93.V形架Vee blocks94.比较仪座Comparator stand95.磁性表座Magnetic stand96.万能表座Universal stand for dial indicator一般术语:1. 几何量geometrical product2. 量值value(of a quantity)3. 真值true value(of a quantity)4. 约定真值conventional true value(of a quantity)5. 单位unit(of measurement)6. 测量measurement7. 测试measurement and test8. 检验inspecte9. 静态测量static measurement10. 动态测量dynamic measurement11. 测量原理principle of measurement12. 测量方法method of measurement13. 测量程序measurement procedure14. 被测量measurand15. 影响量influence quantity16. 变换值transformed value(of a measurand)17. 测量信号measurement signal18. 直接测量法direct method of measurement19. 间接测量法indirect method of measurement20. 定义测量法definitive method of measurement21. 直接比较测量法direct-comparison method of measurement22. 替代测量法substitution method of measurement23. 微差测量法differential method of measurement24. 零位测量法nulll method of measurement25. 测量结果result of a measurement26. 测得值measured value27. 实际值actual value28. 未修正结果uncorrected result (of a measurement)29. 已修正结果corrected result(of a measurement)30. 测量的准确度accuracy of measurement31. 测量的重复性repeatability of measurement32. 测量复现性reproducibility of measurements33. 实验标准偏差experimental standard deviation34. 测量不确定度uncertainty of measurement35. 测量绝对误差absolute error of measurement36. 相对误差relative error37. 随机误差random error38. 系统误差systematic error39. 修正值correction40. 修正系数correction factor41. 人员误差personal error42. 环境误差environmental error43. 方法误差error of method44. 调整误差adjustment error45. 读数误差reading error46. 视差parallax error47. 估读误差interpolation error48. 粗大误差parasitic error49. 检定verification50. 校准calibration51. 调准gauging52. 调整adjustment几何量测量器具术语1. 几何量具测量器具dimensional measuring instruments2. 长度测量器具length measuring instruments3. 角度测量器具angle measuring instruments4. 坐标测量机coordinate measuring machine5. 形状和位置误差测量器具form and position error measuring instruments6. 表面质量测量器具surface quality measuring instruments7. 齿轮测量器具gear measuring instruments8. 实物量具(简称“量具”)material measure9. 测量仪器(简称“量仪”)measuring instruments10. 测量链measuring chain11. 测量装置measuring system12. 指示式测量仪器indicating(measuring )instrument13. 记录式测量仪器recording(measuring)instrument14. 累计式测量仪器totalizing(measuring)instrument15. 积分式测量仪器integrating(measuring)instrument16. 模拟式测量仪器analogue(measuring)instrument17. 数字式测量仪器digital(measuring)instrument18. 测量变换器measuring transducer19. 传感器sensor20. 指示装置indicating device21. 记录装置recording device22. 记录载体recording medium23. 标尺标记scale mark24. 指示器index25. 标尺scale26. 度盘dail测量器具术语1. 标称值nominal value2. 示值indication(of a measuring instrument)3. 标尺范围scale range4. 标称范围nominal range5. 标尺长度scale length6. 标尺分度scale division7. 分度值value of a scale division8. 标尺间距scale spacing9. 线性标尺linear scale10. 非线性标尺non-linear scale11. 标尺标数scale numbering12. 测量仪器的零位zero of a measuring instrument13. 量程span14. 测量范围measuring range15. 额定工作条件vated operating conditions16. 极限条件reference condition17. 标准条件reference condition18. 仪器常数instrument constant19. 响应特性response characteristic20. 灵敏度senstivity21. 鉴别力discrimination22. 分辨力resolution(of an indicating device)23. 死区dead band24. 准确度accuracy of a measuring instruments25. 准确度等级accuracy class26. 重复性repeatability of a measuring instrument27. 示值变动性varation of indication28. 稳定度stability29. 可靠性reliability30. 回程hysteresis31. 漂移drift32. 响应时间response time33. 测量力(简称“测力”)measuring force测量器具术语1. 实物量具示值误差error of indication of a material measure2. 测量仪器示值误差error of indication of a measuring instrument3. 重复性误差repeatability error of a measuring instrument4. 回程误差hysteresis error5. 测量力变化variation of measuring force6. 测量力落差hysteresis of measuring force7. 偏移误差bias error (of a measuring instrument)8. 允许误差maximum permissible errors(of measuring instruments)9. 跟踪误差tracking error (of a measuring instrument)10. 响应率误差response-law error (of a measuring instrument)11. 量化误差quantization error (of a measuring instrument)12. 基值误差datum error (of a measuring instrument)13. 零值误差zero error (of a measuring instrument)14. 影响误差influence error15. 引用误差fiducial error16. 位置误差position error17. 线性误差linear error18. 响应特性曲线response characteristic curve19. 误差曲线error curve20. 校准曲线calibration curve21. 修正曲线correction curve。
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heodolite 经纬仪Water Level 水位仪Level Ruler 水平尺Casing gradienterCoating thickness Measurer 涂层测厚仪Ultrasonic thickness measurer 超声波测厚仪Ultrasonic crack detector 超声波裂纹测试仪Digital thermometer 数字温度计radiation thermometer 辐射温度计Gradient Reader 坡度读数器Electric spark leak hunter 电火花追踪器Volometer 万用表MegaOhmmeter 兆欧表Earthing resistance Reader 接地电阻读数表Plug gauge 圆柱塞规Magnifying glass 放大镜Plummet 铅锤Profile projector 投影仪Pin Gauge 针规(不知道和plug gauge 的区别在哪里,知道的请指正)Gauge block 块规Bore gauge 百分表A vernier caliper 游标卡尺Coordinate Measureing Machine(CMM) 三尺元Pressure gague寸压力计+电度厚度测试仪(Electroplating THK.Tester)转(扭)力仪(Twisting Meter)螺纹规(Thread Gauge)块规(Block Gauge)环规(Ring Gauge)力矩计(Torque Meter)塞规(Plug gage)高度仪(Altitude gauge)塞尺/间隙规(Clearance gauge)千分卡尺(Micrometer Calipers )“过” -- “不过”验规(通-止规) [go-no-go gauge] 游标卡尺(Vernier Caliper)电子卡尺(Digital caliper)深度千分尺(Depth Micrometer)销(针)规(Pin Gauge)投影仪(Projector )数字高度测量仪(Digital Height Gauge)表面处理测试仪(Surface Finish Tester)内/外径千分尺(Inside/outer Micrometer)洛(威)氏硬度仪[(HRC/HV) Hardness Tester)]温度计(Thermometer)孔规(Bore Gauge)电子称(Electric/digital Balance)三坐标测试仪 (CMM)万用表(Multimeter)1.刀口型直尺:knife straigjht edge2.刀口尺: knife straigjht edge3.三棱尺three edges straigjht edge4.四棱尺four edges straigjht edge5.条式和框式水平仪bar form and square levels6.合像水平仪 imaging level meter7铸铁平板 cast iron surface plate8.岩石平板 granite surface plate9.铸铁平尺cast iron straigjht edge10.钢平尺和岩石平尺steel and granite straigjht edge11.圆度仪 roundness measuring instrument12.电子水平仪electronic level meter13.表面粗糙度比较样块铸造表面 roughness comparison specimens cast surface14.表面粗糙度比较样块磨、车、铣、插及刨加工表面roughness comparison specimens-ground,turned,bored,milled,shape and planed15.表面粗糙度比较样块电火花加工表面roughness comparison specimens spark-erostion machining surfaces16.表面粗糙度比较样块抛光加工表面roughness comparison specimens pollshed surfaces17.接触式仪器的标称特性18.轮廓profiles19.轨迹轮廓 traced profile20.基准轮廓 reference profile21.总轮廓 total profile22.原始轮廓 primary profile23.残余轮廓residual profile24.触针式仪器stylus instrument25.感应位移数字存储触针式量仪displacement sensitive,digitally storing stylusinstrument26.触针式仪器的部件stylus instrument components27.测量环measurement loop28.导向基准renfence guide29.驱动器drive unit30.测头(传感器)probe(pick-up)31.拾取单元tracing element32.针尖stylus tip33.转换器transducer34.放大器amplifier35.模/数转换器analog-to-digital converter36.数据输入data input37.数据输出data output38.轮廓滤波和评定profile filtering and evaluation39.轮廓记录器profile recorder40.仪器的计量特性metrological characteristics of the instrument41.静测力的变化change of static measuring force42.静态测力 static measuring force43.动态测量力 dynamic measuring force44.滞后hysteresis45.测头的测量范围 transmission function for the sine waves46.仪器的测量范围measuring range of the instrument47.模数转换器的量化步距quantization step of the ADC48.仪器分辨力 instrument resolution49.量程分辨力比range-to-resolution ratio50.测头线性偏差probe linearity deviation51.短波传输界限short-wave transmission limitation52.轮廓垂直成分传输 vertical profile component transmission53表面粗糙度比较样块抛丸、喷砂加工表面roughness comparison specimens shot blasted and blasted surfaces54产品结构几何量计术规范(GPS)geometrical product specifications(GPS)55表面结构 surface texture56接触式仪器的标称特性 nominal characteristics of contact instruments57公法线千分尺micrometer for mearsuring root tangent lenghths of gear teeth 58最大允许误差 maximum permissible error59圆柱直齿渐开线花键量规 gauges for straight cylindrical involute splines 60齿厚游标卡尺 Gear tooth verniercalipers61齿轮渐开线样板the involute master of gear62齿轮螺旋线样板 the helix master of gear63矩形花键量规 gauges for straight –sided splines64测量蜗杆 master worm65万能测齿仪 universal gear measuring instrument66万能渐开线检查仪universal involute measuring instrument67齿轮齿距测量仪gear circular pictch measuring instrument68万能齿轮测量机 Universal gear measuring machine69齿轮螺旋线测量仪gear helix measuring instrument70便携式齿轮齿距测量仪 manual gear circular pitch measuring instrument71便携式齿轮基节测量仪manual gear base pitch measuring instrument72立式滚刀测量仪vertical hob measuring instrument73齿轮双面啮合综合测量仪Gear dual-flank measuring instrument74齿轮单面啮合整体误差测量仪Gear single-flank meshing integrated error measuring instrument75梯形螺纹量规 gauges for metric trapezoidal screw threads76工作螺纹量规work gauges for metric trapezoidal screw threads77校对螺纹量规check gauges for metric trapezoidal screw threads78.梯形螺纹量规型式与尺寸 Types and dimensions of metric trapezoidal screw threads79.普通螺纹量规型式与尺寸 Types and dimensions of gauges purpose screw threads80.非螺纹密封的管螺纹量规 Gauges for pipe threads prcessure-tight joints are not made on the threads81.螺纹千分尺Screw thread micrometer82.最大允许误差 maximum permissible error83.间隙螺纹量规 Clearance screw gauge84.量针Bar gauge85.螺纹样板 Screw thread template86.用螺纹密封的管螺纹量规Gauges for pipe threads where pressure-tight joints are made on the threads87.刀具预调测量仪? 精度Accuracy of the presetting instrument88.薄膜式气动量仪Membrane type pneumatic measuring instrument89.光栅线位移测量系统Grating linear displacement measuring system90.光栅角位移测量系统Grating angular displacement measuring system91.磁栅线位移测量系统Magnet-grid linear displacement measuring system92.量块附件Accessories for gauge blocks93.V形架Vee blocks94.比较仪座Comparator stand95.磁性表座Magnetic stand96.万能表座Universal stand for dial indicator一般术语:1.几何量 geometrical product2.量值value(of a quantity)3.真值true value(of a quantity)4.约定真值 conventional true value(of a quantity)5.单位unit(of measurement)6.测量measurement7.测试measurement and test8.检验inspecte9.静态测量static measurement10.动态测量dynamic measurement11.测量原理principle of measurement12.测量方法method of measurement13.测量程序measurement procedure14.被测量measurand15.影响量influence quantity16.变换值transformed value(of a measurand)17.测量信号measurement signal18.直接测量法direct method of measurement19.间接测量法indirect method of measurement20.定义测量法definitive method of measurement21.直接比较测量法direct-comparison method of measurement22.替代测量法substitution method of measurement23.微差测量法differential method of measurement24.零位测量法nulll method of measurement25.测量结果result of a measurement26.测得值measured value27.实际值actual value28.未修正结果uncorrected result (of a measurement)29.已修正结果corrected result(of a measurement)30.测量的准确度accuracy of measurement31.测量的重复性repeatability of measurement32.测量复现性reproducibility of measurements33.实验标准偏差experimental standard deviation34.测量不确定度uncertainty of measurement35.测量绝对误差 absolute error of measurement36.相对误差 relative error37.随机误差random error38.系统误差 systematic error39.修正值correction40.修正系数correction factor41.人员误差personal error42.环境误差environmental error43.方法误差error of method44.调整误差adjustment error45.读数误差reading error46.视差parallax error47.估读误差 interpolation error48.粗大误差parasitic error49.检定verification50.校准calibration51.调准gauging52.调整adjustment几何量测量器具术语1.几何量具测量器具dimensional measuring instruments2.长度测量器具length measuring instruments3.角度测量器具angle measuring instruments4.坐标测量机coordinate measuring machine5.形状和位置误差测量器具form and position error measuring instruments6.表面质量测量器具surface quality measuring instruments7.齿轮测量器具gear measuring instruments8.实物量具(简称“量具”)material measure9.测量仪器(简称“量仪”)measuring instruments10.测量链measuring chain11.测量装置measuring system12.指示式测量仪器indicating(measuring )instrument13.记录式测量仪器recording(measuring)instrument14.累计式测量仪器totalizing(measuring)instrument15.积分式测量仪器integrating(measuring)instrument16.模拟式测量仪器analogue(measuring)instrument17.数字式测量仪器digital(measuring)instrument18.测量变换器measuring transducer19.传感器sensor20.指示装置indicating device21.记录装置recording device22.记录载体recording medium23.标尺标记scale mark24.指示器index25.标尺scale26.度盘dail测量器具术语1.标称值nominal value2.示值indication(of a measuring instrument)3.标尺范围scale range4.标称范围nominal range5.标尺长度scale length6.标尺分度scale division7.分度值value of a scale division8.标尺间距scale spacing9.线性标尺linear scale10.非线性标尺non-linear scale11.标尺标数scale numbering12.测量仪器的零位zero of a measuring instrument13.量程span14.测量范围measuring range15.额定工作条件vated operating conditions16.极限条件reference condition17.标准条件reference condition18.仪器常数instrument constant19.响应特性response characteristic20.灵敏度senstivity21.鉴别力discrimination22.分辨力resolution(of an indicating device)23.死区dead band24.准确度accuracy of a measuring instruments25.准确度等级accuracy class26.重复性repeatability of a measuring instrument27.示值变动性varation of indication28.稳定度stability29.可靠性reliability30.回程hysteresis31.漂移drift32.响应时间response time33.测量力(简称“测力”)measuring force测量器具术语1.实物量具示值误差error of indication of a material measure2.测量仪器示值误差error of indication of a measuring instrument3.重复性误差repeatability error of a measuring instrument4.回程误差hysteresis error5.测量力变化variation of measuring force6.测量力落差hysteresis of measuring force7.偏移误差bias error (of a measuring instrument)8.允许误差maximum permissible errors(of measuring instruments)9.跟踪误差tracking error (of a measuring instrument)10.响应率误差response-law error (of a measuring instrument)11.量化误差quantization error (of a measuring instrument)12.基值误差datum error (of a measuring instrument)13.零值误差zero error (of a measuring instrument)14.影响误差influence error15.引用误差fiducial error16.位置误差position error17.线性误差linear error18.响应特性曲线response characteristic curve19.误差曲线error curve20.校准曲线calibration curve21.修正曲线correction curve长度测量器具量具类1.量块gauge block2.光滑极限量规plain limit gauge3.塞规plug gauge4.环规ring gauge卡规snap gauge5.塞尺feeler gauge6.钢直尺steel gauge7.精密玻璃线纹尺precision glass linear scale8.精密金属线纹尺precision metal linear scale9.半径样板radius template卡尺类1.游标卡尺vernier caliper2.带表卡尺dial caliper3.电子数显卡尺calliper with electronic digital display4.深度标游卡尺depth vernier caliper5.电子数显深度卡尺depth caliper with electronic digital display6.带表高度卡尺dial height calliper7.高度游标卡尺height vernier caliper8.电子数显高度卡尺height caliper with electronic digital display9.焊接检验尺calliper for welding inspection千分尺类1.测微头micrometer head2.外径千分尺external micrometer3.杠杆千分尺micrometer with dial comparator4.带计数器千分尺micrometer with counter5.电子数显外径千分尺micrometer with electronic digital display6.小测头千分尺small anvil micrometer7.尖头千分尺point micrometer8.板厚千分尺sheet metal micrometer9.壁厚千分尺tube micrometer10.叶片千分尺blade micrometer11.奇数沟千分尺odd fluted micrometer12.深度千分尺depth micrometer13.内径千分尺internal micrometer14.单杆式内径千分尺single-body internal micrometer15.表式内径千分尺 dail internal micrometer16.三爪式内径千分尺three point internal micrometer17.电子数显三爪式内径千分尺three point internal micrometer18.内测千分尺inside micrometer指示表类1.指示表 dial indicator2.深度指示表depth dial indicator3.杠杆指示表dial test indicator4.内径指示表bore dial indicator5.涨弹簧式指示表 expanding head bore dial indicator6.钢球式内径指示表ball type bore dial indicator7.电子数显指示表dial indicator with electronic digital display8.杠杆卡规indicating snap gauge9.带表卡规dial snap gauge10.带表外卡规outside dial snap gauge11.带表内卡规inside dial snap gauge12.测厚规thickness gauge13.扭簧比较仪microcator14.杠杆齿轮比较仪mechanical dial comparator15.电子量规electronic gauge16.电感式传感器inductance type transducer17.指示装置indicating device18.电感测微仪inductance micrometer19.峰值电感测微仪peak inductance micrometer20.电感内径比较仪inductance bore comparator21.瞄准传感器aiming transducer角度测量器具1.角度块angle block gauge2.正多面棱体regular polygon mirror3.刀具角度样板cutter angular template4.直角尺square5.平行直角尺parallel square6.宽座直角尺wide-stand square7.刀口形直角尺edge square8.矩形直角尺square square9.三角形直角尺three angle square10.圆柱直角尺cylinder square11.方形角尺square guage12.万能角度尺universal bevel protractor13.游标式万能角度尺vernier universal bevel protractor14.表式万能角度尺dial universal bevel protractor15.光学分度头optical dividing head16.目镜式光学分度头optical dividing head with microscope reading17.投影式光学分度尺optical dividing head with projection reading18.光电分度头optical-electronic dividing head19.多齿分度台multi-tooth division table20.分度转台division rotary table21.正炫规sine bar22.普通正炫规general sine bar23.铰链式正炫规hinge type sine bar24.双向正炫规dual-directional sine bar25.圆锥量规cone gauge26.圆锥塞规plug cone gauge27.圆锥环规ring cone gauge28.直角尺测量仪square measuring instrument形位误差测量器具1.平晶optical flat2.单面平晶optical flat3.双面平晶parallel optical flat4.刀口形直尺knife straight edge5.刀口尺knife straight edge6.三棱尺three edges straight edge7.四棱尺four edges straight edge8.平尺straight edge9.矩形平尺square straight edge10.工字形平尺i-beam straight edge11.角形平尺angle straight edge12.桥形平尺bridge type straight edge13.平板surface plate14.铸铁平板cast iron surface plate15.岩石平板granite surface plate16.方箱square box17.水准器式水平仪level meter18.条式水平仪bar level meter19.框式水平仪frame level meter20.合像水平仪imaging level meter21.光学倾斜仪optical inclinometer22.电子水平仪electronic level meter23.指针式电子水平仪electronic level meter with indicator24.数显式电子水平仪electronic level meter with digital display25.平直度测量仪straightness measuring instrument26.光学式平直度测量仪optical straightness measuring instrument27.光电式平直度测量仪photoelectrical straightness measuring instrument28.圆度测量仪roundness measuring instrument29.转轴式圆度测量仪spindle-rotating type roundness measuring instrument30.转台式圆度测量仪table-rotating type roundness measuring instrument表面质量测量器具表面粗糙度比较样块surface roughness comparison specimen铸造表面粗糙度比较样块surface roughness comparison specimen for cast surface磨、车、镗、铣、插及刨加工表面粗糙度比较样块surface roughness comparison specimen for ground,turned,bored,milled,shaped and planed surface电火花加工表面粗糙度比较样块surface roughness comparison specimen for spark-erosion machined surface抛(喷)丸、喷砂加工表面粗糙度比较样块surface roughness comparison specimen for shot blasted and grit blasted surface抛光加工表面粗糙度测量仪portable surface roughness comparison specimen for polished surface便携式表面粗糙度测量仪portable surface roughess measuring instrument驱动箱driving box台式表面粗糙度测量仪bench type surface roughness measuring instrumentNose bridge 鼻中 Tip 脚套Temple 脚丝 Plating 电镀Printing 印字 Lase 镭射Spectacle frames 眼镜架 Sunglasses 太阳眼镜Sports spectacles 运动眼镜 kid's eyewear 儿童眼镜Reading glasses 老花镜 Contact lens 隐形眼镜Glass optical lenses 玻璃镜片 Plastic optical lenses 塑胶镜片Sunglasses lenses, sun clips 太阳镜片、镜夹 Progressive lenses 渐进多焦点镜片Photochromic lenses 变色镜片 Othro k lenses 角膜矫形接确镜片Optical blanks 镜片毛胚 Accessories for contact lens 隐形眼镜附件Spectacle spare parts and accessories 眼镜零件及配件 Components of frames 镜架组件Spectacle cases & accessories 眼镜盒及附件 Eyecare products and solution for lenses and contace lenses 眼睛护理产品及隐形眼镜洁液Spectacle cases & accessories 眼镜盒及其它配件 Lens demisting cloths and solutions 镜片除雾喷剂及清洁布Spectacle assembling & adjusting tools 眼镜加工、装配、调较工具 Visual test equipment 验眼设备Edger 磨边机 Eyeglasses and frame making machinery 眼镜架制造机械Lens manufacturing and processing machinery 镜片造机械及加工机械 Contact lens processing machinery 隐形眼镜加工机械Lathe 车床 Coating machine 镀膜机Coating materials 镀膜原料 Electroplating equipment, welding machine 电镀机械、焊接机械Price labeling, stamp printing and screen printing mahcinery 标签机、移印机、丝网印刷 Ultrasonic cleaning equipment 超声波清洁仪器Ophthalmic products 眼科用品 Concentrates for ultrasonic cleaning 超声波清洁剂Lens grinding and polishing filtration systems 镜片研磨及抛光过滤系统 Optical processing equipmentand materials 光学加工设备及原料Measurement instrucments for optical elements and systems 光学用品及系统之测量仪器 Store and workshop fitting and furniture 眼镜店及工场设备及家具Moulds for ophthalmic lenses 镜片模具 Raw materials for frames 眼镜原料Raw materials for lenses 镜片原料 Lens abrasive and polishing materials 打磨镜片原料Electroplating, welding materials 电镀、焊接原材料Opto-laser equipment and instruments 激光科技设备和仪器机械英语单词冲床punching machine机械手robot油压机hydraulic machine车床 lathe刨床planer |'plein?|铣床miller磨床grinder(钻床)driller线切割linear cutting金属切削 metal cutting机床 machine tool金属工艺学 technology of metals刀具 cutter摩擦 friction联结 link传动 drive/transmission轴 shaft弹性 elasticity频率特性 frequency characteristic误差 error响应 response定位 allocation机床夹具 jig动力学 dynamic运动学 kinematic静力学 static分析力学 analyse mechanics拉伸 pulling压缩 hitting剪切 shear扭转 twist弯曲应力 bending stress强度 intensity三相交流电 three-phase AC磁路 magnetic circles 变压器 transformer异步电动机 asynchronous motor几何形状 geometrical精度 precision正弦形的 sinusoid交流电路 AC circuit机械加工余量 machining allowance变形力 deforming force变形 deformation应力 stress硬度 rigidity热处理 heat treatment退火 anneal正火 normalizing脱碳 decarburization渗碳 carburization电路 circuit半导体元件 semiconductor element反馈 feedback发生器 generator直流电源 DC electrical source门电路 gate circuit逻辑代数 logic algebra外圆磨削 external grinding内圆磨削 internal grinding平面磨削 plane grinding变速箱 gearbox离合器 clutch绞孔 fraising绞刀 reamer螺纹加工 thread processing螺钉 screw铣削 mill铣刀 milling cutter功率 power工件 workpiece齿轮加工 gear mechining齿轮 gear主运动 main movement主运动方向 direction of main movement进给方向 direction of feed进给运动 feed movement合成进给运动 resultant movement of feed合成切削运动 resultant movement of cutting合成切削运动方向 direction of resultant movement of cutting 切削深度 cutting depth前刀面 rake face刀尖 nose of tool前角 rake angle后角 clearance angle龙门刨削 planing主轴 spindle主轴箱 headstock卡盘 chuck加工中心 machining center车刀 lathe tool车床 lathe钻削镗削 bore车削 turning磨床 grinder基准 benchmark钳工 locksmith锻 forge压模 stamping焊 weld拉床 broaching machine拉孔 broaching装配 assembling铸造 found流体动力学 fluid dynamics流体力学 fluid mechanics加工 machining液压 hydraulic pressure切线 tangent机电一体化 mechanotronics mechanical-electrical integration 气压 air pressure pneumatic pressure稳定性 stability介质 medium液压驱动泵 fluid clutch液压泵 hydraulic pump阀门 valve失效 invalidation强度 intensity载荷 load应力 stress安全系数 safty factor可靠性 reliability螺纹 thread螺旋 helix键 spline销 pin滚动轴承 rolling bearing滑动轴承 sliding bearing弹簧 spring制动器 arrester brake十字结联轴节 crosshead联轴器 coupling链 chain皮带 strap精加工 finish machining粗加工 rough machining变速箱体 gearbox casing腐蚀 rust氧化 oxidation磨损 wear耐用度 durability随机信号 random signal离散信号 discrete signal超声传感器 ultrasonic sensor集成电路 integrate circuit挡板 orifice plate残余应力 residual stress套筒 sleeve扭力 torsion冷加工 cold machining电动机 electromotor汽缸 cylinder过盈配合 interference fit热加工 hotwork摄像头 CCD camera倒角 rounding chamfer优化设计 optimal design工业造型设计 industrial moulding design有限元 finite element滚齿 hobbing插齿 gear shaping伺服电机 actuating motor铣床 milling machine钻床 drill machine镗床 boring machine步进电机 stepper motor丝杠 screw rod导轨 lead rail组件 subassembly可编程序逻辑控制器 Programmable Logic Controller PLC 电火花加工 electric spark machining电火花线切割加工 electrical discharge wire - cutting 相图 phase diagram热处理 heat treatment固态相变 solid state phase changes有色金属 nonferrous metal陶瓷 ceramics合成纤维 synthetic fibre电化学腐蚀 electrochemical corrosion车架 automotive chassis悬架 suspension转向器 redirector变速器 speed changer板料冲压 sheet metal parts孔加工 spot facing machining车间 workshop工程技术人员 engineer气动夹紧 pneuma lock数学模型 mathematical model画法几何 descriptive geometry机械制图 Mechanical drawing投影 projection视图 view剖视图 profile chart标准件 standard component零件图 part drawing装配图 assembly drawing尺寸标注 size marking技术要求 technical requirements刚度 rigidity内力 internal force位移 displacement截面 section。
有限元曲轴疲劳试验英文回答:Finite element crankshaft fatigue testing is a crucial step in evaluating the durability and reliability of crankshafts used in various engines. It involves subjecting the crankshaft to cyclic loading conditions that simulate the real-world operating conditions. This type of testing helps determine the fatigue life of the crankshaft and identify potential failure points.To conduct a finite element crankshaft fatigue test, several steps need to be followed. First, a detailed finite element model of the crankshaft is created using specialized software. This model includes all the necessary geometrical features and material properties of the crankshaft. The model is then meshed to discretize the geometry into smaller elements to facilitate the analysis.Next, the loading conditions are applied to the finiteelement model. These loading conditions typically include both steady-state and transient loads that mimic the actual engine operating conditions. The model is then subjected to a predetermined number of load cycles, which can be thousands or even millions, depending on the desiredfatigue life evaluation.During the analysis, the stresses and strains within the crankshaft are calculated at each load cycle. These values are used to assess the fatigue life of the crankshaft using appropriate fatigue criteria, such as the S-N curve or the damage accumulation approach. The analysis also helps identify potential failure points, such as high-stress concentrations or areas prone to crack initiation.Once the analysis is complete, the results are evaluated to determine the fatigue life of the crankshaft. This information is crucial for engineers and designers to make informed decisions regarding the design and material selection of crankshafts. It helps ensure that the crankshaft can withstand the expected cyclic loading conditions without premature failure.In conclusion, finite element crankshaft fatiguetesting is an essential tool for evaluating the durability and reliability of crankshafts. By simulating real-world operating conditions and analyzing the stresses and strains, engineers can accurately predict the fatigue life of the crankshaft and identify potential failure points. This information is crucial for designing robust and reliable crankshafts.中文回答:有限元曲轴疲劳试验是评估各种发动机中使用的曲轴的耐久性和可靠性的关键步骤。
英文经典知识缩写AF Acceleration factorALT Accelerated life testANOVA Analysis of VarianceAOQL Average Outgoing Quality LevelAPO Auto Power OffAPQP Advanced Product Quality Planning and Control PlanARE Area OptionsASIC Application Specific Integrated CircuitASSP Application Specific Standard PartATE Automatic test equipmentATO Assembly To OrderAVL RFQ IMPUT CHECKLIST里面用到BAC BackupBCI Bulk current injectionBD Business DeveloperBFR Batch Failure Ratebo BochumBOM Bill of MaterialBU Business Unitc acceptance level (= number of failed components accepted) CBD Cost Break DownCDM Contract Design ManufacturerCDM Charge Device Model –discharge typeCDM Original Design done by Partner specifically to support NokiaCDN Coupling and Decoupling Network.CE Concurrent EngineeringCE Concurrent Engineering (used for product development) CE. E0...E5 Concurrent Engineering (CE) Product Program MilestonesCEM Contract Electronic ManufacturerCER. FILTERS, MONOBL. DUPLEXERS Powder mixing, Block pressing, FiringCI Capacity ImplementationCIM Custom In MouldCLUSTER Group of companies, head by one Cluster leaderCM Cost ManagementCMO Customer & Market Operationsco CopenhagenCOC Certificate of complianceCOO Country of OriginCp, Cpk Process Capability indicesCpk Capability IndexCPL Cost Part listCQE Component Quality EngineerCQP Component Quality PlanningCQS Component Quality SpecialistCR Change RequestCRR Component review reportCRYSTALS Crystal wafer manufacturingCSA Current State AnalysisCSMC-TPAT Customs-Trade Partners Against TerrorismCTS Cost Target SettingD Draft, first version of the documentda DallasDC DirectDC Direct CurrentDCN Design change noticeDES Deselect allDFA Design For AssemblyDFBA Design for Board AssemblyDFDS Design for Demand SupplyDfE Design for EnvironmentDFFA Design for Final AssemblyDFM Design For Manufacturing (includes DFPT, DFBA, DFFA) DFMEA Design Failure Mode and Effects AnalysisDFPT Design for Production TestDGDI-EL. DUPLEXERS Resonator preparingDIR Design Improvement ReportsDocMan Type of Lotus Notes database (for documents) DOE Design Of ExperimentDOE Design Of ExperimentDPM Defects Per MillionDSB Demand Supply BalanceDSN Demand Supplier NetworkDUT Device Under TestDV Demand VolumeDVRE0...E5 Concurrent Engineering (CE) MilestonesE0..E5 Concurrent engineering (CE) milestonesECN Engineering Change NoticeEFR Early Failure RateELMECH Electro MechanicalEMC Electro Magnetic CompatibilityEMI Electro Magnetic InterferenceEMS Environmental Management Sys-temEN European NormEoL End of LifeEPA ESD protected areaERPes EspooESD Electrostatic dischargeESDS Electrostatic discharge sensitive deviceESI Early Supplier InvolvementETA Estimate to be arriveEUT Equipment Under TestEV Enclosed volumeEVM Enhancements Version ManagementF Final, document to be archivedFA Failure AnalysisFAC Fully anechoic chamberFAQ Frequently Asked QuestionsFAI First article inspectionFEM Finite Element ModellingFFR Field Failure RateFIL Filter..FIML Fabric Inmold Labeling, same with CIM Custom In Mould FIT Failures in TimeFMEA Failure Mode and Effect AnalysisFORFOT 第一次试模FR Failure RateG.A. General AssemblyGauge R&R Gauge Repeatability and ReproducibilityGCPMGD&T Geometrical Dimensioning & TolerancesGRP ground reference planeGRR Gauge Repeatability and ReproducibilityHBM Human Body ModelHBM Human Body Model –discharge typeHCP horizontal coupling planeHIGH Highlight selectedhk Hong KongHUB Warehousing and Shipping functionality locationICDR Integrated Circuit Design ReviewsICDR IC Design ReviewID Industrial DesignIFR Intrinsic Failure RateIMD Insert Mold DecorationIME Inject Mold EquipmentIML Insert Mold LabelingIML IN MOLD LABELINGIPQC In Process Quality ControlIPR Intellectual Property RightsISO International Standardization Organization jk JyväskyläJR&D Joint Research and developmentKCR Key Component ReviewKO Kick OffLA License Agreementla Los AngelesLAB LabelLCL Lower Control LimitLL Lesson LearnedLRVP Long Range Volume PlanLSL Lower Specification LimitLSSE Light SW Subcontractor EvaluationM&O Mechanics & OutsourcingM/C machineM3 Global quality databaseMAR Mechanics Acceptance ReportMAR’s Mechanical Acceptance Report’s MatCoMaMC Measuring CentreMD Mechanics DesginMDF Material Data FormMDFs material data formsME Manufacturing EngineerMECH MechanicsMFI Melt flow indexMISMM Machine Model –discharge typeMOR Monthly Operation ReviewMOSS Visual Quality Criteria’s procedureMPL Material Project LeaderMPL / M Material Project Leader / Manager MPL/MPM Material Project Leader/ ManagerMPM Material Project ManagerMR Measurements ReportMRPⅡMS Manufacturing SolutionsMS MilestoneMSA Measurement System AnalysisMSID Moisture-Sensitive IdentificationMSM Mechnical Supplier ManagementMSM Mechanics Sourcing ManagerMTO Make TO OrderMTS Mechanical Technology SourcingMULTIL.PRODUCTS Ceramic powder manuf, Sheet forming, Cutting, Printing, FiringNC non connectNCTNDA Non Disclosure AgreementNET Nokia NetworksNET NetworksNGP Nokia Global ProcessesNGS Nokia Global StandardsNGSW Nokia Global Supplier WebNMP Nokia Mobile Phones LtdNOSS Nokia Supplier Status databaseNPI Nokia Product IntegrationNPI New Product IntroductionNPSQS Nokia Part Specific Quality StandardsNRT Nokia Rapid ToolingNSL Nokia Substance ListNSM Nokia Supplier ManualNSR Nokia Supplier RequirementNTP Normal temperature and pressure, see laboratory environment OAP Original Accessory PartnerOCAP Out-of-Control Action PlanOCV Open Circuit VoltageODM Original Design ManufacturerODM Original Design done by Partner independentlyOEM Original Equipment ManufactureOEM Original Design done by NokiaOPL Operations Project LeaderOQC Outgoing Quality ControlORS Operating Resource SourcingOT Over timeOTD On time deliveryou OuluPA Process AssessmentPA Product AgreementPC Product CreationPC PolycarbonatePCBAPCN Process Change NoticePCNs product change notification casesPCQE Program Component Quality EngineerPCQM Program Component Quality ManagerPD Product DeliveryPDM Product Development ManagerPDM Product Data ManagementPDM Product Data Management SystemPDT Project Development TeamPE Product Engineering (used for product in mass production) PFMEA Process Failure Mode and Effect AnalysisPGP Pretty Good PrivacyPI Product ImplementationPIRPLM Product Line ManagementPLP Product Lifetime ProfitabilityPLRM Program Loading Road mapPM Product ManagerPM Purchasing ManagerPM Project ManagerPM/MP Partner Manufacturing/Manufacturing PartnerPMA Project Manager AssistantPMCPMM Program Portfolio ManagementPMT Project Management TeamPO Purchasing OrderPOKA-YOKE Mistake ProofingPOP Package Operation ProcedurePop-Port System connector in NOKIA mobile devicesPOWER AMPS MMIC and/or IC manufacturingPp, Ppk Process Performance IndicesPPA Product Purchase AgreementPPAP Production Part Approval ProcessPPM Product Program Managerppm Parts per millionPQ Process QualificationPQGFP Package qualification guideline for programsPQM Program Quality ManagerPQP Program Quality PlanPQP Package Qualification ProcedurePR1/2PTO Package TO OrderPV Product ValidationPVD Physical Vapor DepositionPWB Printed Wire BoardQA quality assurenQBR Quarterly Business ReviewQC quality controlQE Quality EngineerQFD Quality Function DeploymentQM quality managementQSR Quality System RequirementQTE Quality Technician EngineerQTE Quality and Technology EngineerQTE / QTM Quality Technology Engineer / ManagerQTE / QTM Quality Technology Engineer / ManagerQTM Quality and Technology ManagerQTY QuantityR&D Research and DevelopmentR&R Roles and ResponsibilitiesR&T Research and TechnologyRAM Random Access MemoryRamp Up/SAREC ReconsiderREL Related toRFP Request For ProposalRFQ Request For QuotationRIPS Recently Introduced Product SupportRMA Return Material AuthorizationSASAC semi anechoic chamberSAW /BAW FILTERS, SAW DUPLEXERS Die wafer manufacturing SCP Service Channel PreparationSEM Scanning Electron MicroscopeSG Save as groupSHO Showsi SingaporeSIDSIP Standard Inspection ProcedureSLI Supply Line Implementation processSLM Supply Line ManagementSLP Supply Line Preparation processSO Solution OfferingSOP Standard Operation ProcedureSOW statement of workSPC Statistical Process ControlSPPM Senior Product Program ManagerSPR Standard Product Requirement (Nokia)SQA Supplier Quality AssuranceSQC statistical quality controlSQE Supply Quality EngineerSQM Supply Quality Managerss sample sizeSTA Short Term AvailabilitySVP Senior Vice PresidentSW Softwaresy SydneyTCRM Technology Competence RoadmapTEC Technology Platformto TokyoTP Technology PlatformTPETPR Technical Product RequirementTPUtre TampereU Update, all updated documents that are not final U/I Voltage / CurrentU/I Voltage / CurrentUCL Upper Control LimitUG Use groupUI User Interfaceul Ulmvc Vancouver¨VCO IC manufacturing (discrete transistors, other ICs) VCTCXO Crystal wafer and IC (LSI-VCTCXO) manufacturing VIS VisibleVPQCT Volume Production Quality Control TestVQD Visual Quality EngineerVQE Visual Quality EngineerVQR Visual Quality RequirementsWBS Work Breakdown Structure。
外文翻译题目亭口水利枢纽斜墙坝设计及工程量计算专业水利水电工程班级 _________________ 学生 _________________ 指导教师_________________2014 年基于离散单元法的砌石重力坝安全分析工具摘要介绍…种基于离散单元法的砌石重力坝分析数值模型。
大坝和岩基用3到4节点的基本块组成的块集合表示。
复杂的块形状通过把基本块整合到宏模块来得到,允许模型应用在从等效连续到完全不连续分析的各种情形。
开发了一个接触面公式,能够根据基本块之间建立的接触面, 基于一种精确的边边方法表示宏模块之间的相互作用。
描述了模型的主要数值方面,特别介绍了接触面的创建和更新步骤以及一个支持一种高效且能够得到明显结果的算法的数值设备。
讨论了一个现有的砌石坝的安全评价的应用,包折结构的应力分析和涉及大坝岩石界面附近不同路径的滑动失效机制的评估。
砌石坝;离散元;应力分析;失效机制1简介结构分析必须使用适当的手段来实现它的最终H的。
这些手段必须能够:(1)模拟建筑物的儿何和物理特征,尤其是不连续的和共有的特征;(2)用一套完整的方法来模拟荷载,能够考虑所涉及的不同现象间的相互影响;(3)评价非线性作用,特别是能够界定失效结构。
砌石重力坝应该被理解为一个包含坝体本身,水库,岩石基础的系统。
坝体和岩石是不均匀且不连续的介质。
坝体和围岩的交界面也是不连续的,需要特别注意。
不连续面控制着砌石坝的强度,因为它们是薄弱面,决定着主要失效机制。
另外,大坝所受的各种不同的荷载需要一套完整的方法来处理,因为它们之间相互关联。
这些独特的特点使得大多数的数值工具,无论商业的还是科学的,都不能完全适合地模拟浆砌石重力坝。
在这种背景下,新的数值工具的发展就显得尤为重要。
本文将描述一种为砌石重力坝的静力、动力及流体力学的分析量身定做的数值工具,离散单元法。
离散单元法最初是为了处理岩石力学问题而提出的替代有限元法的方法。
Education is a cornerstone of society,shaping the minds of future generations and influencing the development of nations.The educational systems of the East and West have evolved over centuries,each with its unique characteristics and philosophies.Here is a detailed comparison of the two systems in an English composition. Introduction:Education is a fundamental aspect of human development,and the methods and philosophies of teaching vary significantly between Eastern and Western cultures.This essay will explore the key differences in educational approaches,focusing on pedagogical methods,studentteacher relationships,and the overall goals of education in both regions. Pedagogical Methods:In Western education,the pedagogical approach is often studentcentered,emphasizing critical thinking,creativity,and individual expression.Teachers encourage students to question,explore,and form their own opinions.This is in contrast to Eastern education, which traditionally places a strong emphasis on rote memorization and respect for authority.Students are expected to absorb knowledge as it is presented to them,with less emphasis on questioning or challenging the information.StudentTeacher Relationship:The relationship between students and teachers in Western classrooms tends to be more informal and egalitarian.Teachers are seen as facilitators and guides rather than absolute authorities.In Eastern education,however,the teacher is often revered as a figure of authority and wisdom,and students are expected to show deference and respect.This difference in the studentteacher dynamic can affect the way students engage with the material and their willingness to participate in class discussions.Curriculum and Subject Emphasis:Western curricula often prioritize a broad range of subjects,including humanities,social sciences,and arts,alongside traditional subjects like mathematics and science.The goal is to produce wellrounded individuals with diverse interests and skills.Eastern curricula, on the other hand,may place a heavier emphasis on core subjects like math,science,and language,with less focus on the arts and humanities,reflecting a more utilitarian view of education.Assessment and Evaluation:Western education systems often use a variety of assessment methods,including essays, presentations,and group projects,in addition to traditional exams.This approach aims to evaluate a students ability to apply knowledge in different contexts.In contrast,Eastern systems typically rely more heavily on standardized testing,which can place a premiumon memorization and factual recall over analytical and creative skills.Cultural Values and Goals of Education:The goals of education in the West often include fostering independence,creativity,and the ability to think critically.There is a strong emphasis on personal growth and the development of individual talents and interests.Eastern education,in contrast,may prioritize collective values,discipline,and the cultivation of respect for social hierarchy and traditional values.Conclusion:While both Eastern and Western educational systems have their merits,they also face unique challenges.The Western approach may struggle to instill discipline and a deep understanding of core subjects,while the Eastern system can sometimes stifle creativity and independent thought.A balanced approach that incorporates the strengths of both systems could potentially offer the best of both worlds,preparing students to thrive in an increasingly globalized and interconnected world.In conclusion,understanding the differences between Eastern and Western education is crucial for appreciating the diverse ways in which knowledge is imparted and acquired. As we move forward,it is essential to learn from these differences and strive for an educational system that values both individual expression and collective harmony.。
a rXiv:h ep-th/986248v13J un1998MZ-TH/98-26hep-th/9806248June 1998Geometrical approach to the evaluation of multileg Feynman diagrams ∗A.I.Davydychev a,b,†and R.Delbourgo b,‡a Department of Physics,University of Mainz,Staudingerweg 7,D-55099Mainz,Germany b Physics Department,University of Tasmania,GPO Box 252-21,Hobart,Tasmania,7001Australia AbstractA connection between one-loop N -point Feynman diagrams and certain geo-metrical quantities in non-Euclidean geometry is discussed.A geometrical way to calculate the corresponding Feynman integrals is considered.1IntroductionAs a rule,explicit results for diagrams with several external legs possess a rather com-plicated analytical structure.This structure can be better understood if one employs a geometrical interpretation of kinematic invariants and other quantities.For example,the singularities of the general three-point function can be described pictorially through a tetrahedron constructed out of the external and internal momenta.This method can beused to derive Landauequations defining the positions of possible singularities[1](seealso in[2])and a similar approach can be applied to the four-point function[3]too.An-other known example of using geometrical ideas is the massless three-point function with arbitrary off-shell external momenta(see[4,5]).In this paper,we briefly describe how some geometrical ideas can be used to calculate multileg Feynman diagrams.In particular,we show that there is a direct transition from the Feynman parametric representation to the geometrical description connected with an N-dimensional simplex.A more detailed discussion can be found in[6](see also in[7]). 2A simplex related to the N-point functionThe scalar integral corresponding to the one-loop N-point function isJ(N)(n;ν1,...,νN)≡ d n q N i=1 (p i+q)2−m2i −νi,(1)where n is the space-time dimension andνi are the powers of the propagators.In general, it depends on12 Γ(νi) −1× 10... 10 ανi−1i dαiδ αi−1× α2i m2i+2 j<lαjαl m j m l c jl n/2−Σνi,(2)wherec jl≡(m2j+m2l−k2jl)/(2m j m l).(3) In the region between the corresponding two-particle pseudo-threshold,k2jl=(m j−m l)2, and the threshold,k2jl=(m j+m l)2,we have|c jl|<1,and therefore in this region they can be understood as cosines of some anglesτjl,c jl=cosτjl.At the pseudo-threshold c jl=1andτjl=0,whereas at the threshold c jl=−1andτjl=π.Note that the limits of integration in eq.(2)can be extended from(0,1)to(0,∞),since the actual region of integration is defined by theδfunction.The expressions in other regions should be understood in the sense of analytic continuation,using(when necessary)the causal prescription for the propagators.Let us consider a set of N -dimensional Euclidean “mass”vectors whose lengths are m i .Let them be directed so that the angle between the j -th and the l -th vectors is τjl .If we denote the corresponding unit vectors as a i (so that the “mass”vectors are m i a i ),we get (a j ·a l )=cos τjl =c jl .If we put all “mass”vectors together as emanating from a common origin,they,together with the sides connecting their ends,will define a simplex which is the basic one for a given Feynman diagram.In two dimensions,the simplex is just a triangle,whereas in three dimensions we get a tetrahedron.It is easy to see that the length of the side connecting the ends of the j -th and the l -th mass vectors is 2N (N +1)sides,among them N mass sides (corresponding to the masses m 1,...,m N )and 1N ! N i =1m i√2 Γ(νi )−1m −νi i× ∞0... ∞0 ανi −1i d αi δ αT c α−1 αiaxes,αT c α⇒ λiβ2i,whereλ1...λN=D(N).Let us assume that allλi are realand positive,i.e.the hypersurface is an N-dimensional ellipsoid(if some of theλ’s are√negative,the analytic continuation should be used).Now we can rescaleβi=γi/Ω(N)N!2 m n−N0Ω(N;n).(11)cos n−NθGeometrically,θcan be understood as the angle between the“running”vector of integra-tion and the direction of the height of the basic simplex,H0.Denoting the angle between H0and the i-th mass side asτ0i,we getcosτ0i=m0/m i,m0≡|H0|= N i=1m ibe presented asJ (N )(n ;1,...,1)=N i =1V (N )i k 212.Furthermore,V (2)=1m 1m 2τ12√cos 2−2εθ=2tan τ0i 2F 1 1/2,ε3/2 −tan 2τ0i ,(16)where τ01and τ02are defined in eq.(12),τ01+τ02=τ12.For the three-point function,the three-dimensional basic simplex is a tetrahedron with three mass sides (the angles between these mass sides are τ12,τ13and τ23)and three momentum sides.The volume of this tetrahedron is defined by eq.(5)at N =3.Furthermore,Ω(3)is the usual solid angle at the vertex derived by the mass sides.Its value can be defined as the area of a part of the unit sphere cut out by the three planar faces adjacent to the vertex;in other words,this is the area of a spherical triangle corresponding to this section.The sides of this spherical triangle are obviously equal to the angles τ12,τ13and τ23while its angles,ψ12,ψ13and ψ23,are equal to those between the plane faces.The area of this spherical triangle isΩ(3)=ψ12+ψ13+ψ23−π=2arctan√2m 1m 2m 3Ω(3)D (3)(18)corresponds to one obtained in [11]in a different way.If we consider the four-dimensional three-point function,the only (but very essential!)difference is that we should divide the integrand by cos θ.We split the spherical triangle with the sides τ12,τ13and τ23into three spherical triangles,corresponding to the solidangles of rectangular tetrahedra.Calculating the corresponding integrals,we obtain the result in terms of the dilogarithms,or the Clausen function(see e.g.in[12]).For the four-point function,the corresponding four-dimensional simplex has four mass sides and six momentum sides.It hasfive vertices andfive three-dimensional hyperfaces. Four of these hyperfaces are the reduced ones,corresponding to three-point functions, whereas thefifth one is the momentum hyperface.This four-dimensional simplex is com-pletely defined by its mass sides m1,m2,m3,m4and six“planar”angles between them,τ12,τ13,τ14,τ23,τ24andτ34.The content(hyper-volume)of this simplex is given by eq.(5) at N=4,with D(4)=det c jl .The four-dimensional four-point function can be exhibited as(cf.eq.(9))J(4)(4;1,1,1,1)=1V(4)=2iπ2√integrals.When N=n+1,each integral J(N)i (see eq.(13))corresponding to one of theresulting rectangular tetrahedra can be reduced to an(N−1)-point function(cf.also in [16,11]).In the resulting expressions,all arguments of functions arising possess a straightfor-ward geometrical meaning in terms of the dihedral angles,etc.In particular,this is quite useful for choosing the most convenient kinematic variables to describe the N-point diagrams.We suggest that this approach can help in understanding the geometrical struc-ture of loop integrals with several external legs,as well as the structure of phase-space integrals.We also note a connection with3-loop vacuum graphs in three dimensions[17].Acknowledgements. A.D.is grafeful for hospitality to the Physics Department, University of Tasmania,where this work was started. A.D.’s research was essentially supported by the Alexander von Humboldt Foundation,and partly by the grants INTAS–93-0744,RFBR–98-02-16981and Volkswagen–I/73611.A.D.is grateful to the organizers (DESY-Zeuthen)for partial support of his participation in the Rheinsberg workshop. References[1]ndau,Nucl.Phys.13,181(1959);G.K¨a llen,A.Wightman,Mat.Fys.Skr.Dan.Vid.Selsk.1(No.6),1(1958).[2]S.Mandelstam,Phys.Rev.115,1742(1959);R.E.Cutkosky,J.Math.Phys.1,429(1960);R.J.Eden,ndshoff,D.I.Olive,J.C.Polkinghorne,The analytic S-matrix (Cambridge UP,1966).[3]R.Karplus,C.M.Sommerfield,E.H.Wichmann,Phys.Rev.114,376(1959);A.C.T.Wu,Mat.Fys.Medd.Dan.Vid.Selsk.33(No.3),1(1961).[4]J.S.Ball,T.-W.Chiu,Phys.Rev.D22,2550(1980);A.I.Davydychev,J.Phys.A25,5587(1992);H.J.Lu,C.A.Perez,preprint SLAC-PUB-5809(1992).[5]A.I.Davydychev,J.B.Tausk,Phys.Rev.D53,7381(1996).[6]A.I.Davydychev,R.Delbourgo,J.Math.Phys.,to appear,hep-th/9709216.[7]N.Ortner,P.Wagner,Ann.Inst.Henri Poincar´e(Phys.th´e or.)63,81(1995).[8]R.Scharf,Doctoral Thesis,W¨u rzburg(1994);R.Scharf,J.B.Tausk,Nucl.Phys.B412,523(1994).[9]G.’t Hooft,M.Veltman,Nucl.Phys.B44,189(1972);C.G.Bollini,J.J.Giambiagi,Nuovo Cimento12B,20(1972).[10]U.Nierste,D.M¨u ller,M.B¨o hm,Z.Phys.C57,605(1993);F.A.Berends,A.I.Davydychev,V.A.Smirnov,Nucl.Phys.B478,59(1996);E.Remiddi,Nuovo Cimento110A,1435(1997).[11]B.G.Nickel,J.Math.Phys.19,542(1978).[12]G.’tHooft and M.Veltman,Nucl.Phys.B153,365(1979);A.Denner,Fortschr.Phys.41,307(1993).[13]A.Denner,U.Nierste,R.Scharf,Nucl.Phys.B367,637(1991).[14]N.I.Lobatschefsky,Imagin¨a re Geometrie,Kasaner Gelehrte Schriften,1836(¨Uber-setzung mit Anmerkungen von H.Liebmann,Leipzig,1904);L.Schl¨afli,Quart.J.Math.3,54(1860);3,97(1860);Gesammelte matematische Abhandlungen,Band II(Birkh¨a user,Basel,1953).[15]H.S.M.Coxeter,Quart.J.Math.6,13(1935);E.B.Vinberg,Uspekhi Mat.Nauk48(No.2),17(1993)[Russian Math.Surveys48(No.2),15(1993)];R.Kellerhals,in Structural properties of Polylogarithms(ed.L.Lewin),AMS Math.Surveys and Monographs,vol.37,p.301(1991).[16]L.M.Brown,Nuovo Cimento22,178(1961);F.R.Halpern,Phys.Rev.Lett.10,310(1963);G.K¨a ll´e n and J.Toll,J.Math.Phys.6,299(1965);B.Petersson,J.Math.Phys.6,1955(1965);D.B.Melrose,Nuovo Cimento40A,181(1965);W.L.van Neerven,J.A.M.Vermaseren,Phys.Lett.B137,241(1984);Z.Bern,L.Dixon,D.A.Kosower,Phys.Lett.B302,299(1993);Nucl.Phys.B412, 751(1994).[17]D.J.Broadhurst,preprint OUT-4102-74(1998),hep-th/9806174.。