Automatic differentiation tools in optimization software
耐久性分析在汽车研发中的应用
汽车设计寿命的定义
99% User Specification 100，000miles 1 Design margin Design Target
2 97%
150，000miles 3
3%
Customer Use
Part Strength
耐久性开发技术体系
耐久性开发技术体系
VDS SDS DVP CETP CAE-CETP Check list
simulation driven design
• Simulation used to develop concept prior to design actitivities –Efficient use of time and CAD resource –Reduced number of ‘photo real’ confirmation analyses –Much better understanding of component and system
VDS(Vehicle Design Specification)/ARL(Attribute Requirement List) SDS(System/Subsystem Design specification) DVP(Design Verification Plan)---FDVS(Ford Design Verification Plan) CETP(Corporate Engineering Test Procedure) CAE-CETP
车子质量是影响消费者购买的关键考虑因素
(消费者对车子质量的重视程度在不断上升)
%车子质量/ 耐久性是购车过程的重要考虑因 素
前5位的购买考虑因素
48% 42%
t细胞淋巴瘤tcrγ基因重排特征的分析及检测方法优化
Ｔ细胞淋巴瘤ＴＣＲＴ基Ｎ重排特征分析及检测方法的优化摘要研究背景与目的淋巴瘤在组织和细胞形态学方面与高度反应增生性淋巴组织的鉴别诊断十分困难，容易造成误诊。
淋巴瘤病理诊断是临床病理工作的难题之一。
目前国内主要依靠以形态学为主、免疫组化为辅的诊断手段。
随着分子生物学的发展，从基因水平研究和分析诊断疾病的技术不断出现并且日趋成熟，为淋巴瘤诊断提供了有效工具。
淋巴瘤是由单克隆淋巴细胞增生所致，而反应增生性淋巴组织则来自于多克隆淋巴细胞，这是二者的重要区别。
编码免疫球蛋白（Ｉｇ）或Ｔ细胞受体（ＴＣＲ）的基因经过重排以后，不同克隆之间的重排基因互不相同，因此，基因重排对淋巴瘤的诊断具有特异性价值。
以ＰＣＲ技术为基础的方法以其简便、高效、廉价及适用面广而在淋巴瘤基因重排研究方面越来越受重视。
但不同研究文献中所采用的引物、ＰＣＲ条件、ＰＣＲ产物检测方法等都不尽相同，结果也有差异。
因此，难以找到适于常规临床病理诊断之用的标准程序。
Ｊｕｒｋａｔ细胞是Ｔ细胞淋巴瘤基因重排研究中常用的阳性对照细胞，但有关Ｊｕｒｋａｔ细胞基因重排的详细情况也未见报道。
假基因是Ｉｇ和ＴＣＲ胚系ＤＮＡ中常见的基因，有关假基因参与重排的情况以及在设计引物方面是否应将假基因包括在内也未见有关研究报道。
本实验以ＴＣＲ基因重排为研究对象，通过优化引物选择、ＰＣＲ条件及ＰＣＲ产物的检测方法等，分析Ｔ细胞淋巴瘤基因重排检测的最佳方法。
同时，分析ＴＣＲ基因重排的特点，为进一步研究ＴＣＲ基因重排提供理论和技术支持。
方法１以ＴＣＲｙ基因重排为研究对象，选用通用引物ＴＶＧ、ＶｖＩ及ＴＣＲ７家族特异性引物为工具。
用正交设计实验优化ⅥＩ引物的ＰＣＲ条件。
另选一对ＴＣＲ［ｊ通用引物作为ＴＣＲｙ引物的补充和比较。
２利用ＰＣＲ和测序研究Ｊｕｒｋａｔ细胞基因重排情况，分析ＴＣＲ基因重排的基本特点。
３ＰＣＲ产物检测方法①利用ＴＣＲ通用引物检测淋巴瘤克隆性基因重排阳性率，分别用琼脂糖电泳和ＳＳＣＰ分析ＰＣＲ产物；②将ＰＣＲ产物分别进行直接测序和克隆后测序，分析ＴＣＲ基因重排的特点及探索测序方法在基因重排检测中的应用；⑧分析ＰＣＲ产物中ＤＮＡ的克隆数与ＳＳＣＰ中条带数目的关系。
Essential Mathematics for Economic Analysis 5th Ed
Essential Mathematics for Economic Analysis 5th Edition Sydsaeter Solutions ManualFull Download: https:///product/essential-mathematics-for-economic-analysis-5th-edition-sydsaeter-solutionsInstructor’s ManualEssential Mathematics forEconomic AnalysisFifth editionKnut SydsæterPeter HammondArne StrømAndrés CarvajalFor further instructor materialplease visit:/sydsaeterISBN: 978-1-292-07468-9Pearson Education Limited 2017Lecturers adopting the main text are permitted to download and photocopy the manual asrequired.PEARSON EDUCATION LIMITEDEdinburgh GateHarlow CM20 2JEUnited KingdomTel: +44 (0)1279 623623Web: /uk-----------------------------------First edition published 2002Second edition published 2006Third edition published 2008Fourth edition published 2012This edition published 2016© Knut Sydsæter, Peter Hammond, Arne Strøm and Andrés Carvajal 2017The rights of Knut Sydsæter, Peter Hammond, Arne Strøm and Andrés Carvajal to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.ISBN 978-1-292-07468-9All rights reserved. Permission is hereby given for the material in this publication to be reproduced for OHP transparencies and student handouts, without express permission of the Publishers, for educational purposes only. In all other cases, no part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise without either the prior written permission of the Publishers or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd., Barnard’s Inn, 86 Fetter Lane, London EC4A 1EN. This book may not be lent, resold, hired out or otherwise disposed of by way of trade in any form of binding or cover other than that in which is it is published, without the prior consent of the Publishers.Pearson Education is not responsible for the content of third-party internet sites.PrefaceThis Instructor’s Manual accompanies Essential Mathematics for Economic Analysis, 5th Edition. Its main purpose is to provide instructors with a collection of problems that might be used for tutorials and exams. It supplements the problems in MyMathLab.Most of the problems are taken from previous exams and problem sets at the Department of Economics, University of Oslo, and at Stanford University. We have endeavoured to select problems of varying difficulty, including some problems that might challenge even the best students. The number in parentheses after each problem indicates the appropriate section of the text that should be covered before attempting the (whole) problem.For each chapter we offer some comments on the text. Sometimes we explain why certain topics are included and others are excluded. There are also occasional hints based on our experience of teaching the material. In some cases, we also comment on alternative approaches, sometimes with mild criticism of other ways of dealing with the material that we believe to be less suitable.Chapters 2 and 3 in the main text review elementary algebra. This manual includes a Test 1 (page 213), designed for the students themselves to see if they need to review particular sections of Chapters 2 and 3. Many students using our text will probably have some background in calculus. The accompanying Test 2 (page 216) is designed to give information to both the students and the instructors about what students actually know about single variable calculus, and about what needs to be studied more closely, perhaps in Chapters 6–9 of the text.For instructors who are unwilling to spend more than 5–10 minutes for a test of essentials, we have made Test 0 (page 211). Based on our experience, some instructors might be in for a shock if this test is given to students who have been away from mathematics for some time, even if they have an acceptable mathematical background.As with the main text, we would like to acknowledge the extensive help from Cristina Maria Igreja in converting the original plain T E X files for this manual into L A T E X.Oslo and Coventry, April 2016Arne Strøm(*******************.no)Peter Hammond(**********************.uk)Contents1 Essentials of Logic and Set Theory 52 Algebra 73 Solving Equations 144 Functions of One Variable 175 Properties of Functions 236 Differentiation 277 Derivatives in Use 348 Single-Variable Optimization 419 Integration 4910 Topics in Financial Mathematics 5811 Functions of Many Variables 6312 Tools for Comparative Statics 6813 Multivariable Optimization 7514 Constrained Optimization 8215 Matrix and Vector Algebra 9316 Determinants and Inverse Matrices 9717 Linear Programming 109Answers 112 Test 0 (Trivial Test) 211 Test 1 (Elementary Algebra) 213 Test 2 (Elementary Mathematics) 216C H A P T E R 1Essentials of Logic and Set TheorySection 1.2 offers a very brief introduction to some key concepts in logic, and Section 1.3 attempts to give ambitious students a short discussion of proofs. Set theory, treated in Section 1.1, is in our opinion, not crucial for economics students, except when the need for it arises in their statistics courses.Problem 1-01 (1.1)In a group of 100 students, 25 study economics, 30 study political science, and 5 study both subjects. How many students study neither economics nor political science?Problem 1-02 (1.1)Given the sets A = {2, 3, 4, 5}, B = {1, 2, 3, 4, 7}, and C = {1, 3, 6, 7}, which of the following statements are true?(a) 2 ∈ A ∩ B (b) (A ∪ B ) ∩ C = {1, 3, 7} (c) (A \ B ) ∩ C = {2} (d) A ∩ C ⊆ BProblem 1-03 (1.1)Let A , B , and C be three sets. Which of the following statements are true? (Use Venn diagrams.) (a) A ∩ B = A ∩ C and A ≠ 0/ ⇒ B = C(b) A ∩ (B ∪ C ) = (A ∩ B ) ∪ (A ∩ C ) (c) (A \ B ) \ C = A \ (B ∪ C )(d) A ⊆ B ⇒ A ∪ (B \ A ) = BProblem 1-04 (1.2)Which of the following statements are true? (a) x 3 + y 3 = 0 ⇔ x = y = 0 (b) x 2(1 + x ) > 0 ⇔ x > −1 and x ≠ 0(c) 216x x =⇒=(d) x = 3 and y = 5 ⇒ 2x + 4y = 26Problem 1-05 (1.2)Which of the following implications can be reversed? (a) x = 3 ⇒ x 3 = 27(b) x = 0 ⇒ x (x 4 + 1) = 0(c) x ≥ 3 ⇒ (x + 2)2(x − 3) ≥ 0(d) 35x x =⇒=−Sydsæter et al., Essential Mathematics for Economic Analysis , 5e, Instructor’s ManualProblem 1-06 (1.2)Consider the statement: “A matrix can have an inverse only if its determinant is not 0.” Which of the following statements express the same? (You do not need to know the meaning of the concepts.)(a) A sufficient condition for a matrix to have an inverse is that its determinant is not 0. (b) A matrix with determinant equal to 0 has no inverse.(c) A necessary condition for a matrix to have an inverse is that its determinant is not 0.Problem 1-07 (1.3)3+ is irrational.Problem 1-08 (Harder problem.) (1.3)Let a and b+Problem 1-09 (1.4)Prove by induction that for all natural numbers n ≥ 3,212n n +<(*)Problem 1-10 (1.4)Prove by induction that the following equations hold for all natural numbers n .(a) 11223(1)(1)(2)3n n n n n ⋅+⋅+++=++(b) 33322112(1)4n n n +++=+Problem 1-11Let n be a positive integer and consider the expression s n = n 2 − n + 41. Verify that s n is a prime number (and so has no factor except 1 and itself) for n = 1, 2, 3, 4, and 5. With some effort, one can prove that s n is a prime number for n = 6, 7, …, 40 as well. Is s n a prime for all n ? (This problem was first suggested by the Swiss mathematician L. Euler.)Essential Mathematics for Economic Analysis 5th Edition Sydsaeter Solutions ManualFull Download: https:///product/essential-mathematics-for-economic-analysis-5th-edition-sydsaeter-solutions。
泰勒公式及其应用
泰勒公式及其应用许文锋华南师范大学数学科学学院信息与计算科学专业 2007级6班指导老师：谢骊玲中文摘要文章简要介绍了泰勒公式的证明及其推导过程，详细讨论了泰勒公式在高等数学、数值分析、数值最优化理论、其他非数学领域等应用,其中包括利用泰勒公式求近似值、证明积分、不等式、求行列式等高等数学问题；在数值分析问题上面主要讨论了泰勒公式在数值微积分及微分方程数值解上的应用；在最优化问题上面，分别讨论了泰勒公式在理论证明和算法设计上面的应用.关键词：泰勒公式，高等数学，数值分析，数值最优化，应用Taylor Formula and its ApplicationXu WenFeng（Grade 07,Class 6, Major in Information and Computing Science,School ofMathematics,South China Normal University)Tutor:Xie LiLingAbstractThis paper briefly introduces the proof of Taylor and its derivation. And we discuss the application of Taylor formula in detail in some fields such as advanced mathematics, numerical analysis, numerical optimization theory and other applications in some non—mathematical fields ,including using Taylor formula to solve some advanced mathematical problems such as approximation, proof of integral, inequality, solution of determinant etc. In numerical analysis we mainly discuss the applications of Taylor formula in numerical differentiation and numerical integration.As for numerical optimization ，we discuss the applications of Taylor formula in theoretical proof and algorithm design.Keyword ： Taylor formula, advanced mathematics, numerical analysis, numerical optimization, applications一、前言对于某些函数，如果我们要求其在某一点上的值，有时是无法通过直接计算得到的.在学习了导数和微分概念时我们已经知道，如果函数f在0x 点可导，则)())(()()(0000x x x x x f x f x f -+-'+=ο，即在点x 附近，用一次多项式))(()(000x x x f x f -'+逼近函数)(x f 时，其误差为)(0x x-的高阶无穷小.然而在通常的场合中，取一次的多项式逼近是不够的，往往需要用二次或高于二次的多项式去逼近，因此我们提出了用一个多项式去逼近一个函数，泰勒公式就是满足上述逼近性质的多项式.泰勒公式尤其在一些近似计算和数值方法上发挥着举足轻重的作用.本文分为三部分，第一部分是给出了本文所需要用的定理和推论；第二部分是一元泰勒公式的推导和证明以及多元泰勒公式的介绍；第三部分是通过多个实例介绍泰勒公式的应用，包括在高等数学和数值计算方面的应用。
中高级前端工程师等级划分要求
中高级前端工程师等级划分要求英文回答：Mid-Senior Frontend Engineer Grade Differentiation Requirements.Core Competencies:Technical Expertise:Strong foundational knowledge in HTML, CSS, and JavaScript.Proficiency in modern Frontend frameworks (e.g., React, Angular, Vue.js)。
In-depth understanding of browser rendering and performance optimization.Familiarity with server-side technologies (e.g.,Node.js, Python)。
Software Development Best Practices:Agile development methodologies and CI/CD pipelines.Test-driven development and unit testing.Version control and code collaboration.Design Principles:User experience (UX) fundamentals and responsive design.Accessibility guidelines and assistive technologies.Cross-browser compatibility and multi-device support.Experience and Skills:2+ years of experience as a Frontend Engineer.Experience in building and maintaining complex Frontend applications.Strong problem-solving and debugging skills.Excellent communication and collaboration abilities.Leadership and Mentorship:Mentoring junior Frontend Engineers.Leading and contributing to code reviews.Proposing and implementing technical improvements.Continuous Learning and Professional Development:Staying up-to-date with industry trends and emergingtechnologies.Actively participating in open-source projects and online communities.Pursuing further certifications or education.Additional Requirements:Bachelor's degree in Computer Science or a related field (preferred)。
英语词汇
Performance 性能业绩high performance高性能的；高效能；性能优先；高性能模式performance evaluation 业绩评估；业绩评价；绩效评估；成绩考核Performance Settings性能设置；指定执行设置；执行设置；能设置Large scale wind turbines大型风力涡轮vetical axis wind turbines垂直轴风力发电机idling (wind turbines)空转Denmark Strait 丹麦海峡glassfiber：玻璃纤维hub bearing轮毂轴承hub brake车轮制动器，轮闸deepen the reform 深化改革clippers n. 钳子；轧刀；修剪工具（clipper的复数）wingspan (n.)翼展；翼长component [kəm'pəunənt] adj. 组成的，构成的n. 成分；元件；组件nacelle [nə'sel, næ-] n. 气球吊篮；飞机的驾驶员室；飞机的引擎机舱defect density缺陷密度rotorblade：转子叶片；转子刀片；转动叶片warranty card保修卡；保证卡；联保单toughnessn. 韧性；强健；有粘性cyclic ['saiklik] adj. 环的；循环的；周期的soil degradation土壤退化environmental degradation[环境] 环境恶化；环境退化；环境质量下降；环境质损Adaptive Degradation自动降级；自适应降级；自适应降级切换composite ['kɔmpəzit] n. 合成物；复合材料；合成的；复合的；vt. 使合成；使混合coupling 耦合，联轴器clutch n离合器v 使离合器接合shaft coupling联轴器line shaft 主传动轴propeller 螺旋桨推进器couple v 连接rigid coupling 刚性连接（联轴器）flexible coupling弹性连接（联轴器）misalignment 安装误差deflect v 偏移弯曲shock load 冲击载荷coaxial 同轴的driver motor 主驱动电动机rotor 转子rotational inertia 转动惯量torque 扭矩machine tool 机pulley 皮带轮intermediate shaft 中间轴cross section 横截面mount n 固定件，v 安装flywheel 飞轮crank 曲柄bending 弯曲tension 拉伸fatigue 疲劳static stress 静应力spindle 主轴metallic 金属的cushion n缓冲器v 减震，缓冲restrain 约束delicate 精密的disturbing force 干扰力Multiphysics n. 多重物理量coupled multiphysics processes耦合作用过程tutorial [tju:'tɔ:riəl] adj. 辅导的；家庭教师的，个别指导的n. 个别指导configuration [kən,fiɡju'reiʃən] n. 配置；结构；外形si ngular ['siŋɡjulə] adj. [语]单数的；单一的；非凡的；异常的. [语]单数singular function] 奇异函数exponent [ik'spəunənt] n. 说明者，说明物；典型；指数adj. 说明的exponential equationcomposite ['kɔmpəzit] n. 复合材料；合成物；菊科adj. 复合的；合成的；菊科的vt. 使合成；使混合composite material复合材料合成材料composite layer 复合层composite picture signal 复合图象信号commercial aircraft：商用飞机；Military And Commercial Aircraft：军用和商用飞lubrication 润滑grease 润滑脂，黄油friction wear abrasion摩擦磨损sliding 滑动foreign material contaminant杂质seize 粘结weld 焊接adsorb 吸附，吸取adsorber 减震器，阻尼器，缓冲器，hydrostatical 流体液压静力的hydrodynamical 流体动力的viscous 粘性的viscosity 粘性graphite 石墨fracture 断裂deformation 变形distortion变形，扭曲，畸变cavity 空腔polymer 聚合物，高分子材料ceramics陶器brittle 脆的conductivity 传导率传导系数expansion coefficient膨胀系数foundation 基地底座机座mount 固定（件）安装fastener 紧固件screw 螺钉，螺丝rivet n铆钉，v铆接adhesive 粘附剂assault 冲击concurrent engineering 并行工程vent 通风，排气turbine 涡轮机mach 马赫数，速度与音速之比mainshaft主轴alloy 合金tribological 摩擦学的aeroengine航空发动机stellite 钴（硬质）合金thermal conductivity 导热系数inpurity 杂质modulus of elasticity 弹性模量crystalline 金状体的，结晶的shear 剪断，切断adherence 黏附（力）proprietary 专利的，专有的CNC计算机数字控制drawing 绘图，图纸miniaturization 微型化semi-automated 半自动化的nut 螺帽stainless steel 不锈钢thermal 热量的热力的turbulence 湍流漩涡enclosure 外壳，罩子elastisity 弹性（力学）oscillation 震荡摆动coolant 切削液，冷却液spectrum 光谱领域casting 铸件，浇铸bolt 螺栓，用螺栓固定modulus 模数，系数，模量corrosion 腐蚀锈蚀，侵蚀，asperity 粗糙preservative 防腐剂。
数值计算方法PPT课件
2021/3/9
授课：XXX
7
Topics
Fitting Data
Interpolation Curve Fitting
Numerical Differentiation
Numerical Integration
2021/3/9
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2
Books
◦ 数值方法（MATLAB版）（第四版）（美） 马修斯，（美）芬克 著，周璐 等译,电 子工业出版社
2021/3/9
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3
Numamp; Course Overview
2021/3/9
授课：XXX
Numerical Methods Using MATLAB
Dr. Sheng-Jian Lai
Research Building 713#, UESTC Email: cem@
2021/3/9
授课：XXX
1
Research & Work
◦ Numerical Algorithm
Java - Internet Programming Language
Applications Numerical Errors Computer Types Computer Software
2021/3/9
授课：XXX
10
Applications
Signal Processing CFD (Computational Fluid Dynamics) Structural Analysis Finite Element Analysis
《微积分英文》课件 (2)
Types of Limits
One-sided limits
Limits approached
from one direction
Limits at infinity
Behavior of functions at
infinity
● 02
第2章 Limits and Continuity
01 Definition of a limit
Explanation of what a limit is
02 Properties of limits
Key characteristics of limits
03 Calculating limits algebraically
Graphing functions by analyzing their derivatives and key points
Higher Order Derivatives
Second derivative
Rate of change of the rate of
change
nth derivative
● 03
第3章 Differentiation
Derivatives and Rates of
Change
A derivative is defined as the rate of change of a function at a given point. Notation for derivatives includes symbols such as f'(x) or dy/dx. Derivatives can be interpreted as rates of change in various realworld applications.
Materia Proxima 高性能热设塑料说明书
distributed by:Request Quote or SamplesTABLE OF CONTENTS1.Materia overview and capabilities2.Proxima® resins3.Examples of market segment positioning•Oil & gas•Chemical processing•Electronics•Alternative energy•Defense4.Proxima® resin processing5.The Materia differenceTHE PROXIMA ®RESIN DIFFERENCE110100100050100150200250Glass Transition Temp (°C)N o t c h e d I z o d I m p a c t (J /m )PolyurethanesHigh Temp EpoxiesProxima ®Thermoset ResinsProxima ®resins combine high temperature stability with high impact toughness.PROXIMA® PROCESSING VALUE PROPOSITION HIGHLIGHTS•Processable by a wide variety of methods•Tunable process window from seconds tohours•Lower viscosity enables efficient infusion andVARTM high filler levels•Very low capital investment requiredRTM/RIMMATERIA AT A GLANCE• A manufacturer of high performance thermoset resins with unique performance properties•Founded in 1998•Nobel-prize winning chemistry •90 US and 270 foreign patents•World-class technical services and support•Only resin system that utilizes Grubbs Catalyst® technologyWe enable our global customer baseto be more competitive in the marketwith…•High Temperature SubseaInsulation and Buoyancy Products•Tough, Downhole Tools for HighPressure and High Temperature•High Speed and High FrequencyElectronics•Advanced Composites THERMOSETRESINSCAPABILITIES AND LOCATIONSManufacturing –Huntsville, TXTechnical Center of Excellence –Pasadena, CA•Resin system expertise •Product development •Application development & testing •Prototyping•Resin production•ISO 9001 certified •Tolling services•Located 65 miles north of Houston•Analytical•Process optimization •Molding consultation and sample production •Molded part CNC machining•Resin molding•Reaction injection molding •Molded part CNC machining •Molded part paintingMARKETS SERVEDSubsea InsulationChlorinated Fluid HandlingDownhole ToolsElectronic MaterialsSubsea BuoyancyLightweight Pressure VesselsAuto CompositesProxima ®HPR “super -tough”Proxima ®STR “filler -compatible”Proxima ®HTI “high -temp stability”Proxima ®ACR “advanced composites”YouTubeProxima ®resins offer superior performance in diverse applications. Materia customers include world class global industry leaders throughout the oil and gas value chain, and other industries.PROXIMA®RESINSNORBORNENE MONOMERSPROXIMA®THERMOSET NORBORNENE POLYMER PROXIMA®RESINS•Two-part thermoset resin system•Based on dicyclopentadiene(DCPD) and a family of co-monomers•Ring Opening Metathesis Polymerization enabled by Materia’s proprietary Grubbs Catalyst® technology •Leveraging a portfolio of 15+ monomers and 20+ metathesis catalysts UNREINFORCEDPOLYMERSSYNTACTICFOAMSCONTINUOUSFIBERCOMPOSITESPROXIMA®RESIN FAMILY*010020030040050020406080100120140160180200T e n s i l e M o d u l u s (k s i )Glass Transition Temp (°C)Proxima ®HTI resins for high temp insulationProxima ®ACR resins for GF and CF compositesProxima ®HPRhigh-performance resinsProxima ®STR resinsfor syntactic foams*Product line definitions:Proxima ®ACR = advanced composite resins product lineProxima ®HTI = high temperature insulation resins product line Proxima ®STR = syntactic thermoset resins product line Proxima ®HPR = high performance resins product lineProxima ®resins combine high temperature stability with superior resistance to damage.PROXIMA® RESINS –NOT TRADITIONAL POLY-DCPDMore Robust Grubbs CatalystsFewer processcontrolsFewer defectsLow odorproductsFiller compatibleBroaderMonomerToolboxHigh elongationmonomersLow-DCPD andDCPD-freesystemsFilms / coatingswith Lowdielectric LossTunable, reactivefunctional groupsApplicationEngineeringFormulationsdesigned to meetapplication needsResin/catalystselection for cureprofile targetCompositefabrication-friendlyProcessingRIMMold CastingRTM/VARTMMateria has expanded the potential of DCPD thermosets due to a larger family of monomers from which to select, and due to exclusive use of a more robust catalyst.11ADVANTAGES OF PROXIMA ®RESINS OVER COMPETITIVE pDCPD RESINSProxima®ResinAdvantagesReproducible processing, compatible with additives, glass/carbon fiber composite formulations Pot-life control from seconds to daysControlled curing –no problems with thick parts and exothermsTranslucent properties for subsurface inspection significantly improves quality assurance and part reliabilityPromixa’s translucency allows for subsurface inspectionCompetitive pDCPD resins can have molding defectsthat are very difficult to identify in thick parts 3Proxima ®resins enable customer differentiation due to it high temperature stability with superior resistance to damage.MARKET SEGMENT POSITIONINGMARKET SEGMENTOIL & GASOFFSHORE OIL & GASMateria Focus Area: Thermal insulation productsMateria products: Proxima®HTI polymersCompetition:Silicone, neoprene rubberValue proposition: Exceptional hot wet stability, easy processing for onshore and offshore operations, and excellent adhesion to other polymers1516CASE STUDY: HIGH TEMP SUBSEA INSULATIONSource: Miesner & Leffler, Oil and Gas Pipelines in Nontechnical LanguageIn record time Materia built the capacity to provide on-time delivery of Proxima®resin solutions for 40 miles of pipeline while delivering the highest quality product meeting all performance specifications.PROXIMA®HTI 1400 WATER UPTAKE KINETIC STUDY17•Short duration study –Average of 3 cubesizes (1” , 1.5”, 1.75”). Cube size did not drastically alter uptake values.•Long duration study –ASTM D638 Type I tensile specimens.RESULTS•Very low equilibrium water content <1%•Equilibrium is reached quickly-1.00.01.02.03.04.05.00153045607590105120135150165180% W E I G H T C H A N G ETIME (DAYS)SHORT DURATION UPTAKE VARIABLE TEMPERATURELONG DURATION UPTAKE 204 °C (400 °F)0.01.02.03.04.05.04386693149204% W E I G H T C H A N G ETEMPERATURE (°C)1 DAY UPTAKE3 DAY UPTAKE 7 DAY UPTAKEExtensive testing performed to successfully validate a 30 year service life.OFFSHORE OIL & GAS Focus Area: Subsea buoyancyMateria products: Proxima®STR 3190 Competition: EpoxyValue proposition : Lighter weight and faster processing1819CASE STUDY: SUBSEA BUOYANCY WITH STR RESINSHigh Performance Syntactic Foams for Subsea BuoyancyDefect-free largecastingsLower density than other productsHigher strength (+10%) than epoxy ▪Single pour casting of large units (>60 gallons )▪23-30% lower density than epoxy and polyurethane resins▪A portfolio of thermoset resin products available based on customer requirements.PROXIMA SYNTACTIC FOAMProxima ®syntactic foams give the processing ease of polyurethanes & better-than-epoxy performance.DOWNHOLE OIL & GASFocus Area: Downhole tools, consumables, drillable componentsMateria products: Proxima®HPR polymersCompetition: variousValue proposition : Tough/durable, abrasion resistant, light weight, and fast drill-out2021CASE STUDY: CASING CENTRALIZERSLonger wells and fastercompletions;Greater value in longerhorizontal wellsLower Friction Lighter Weight Higher Ductilitydragw e i g h tProxima ®Thermoset vs. Metals▪A casing centralizer maintains pipe in the center of a wellbore to ensure well completion and integrity▪In horizontal wells, drag must be reduced to facilitate completion and enable longer horizontal well drilling▪Use HPR 2100, HPR 2112 or HPR 2124Proxima ®centralizers provide reduced coefficient of friction and can withstand well conditions of >300°F.22PROXIMA ® RESINS FOR FILLED SYSTEMSPROPERTY METHOD (ASTM)UNIT HPR 2029pure polymerHPR 2029ceramic-filledDensityD792g/mL 1.04 1.55Moisture Absorption D570wt.%< 0.2< 0.2Compressive Strength D695psi 13,60027,000Compressive Modulus D695psi 319,000550,000Tensile Strength D638psi 11,00010,200Tensile Modulus D638psi 372,000820,000Elongation at Break D638%124%Glass Transition TempDMA°C176250Proxima ®HPR 2029 is an example of a low viscosity, filler-compatible formulation designed formaximizing thermal and mechanical properties; enabling metal replacement and light-weighting.23INTRODUCING PROXIMA ®ACR4350You no longer have to sacrifice viscosity, toughness or light weight in order to get a high Tg composite.POLYMER PROPERTY METHOD (ASTM)UNIT TYPICAL VALUE Density D792g/mL 1.05TgDSC °C 189Compressive Strength D695MPa 100Compressive Modulus D695MPa 2,360Tensile Strength D638MPa 72Tensile ModulusD638MPa2,700Elongation @Break D638%11Flexural Strength D790MPa 108Flexural ModulusD790MPa2,760Fracture Toughness, K ICD5045MPa·m 1/22.0When compared to 350 °F cure epoxies:•Higher K IC and elongation equates to improved toughness and damage tolerance•Lower density = lighter weight •Lower water absorption and stable thermal performance under hot/wet aging •Comparable Tg values in excess of 180 °CMARKET SEGMENT CHEMICAL PROCESSINGCHEMICAL PROCESSING Focus Area: Pipe and tank for corrosive fluid handling Materia products: Proxima®HPR polymers Competition: Vinyl ester / fiberglassValue proposition: Longer service life,lighter weight25CASE STUDY: CORROSIVE FLUID HANDLING•Customer needed a material with corrosion resistance to handle a process that converts sea water to Cl2, NaOH and H2at 90 °C•Proxima®HPR polymer provides 6+ years service lifetimes in the caustic environment of chlor-alkali electrolysis.•The cell tops are made in a single cast using ~800 lbs of resin and part thicknesses of 1 –5”.26MARKET SEGMENTELECTRONICSELECTRONICSFocus Area: Printed circuit boards, IC packaging, Electronic adhesives Materia products:Proxima®polymer resinsCompetition: Polyphenylene ether, cyanate esters, AND polyimide Value proposition:Superior dielectric properties and competitive pricing2829ELECTRICAL PROPERTIESMATERIAPROPERTYSTANDARD UNIT VALUE Dielectric constant (@10 GHz)ASTM D2520-13- 2.45Loss tangent (@10 GHz)ASTM D2520-13-0.0012Dielectric Strength ASTM D149V/mil 1800Surface Resistivity ASTM D257Ohms > 9.7 x 1015Volume ResistivityASTM D257Ohm-cm> 2.3 x 1016ADVANCED PCBsIC SUBSTRATE DIELECTRICSProxima ®Ultra-Low Loss Resin (Developmental Products)Proxima ®resins are in development for telecom, military, automotive, and oil & gas applications.Current focus is B-stage resins for prepreg applicationsMARKET SEGMENT ALERNATIVE ENERGYALTERNATIVE ENERGYFocus Area: Matrix thermoset resin for glass and carbon fiber wind blades Materia products: Pre-commercial (targeting product launch in 2020) Competition: EpoxyValue proposition: Lighter weight, superior fracture toughness, longer design life, and faster processing3132TOUGH COMPOSITES USING A TOUGH POLYMERDamage zone of Proxima ®laminate is 48% smaller than that of the epoxy laminatePROPERTYMETHOD(ASTM)UNIT ACR 4100INFUSION EPOXYDamage after impact 3D7136-07mm 24037791Data treatment per Reeder and Crews (NASA) for fracture toughness at crack initiation2 Laminates prepared by VARTM of 1200 gsm unidirectional glass fabric and cured at 120 °C for 2h 3T ested by Delsen T esting LaboratoriesEpoxyACR 4100Proxima ®ACR 4100 outperforms standard epoxies by 5x in crack propagation testsPROPERTYMETHOD (ASTM)UNIT ACR 4100INFUSION EPOXYFracture Toughness,K IC 1D5045MPa∙m 1/2 2.60.5Interlaminar Fracture Toughness, G IC 2D55281,2J/m 21,700330Proxima ®resins are tougher than epoxy resins, one of the primary reasons customers select Proxima.33ACR 4100 –PROPERTY RETENTION & WATER ABSORPTIONMATERIAT g Stability (°C)Day 0Day 55Day 82Epoxylaminate1038386Proximalaminate129133132Proxima laminates absorb less water and retain properties better than market leading epoxy laminatesSalt Water Absorption Test: ~160 Days at 60 °C0.00%0.20%0.40%0.60%0.80%1000200030004000W e i g h t c h a n g eTime (h)Proxima laminate Epoxy laminateNutt et al, Polymer Degradation and Stability, 124, (2016), 35-42.CASE STUDY: LESS CARBON FIBER IN PRESSURE VESSELS$2MM in funding from the Department of Energy to lower the cost of hydrogen storage vesselsREDUCTION IN VOIDS / DEFECTSNew tank manufacturing process ofvacuum pressure infusion of dry woundformsHIGH TOUGHNESS RESINBetter fatigue properties and off-axisproperties for improved performanceafter cyclingNEW WINDING PATTERNSNew patterns supported by the dry-winding that may not be achievable withwet-winding34LOWER VOID CONTENT CONFIRMEDSEM images for void detectionCOPV with low void content (<0.5 vol.%) is achievable through infusionWet-wound epoxy tank with voids (3 to 9% across 7 different regions).Infused tank with no detectable voids across 7 regions.35PROXIMA® COMPOSITES FOR WEIGHT REDUCTION Proxima ®resins enable metal replacement and light-weighting in many industries.36PROXIMA ® -HALF THE CARBON FOOTPRINT OF EPOXY37Cradle-to-gate analysis by Sustainability A to Z123456789ProximaEpoxyk g C O 2e q u i v a l e n t sThe production of Proxima generates ~ 50% less carbon than epoxyMARKET SEGMENTDEFENSEDEFENSEFocus Area: Metal replacement for light-weighting, ballistic protection Materia products:Proxima®HPR and ACR polymers Competition: Steel, Aluminum, various othersValue proposition: Tough, light weight, and filler-compatible3940NEAT RESINS SHOW SUPERIOR PROPERTIES TO EPOXIES1MATERIA1Knorr , D. B. et al, “Overcoming structural versus energy dissipation trade -off in highly crosslinked polymer networks: ultrahigh strain response in polydicyclopentadiene ”, Composites Science and Technology, 114, 2015, 17-25.2KE 50= ½•m(V 50)2, conducted with a 0.22 caliber gas gun.pDCPD Neat Resin PanelDGEBA/D230(Epoxy 1)DGEBA/PACM (Epoxy 2)High speed camera images of the impactevent at the V50 valuesRESINTgKE 50(22 °C)2K ICpDCPD 142 °C 3.31 2.13Epoxy 196 °C 1.420.76Epoxy 2164 °C1.000.69Proxima ®resins are tougher than epoxy resins which is one of the key advantages for ballisticsPROXIMA® COMPOSITE BALLISTIC TESTING V50 Ballistic Limit Test Shot SpacingSize (in.)24 x 24 x0.45Total / V50Shots11/114” TriangleNoPenetrationWeight(lbs)10.61V50 (fps)1,597 1.5” ApartNo PenetrationAreal Density (psf)4.72High Partial(fps)1,5951.25” fromunprotected edgeNoPenetrationThickness0.45LowComplete(fps)1,5974” Triangle (attackside -26 °F)NoPenetrationThreat44 Mag240 LSWC Range ofResults1124” Triangle(Conditioned 120 °F)NoPenetration1Composite was tested by U.S. T est Labs under the MIL-STD-662F V50T est E-Glass Woven RovingCompositeProxima®resins are infusion friendly and the inherent toughness translates to composite partsPROXIMA® RESIN PROCESSINGPROXIMA®RESIN PROCESSING METHODS Materia provides engineering support for a variety of Proxima®resin processing methods.•Mold casting•RIM / RTM•VARTM•Centrifugal casting Vacuum-assisted resin transfer moldingPROCESSING –REACTIVITY CONTROL020*********120140012345678V I S C O S I T Y (C P )TIME (HOURS )WORK TIME AT 30 °CProxima ®resins enable significant formulation flexibility with controlled curing, from seconds to hours;enabling customers to enhance their product portfolios.PROCESSING –VIDEO DEMONSTRATIONSProxima®resins enable significant formulation flexibility with controlled curing, from seconds to hours;enabling customers to enhance their product portfolios.THE MATERIA DIFFERENCE•Materia goes beyond delivery of just a superior polymer but ensures excellence through formulation and applications engineering support•Materia is nimble and can enhance your speed to marketthrough immediate access to functional leaders•Proxima resins can enhance your product portfolio and differentiate your offering in the marketplace•We offer a total cost of ownership advantage: using Proxima®thermoset resins can lower your capital expenditures andenable higher throughputTHANK YOU distributed by:© 2017 Materia, Inc.。
高等数学英文教材书名
高等数学英文教材书名Title: Advanced Calculus - An English TextbookIntroduction:Advanced Calculus is a comprehensive English textbook designed to provide a solid foundation in the principles and applications of higher-level mathematics. This textbook aims to cater to the needs of undergraduate and graduate students studying mathematics, engineering, and other related fields. Its well-structured content, precise explanations, and engaging examples make it an indispensable resource for anyone seeking to deepen their understanding of advanced calculus.Chapter 1: Limits and ContinuityIn this chapter, readers are introduced to the fundamental concepts of limits and continuity. Starting with an overview of the concept of a limit, the textbook gradually delves into the intricacies of one-sided and infinite limits. Through clear explanations and illustrative examples, students will develop a solid understanding of continuity and its various properties, such as the intermediate value theorem and the extreme value theorem.Chapter 2: DifferentiationThis chapter explores the concept of differentiation - a crucial tool in calculus. The textbook provides a step-by-step approach to calculating derivatives of various functions, including polynomials, exponential and logarithmic functions, and trigonometric functions. Additionally, the concept of higher-order derivatives and their applications are extensively covered,allowing students to grasp the intricacies of curve sketching and optimization problems.Chapter 3: IntegrationThe textbook presents integration as a powerful technique for finding areas, volumes, and cumulative sums. Starting with the definite integral and its properties, the chapter progresses to explore various integration methods, such as substitution, integration by parts, and partial fractions. Furthermore, the textbook covers improper integrals and numerical integration methods, equipping students with the necessary tools to solve a wide range of mathematical problems.Chapter 4: Sequences and SeriesThis chapter focuses on the concepts of sequences and series, which play a fundamental role in advanced calculus. Beginning with an introduction to arithmetic and geometric sequences, the textbook moves on to explore the convergence and divergence of sequences. Furthermore, different types of series, including geometric, Taylor, and Fourier series, are presented, along with their convergence properties and applications.Chapter 5: Multivariable CalculusIn this chapter, readers are introduced to the complexities of multivariable calculus. The textbook covers topics such as partial derivatives, directional derivatives, multiple integrals, and vector calculus. Through practical examples and applications, students will develop a deep understanding of how calculus applies to functions of multiple variables, preparing them for more advanced mathematical concepts.Chapter 6: Differential EquationsThe final chapter of this textbook focuses on differential equations, which are essential in modeling real-world phenomena. Starting with first-order differential equations, the textbook progressively introduces higher-order differential equations, separable equations, and systems of linear differential equations. Different solution methods, such as integrating factors and Laplace transforms, are also presented, allowing students to solve a wide range of differential equation problems.Conclusion:Advanced Calculus - An English Textbook provides a comprehensive and rigorous study of advanced mathematical concepts, serving as an invaluable resource for students pursuing mathematics and related disciplines. With its clear explanations, numerous examples, and well-organized content, this textbook equips students with the necessary tools to tackle complex mathematical problems and fosters a deeper understanding of the principles underlying advanced calculus.。