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The 14th National Conference on Algebra
第十四届
全国代数学学术会议
会议程序
扬州大学主办
中国扬州
2016年5月26日——5月31日
注意：各报告场地以本手册为准。
一、会议日程
二、会议日程简表
三、会议日程详单
5月26日（星期四）扬州会议中心报到
5月27日（星期五）开幕式与大会报告地点：杏园楼百畅厅
5月28日（星期六）分组报告(第一组) 地点：群贤楼会议室二
5月28日（星期六）分组报告(第二组) 地点：群贤楼会议室三
5月28日（星期六）分组报告(第三组) 地点：群贤楼贵宾室一
5月28日（星期六）分组报告(第四组) 地点：群贤楼贵宾室二
5月28日（星期六）分组报告(第五组) 地点：群贤楼多功能厅
5月28日（星期六）分组报告(第六组) 地点：群贤楼贵宾室四
5月28日（星期六）分组报告(第七组) 地点：群贤楼会议室六
5月28日（星期六）分组报告(第八组) 地点：群贤楼会议室七
5月29日（星期日上午）分组报告(第二组) 地点：群贤楼会议室三
5月29日（星期日上午）分组报告(第四组) 地点：群贤楼贵宾室二
5月29日（星期日上午）分组报告(第六组) 地点：群贤楼贵宾室四
5月29日（星期日下午）邀请报告(第二组) 地点：群贤楼贵宾室二
5月29日（星期日下午）邀请报告(第三组) 地点：群贤楼贵宾室四
5月30日（星期一）大会报告与闭幕式地点：春晖楼春台庆禧厅。
中国科学英文版模板1.Identification of Wiener systems with nonlinearity being piece wise-linear function HUANG YiQing，CHEN HanFu，FANG HaiTao2.A novel algorithm for explicit optimal multi-degree reduction of triangular surfaces HU QianQian，WANG GuoJin3.New approach to the automatic segmentation of coronary arte ry in X-ray angiograms ZHOU ShouJun，YANG Jun，CHEN WuFan，WANG YongTian4.Novel Ω-protocols for NP DENG Yi，LIN DongDai5.Non-coherent space-time code based on full diversity space-ti me block coding GUO YongLiang，ZHU ShiHua6.Recursive algorithm and accurate computation of dyadic Green 's functions for stratified uniaxial anisotropic media WEI BaoJun，ZH ANG GengJi，LIU QingHuo7.A blind separation method of overlapped multi-components b ased on time varying AR model CAI QuanWei，WEI Ping，XIAO Xian Ci8.Joint multiple parameters estimation for coherent chirp signals using vector sensor array WEN Zhong，LI LiPing，CHEN TianQi，ZH ANG XiXiang9.Vision implants: An electrical device will bring light to the blind NIU JinHai，LIU YiFei，REN QiuShi，ZHOU Yang，ZHOU Ye，NIU S huaibining search space partition and search Space partition and ab straction for LTL model checking PU Fei，ZHANG WenHui2.Dynamic replication of Web contents Amjad Mahmood3.On global controllability of affine nonlinear systems with a tria ngular-like structure SUN YiMin，MEI ShengWei，LU Qiang4.A fuzzy model of predicting RNA secondary structure SONG D anDan，DENG ZhiDong5.Randomization of classical inference patterns and its applicatio n WANG GuoJun，HUI XiaoJing6.Pulse shaping method to compensate for antenna distortion in ultra-wideband communications WU XuanLi，SHA XueJun，ZHANG NaiTong7.Study on modulation techniques free of orthogonality restricti on CAO QiSheng，LIANG DeQun8.Joint-state differential detection algorithm and its application in UWB wireless communication systems ZHANG Peng，BI GuangGuo，CAO XiuYing9.Accurate and robust estimation of phase error and its uncertai nty of 50 GHz bandwidth sampling circuit ZHANG Zhe，LIN MaoLiu，XU QingHua，TAN JiuBin10.Solving SAT problem by heuristic polarity decision-making al gorithm JING MingE，ZHOU Dian，TANG PuShan，ZHOU XiaoFang，ZHANG Hua1.A novel formal approach to program slicing ZHANG YingZhou2.On Hamiltonian realization of time-varying nonlinear systems WANG YuZhen，Ge S. S.，CHENG DaiZhan3.Primary exploration of nonlinear information fusion control the ory WANG ZhiSheng，WANG DaoBo，ZHEN ZiYang4.Center-configur ation selection technique for the reconfigurable modular robot LIU J inGuo，WANG YueChao，LI Bin，MA ShuGen，TAN DaLong5.Stabilization of switched linear systems with bounded disturba nces and unobservable switchings LIU Feng6.Solution to the Generalized Champagne Problem on simultane ous stabilization of linear systems GUAN Qiang，WANG Long，XIA B iCan，YANG Lu，YU WenSheng，ZENG ZhenBing7.Supporting service differentiation with enhancements of the IE EE 802.11 MAC protocol: Models and analysis LI Bo，LI JianDong，R oberto Battiti8.Differential space-time block-diagonal codes LUO ZhenDong，L IU YuanAn，GAO JinChun9.Cross-layer optimization in ultra wideband networks WU Qi，BI JingPing，GUO ZiHua，XIONG YongQiang，ZHANG Qian，LI ZhongC heng10.Searching-and-averaging method of underdetermined blind s peech signal separation in time domain XIAO Ming，XIE ShengLi，F U YuLi11.New theoretical framework for OFDM/CDMA systems with pe ak-limited nonlinearities WANG Jian，ZHANG Lin，SHAN XiuMing，R EN Yong1.Fractional Fourier domain analysis of decimation and interpolat ion MENG XiangYi，TAO Ran，WANG Yue2.A reduced state SISO iterative decoding algorithm for serially concatenated continuous phase modulation SUN JinHua，LI JianDong，JIN LiJun3.On the linear span of the p-ary cascaded GMW sequences TA NG XiaoHu4.De-interlacing technique based on total variation with spatial-t emporal smoothness constraint YIN XueMin，YUAN JianHua，LU Xia oPeng，ZOU MouYan5.Constrained total least squares algorithm for passive location based on bearing-only measurements WANG Ding，ZHANG Li，WU Ying6.Phase noise analysis of oscillators with Sylvester representation for periodic time-varying modulus matrix by regular perturbations FAN JianXing，YANG HuaZhong，WANG Hui，YAN XiaoLang，HOU ChaoHuan7.New optimal algorithm of data association for multi-passive-se nsor location system ZHOU Li，HE You，ZHANG WeiHua8.Application research on the chaos synchronization self-mainten ance characteristic to secret communication WU DanHui，ZHAO Che nFei，ZHANG YuJie9.The changes on synchronizing ability of coupled networks fro m ring networks to chain networks HAN XiuPing，LU JunAn10.A new approach to consensus problems in discrete-time mult iagent systems with time-delays WANG Long，XIAO Feng11.Unified stabilizing controller synthesis approach for discrete-ti me intelligent systems with time delays by dynamic output feedbac k LIU MeiQin1.Survey of information security SHEN ChangXiang，ZHANG Hua ngGuo，FENG DengGuo，CAO ZhenFu，HUANG JiWu2.Analysis of affinely equivalent Boolean functions MENG QingSh u，ZHANG HuanGuo，YANG Min，WANG ZhangYi3.Boolean functions of an odd number of variables with maximu m algebraic immunity LI Na，QI WenFeng4.Pirate decoder for the broadcast encryption schemes from Cry pto 2005 WENG Jian，LIU ShengLi，CHEN KeFei5.Symmetric-key cryptosystem with DNA technology LU MingXin，LAI XueJia，XIAO GuoZhen，QIN Lei6.A chaos-based image encryption algorithm using alternate stru cture ZHANG YiWei，WANG YuMin，SHEN XuBang7.Impossible differential cryptanalysis of advanced encryption sta ndard CHEN Jie，HU YuPu，ZHANG YueYu8.Classification and counting on multi-continued fractions and its application to multi-sequences DAI ZongDuo，FENG XiuTao9.A trinomial type of σ-LFSR oriented toward software implemen tation ZENG Guang，HE KaiCheng，HAN WenBao10.Identity-based signature scheme based on quadratic residues CHAI ZhenChuan，CAO ZhenFu，DONG XiaoLei11.Modular approach to the design and analysis of password-ba sed security protocols FENG DengGuo，CHEN WeiDong12.Design of secure operating systems with high security levels QING SiHan，SHEN ChangXiang13.A formal model for access control with supporting spatial co ntext ZHANG Hong，HE YePing，SHI ZhiGuo14.Universally composable anonymous Hash certification model ZHANG Fan，MA JianFeng，SangJae MOON15.Trusted dynamic level scheduling based on Bayes trust model WANG Wei，ZENG GuoSun16.Log-scaling magnitude modulated watermarking scheme LING HeFei，YUAN WuGang，ZOU FuHao，LU ZhengDing17.A digital authentication watermarking scheme for JPEG image s with superior localization and security YU Miao，HE HongJie，ZHA NG JiaShu18.Blind reconnaissance of the pseudo-random sequence in DS/ SS signal with negative SNR HUANG XianGao，HUANG Wei，WANG Chao，L(U) ZeJun，HU YanHua1.Analysis of security protocols based on challenge-response LU O JunZhou，YANG Ming2.Notes on automata theory based on quantum logic QIU Dao Wen3.Optimality analysis of one-step OOSM filtering algorithms in t arget tracking ZHOU WenHui，LI Lin，CHEN GuoHai，YU AnXi4.A general approach to attribute reduction in rough set theory ZHANG WenXiuiu，QIU GuoFang，WU WeiZhi5.Multiscale stochastic hierarchical image segmentation by spectr al clustering LI XiaoBin，TIAN Zheng6.Energy-based adaptive orthogonal FRIT and its application in i mage denoising LIU YunXia，PENG YuHua，QU HuaiJing，YiN Yong7.Remote sensing image fusion based on Bayesian linear estimat ion GE ZhiRong，WANG Bin，ZHANG LiMing8.Fiber soliton-form 3R regenerator and its performance analysis ZHU Bo，YANG XiangLin9.Study on relationships of electromagnetic band structures and left/right handed structures GAO Chu，CHEN ZhiNing，WANG YunY i，YANG Ning10.Study on joint Bayesian model selection and parameter estim ation method of GTD model SHI ZhiGuang，ZHOU JianXiong，ZHAO HongZhong，FU Qiang。
小学上册英语第一单元综合卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.I like to watch ________ in the summer.2.My favorite holiday is ________ (圣诞节). I like to decorate the ________ (圣诞树).3.My favorite book is ________.4.What do we call the place where you can buy groceries?A. StoreB. MarketC. MallD. Supermarket5.The _______ of a balloon can be affected by altitude.6.The _______ (兔子) hops around quickly when it is excited.7.What is the name of the game where you shoot hoops?A. SoccerB. BasketballC. BaseballD. TennisB8. A thermochemical reaction involves heat and chemical ______.9. (85) is a famous park in New York City. The ____10.The _______ (Apollo 11) mission successfully landed humans on the Moon.11.What is 100 - 25?A. 65B. 70C. 75D. 8012.What is the main ingredient in sushi?A. RiceB. NoodlesC. BreadD. PotatoesA13.The bear roams in the _____ woods.14.__________ are important for environmental sustainability.15.The chemical formula for table salt is ______.16.What is the capital of Honduras?A. TegucigalpaB. San Pedro SulaC. La CeibaD. CholutecaA17. A ______ (狗) has a keen sense of smell.18.The ancient Greeks created _______ to explain natural phenomena. (神话)19.The teacher, ______ (老师), guides us in our studies.20.The cake is _______ (刚出炉).21.The _____ (first) man-made satellite was Sputnik, launched by the USSR.22.The capital of Faroe Islands is __________.23.The __________ can provide critical insights into environmental health and stability.24.What do you call the place where we see many books?A. SchoolB. LibraryC. StoreD. Park25.What do you call the study of the Earth's atmosphere?A. MeteorologyB. GeologyC. AstronomyD. Ecology26.What is the term for the distance around a circle?A. AreaB. DiameterC. CircumferenceD. RadiusC27. A ___ (小蝴蝶) flutters gently in the air.28.My ________ (玩具) is made of plush material.29.What do we call the act of cleaning a room?A. TidyingB. OrganizingC. DeclutteringD. CleaningA30.What do we call the tool we use to write on paper?A. MarkerB. PenC. PencilD. All of the above31.The teacher gives _____ (作业) every week.32.The _______ of matter refers to whether it is a solid, liquid, or gas.33.What is the opposite of short?A. TallB. WideC. NarrowD. ThickA34.I like to play ___ (video games).35.I like to play ________ with my friends after school.36.My _____ (表妹) is visiting this weekend.37.The ________ was a famous treaty that settled disputes in Europe.38.What do you call the action of planting flowers in a garden?A. GardeningB. LandscapingC. CultivatingD. SowingA39.ts can live for ______ (数十年). Some pla40.My family lives near a __________ (水库).41.What is the opposite of right?A. WrongB. CorrectC. TrueD. AccurateA42.The _____ (羊) eats grass in the field.43.What is the term for a person who collects stamps?A. PhilatelistB. NumismatistC. CollectorD. HobbyistA44.Every year, we celebrate ______ (感恩节) with a big feast and share what we are thankful for.45.The ancient Egyptians created vast ________ (陵墓) for their pharaohs.46.I have a _____ (遥控车) that can go super fast. 我有一辆可以跑得非常快的遥控车。
MPX2300DT1Freescale reserves the right to change the detail specifications as may be required to permit improvements in the design of its products.Freescale Semiconductor Document Number: MPX2300DT1Data Sheet: Technical DataRev. 11, 09/2015© 2010, 2012, 2014, 2015 Freescale Semiconductor, Inc. All rights reserved.MPX2300DT1, 0 to 40kPa, Differential Compensated Pressure SensorFreescale Semiconductor has developed a high volume, miniature pressurecompensation and calibration.Features•Integrated temperature compensation and calibration •Ratiometric to supply voltage•Polysulfone case material (ISO 10993)•Provided in easy-to-use tape and reel Typical applications•Medical diagnostics •Infusion pumps•Blood pressure monitors •Pressure catheter applications •Patient monitoringNOTEhousing. Use caution when handling the devices during all processes.Ordering informationDevice name Shipping Package Pressure typeDevice marking GaugeDifferentialAbsoluteMPX2300DT1Tape and Reel98ASB13355C•XXXX = Device code XXX = Trace codeMPX2300DT1Contents1General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1Block diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2Pinout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2Mechanical and Electrical Specifications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1Maximum ratings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2Operating characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3Package Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.1Package description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 4Revision History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Related DocumentationThe MPX2300DT1 device features and operations are described in a variety of reference manuals, user guides, and application notes. To find the most-current versions of these documents:1.Go to the Freescale homepage at:/2.In the Keyword search box at the top of the page, enter the device number MPX2300DT1.3.In the Refine Your Result pane on the left, click on the Documentation link.MPX2300DT1SensorsMPX2300DT1Sensors1General DescriptionThe MPX2300DT1 pressure sensor has been designed for medical usage by combining the performance of Freescale's shear stress pressure sensor design and the use of biomedically approved materials. Materials with a proven history in medical situations have been chosen to provide a sensor that can be used with confidence in applications, such as invasive blood pressure monitoring. It can be sterilized using ethylene oxide. The portions of the pressure sensor that are required to be biomedically approved are the rigid housing and the gel coating.The rigid housing is molded from a white, medical grade polysulfone that has passed extensive biological testing including: ISO 10993-5:1999, ISO 10993-10:2002, and ISO 10993-11:1993.A silicone dielectric gel covers the silicon piezoresistive sensing element. The gel is a nontoxic, nonallergenic elastomer system which meets all USP XX Biological Testing Class V requirements. The properties of the gel allow it to transmit pressure uniformly to the diaphragm surface, while isolating the internal electrical connections from the corrosive effects of fluids, such as saline solution. The gel provides electrical isolation sufficient to withstand defibrillation testing, as specified in the proposed Association for the Advancement of Medical Instrumentation (AAMI) Standard for blood pressure transducers. A biomedically approved opaque filler in the gel prevents bright operating room lights from affecting the performance of the sensor.1.1Block diagramFigure 1 shows a block diagram of the internal circuitry integrated on a pressure sensor chip.Figure 1. Block diagram1.2PinoutFigure 2. Device pinout (front view)Table 1. Pin functionsPin Name Function1V S Voltage supply 2V OUT +Output voltage 3V OUT –Output voltage 4GNDGroundV OUT +V OUT –32V S 1Transducer GND4Thin Film Temperature Compensation and Calibration CircuitrySensingElementV S V O U T +V O U T –G N DMPX2300DT1Sensors2Mechanical and Electrical Specifications2.1Maximum ratings2.2Operating characteristicsTable 2. Maximum ratings (1)1.Exposure beyond the specified limits may cause permanent damage or degradation to the device.RatingSymbol Value Unit Maximum pressure (backside)P max 125PSI Storage temperature T stg -25 to +85°C Operating temperatureT A+15 to +40°CTable 3. Operating characteristics(V S = 6 V DC , T A = 25°C unless otherwise noted)CharacteristicsSymbol Min Typ Max Unit Pressure range P OP 0—300mmHg Supply voltage (1)1.Recommended voltage supply: 6 V ± 0.2 V, regulated. Sensor output is ratiometric to the voltage supply. Supply voltages above +10 V may induce additional error due to device self-heating.V S — 6.010V DC Supply current I O — 1.0—mAdc Zero pressure offset V OFF -0.75—0.75mV Sensitivity — 4.95 5.0 5.05μV/V/mmHgFull-scale span (2)2.Measured at 6.0 V DC excitation for 100 mmHg pressure differential. V FSS and FSS are like terms representing the algebraic difference between full scale output and zero pressure offset.V FSS 2.976 3.006 3.036mV Linearity + Hysteresis (3)3.Maximum deviation from end-point straight line fit at 0 and 200 mmHg.—-1.5— 1.5%V FSS Accuracy V S = 6 V, P = 101 to 200 mmHg —-1.5— 1.5%Accuracy V S = 6 V, P = 201 to 300 mmHg —-3.0— 3.0%Temperature effect on sensitivity TCS -0.1—+0.1%/°C Temperature effect on full-scale span (4)4.Slope of end-point straight line fit to full scale span at 15°C and +40°C relative to +25°C.TCV FSS -0.1—+0.1%/°C Temperature effect on offset (5)5.Slope of end-point straight line fit to zero pressure offset at 15°C and +40°C relative to +25°C.TCV OFF -9.0—+9.0μV/°C Input impedance Z IN 1800—4500ΩOutput impedance Z OUT 270—330ΩR CAL (150 k Ω)(6)6.Offset measurement with respect to the measured sensitivity when a 150 k resistor is connected to V S and V OUT + output.R CAL 97100103mmHg Response time (7) (10% to 90%)7.For a 0 to 300 mmHg pressure step change.t R—1.0—msMPX2300DT1Sensors3Package Dimensions3.1Package descriptionThis drawing is located at /files/shared/doc/package_info/98ASB13355C.pdf .Case 98ASB1335C, Chip Pak packageMPX2300DT1Sensors4Revision HistoryTable 4. Revision historyRevisionnumberRevision date Description910/2012•Added Table 1. Pin Numbers on page 1.1009/2015•Updated format.1109/2015•Corrected pinout on first page and Section 1.2 and Table 1.•Replaced Figure 1, Block diagram.Document Number:MPX2300DT1Rev. 1109/2015Information in this document is provided solely to enable system and software implementers to use Freescale products. There are no express or implied copyright licenses granted hereunder to design or fabricate any integrated circuits based on the information in this document.Freescale reserves the right to make changes without further notice to any products herein. Freescale makes no warranty, representation, or guarantee regarding the suitability of its products for any particular purpose, nor does Freescale assume any liability arising out of the application or use of any product or circuit, and specifically disclaims any and all liability, including without limitation consequential or incidental damages. “Typical” parameters that may be provided in Freescale data sheets and/or specifications can and do vary in different applications, and actual performance may vary over time. All operating parameters, including “typicals,” must be validated for each customer application by customer’s technical experts. Freescale does not convey any license under its patent rights nor the rights of others. Freescale sells products pursuant to standard terms and conditions of sale, which can be found at the following address: /salestermsandconditions .How to Reach Us:Home Page: Web Support:/supportFreescale and the Freescale logos are trademarks of Freescale Semiconductor, Inc., Reg. U.S. Pat. & Tm. Off. All other product or service names are the property of their respective owners.© 2010, 2012, 2014, 2015 Freescale Semiconductor, Inc.MPX2300DT1。
使用代数多重网格进行多聚焦图像融合黄颖;解梅;李伟生;高靖淞【摘要】An adaptive multi-focus image fusion algorithm based on algebraic multigrid (AMG) method is proposed for the capability to extract structural information of an image. The data of the coarse level is extracted to reconstruct the image block, appropriate source image block is selected into the fusion result according to the mean square error between the reconstructed image block and the original image block. For smoothing the fused result, an adaptive strategy is used. Experimental results show that most of the clear objects can be retained in the fused image with the proposed algorithm without loss of effective information.%针对将代数多重网格对图像结构信息的提取能力应用到图像的融合方面进行了研究，提出了一种基于代数多重网格的自适应多聚焦图像融合算法。
首先提取图像的粗网格数据，然后进行分块重建，根据分块重建结果与原始图像的均方差选择合适的源图像分块进入融合图像。
为了避免分块之间的不连续性，采用了自适应的策略。
实验结果表明，自适应图像融合的结果没有丢失有效信息，能够最大程度地将清晰物体保留在融合图像之中。
代数学教程英文版Algebra Tutorial (English Version) Chapter 1: Introduction to Algebra- What is Algebra?- Algebraic Operations- Algebraic Expressions- Simplifying Expressions- Evaluating ExpressionsChapter 2: Solving Equations- Solving Linear Equations- Solving Quadratic Equations- Solving Systems of Equations- Solving Exponential Equations- Solving Radical EquationsChapter 3: Graphing and Functions- Cartesian Coordinate System- Graphing Linear Equations- Graphing Quadratic Equations- Graphing Exponential Functions- Domain and Range of Functions Chapter 4: Polynomials- Introduction to Polynomials- Adding and Subtracting Polynomials- Multiplying Polynomials- Factoring Polynomials- Synthetic DivisionChapter 5: Rational Expressions- Simplifying Rational Expressions- Multiplying and Dividing Rational Expressions - Adding and Subtracting Rational Expressions- Complex Fractions- Rational EquationsChapter 6: Exponents and Radicals- Laws of Exponents- Simplifying Exponential Expressions- Properties of Radicals- Simplifying Radicals- Rationalizing DenominatorsChapter 7: Inequalities- Solving Linear Inequalities- Solving Quadratic Inequalities- Solving Rational Inequalities- Compound Inequalities- Absolute Value InequalitiesChapter 8: Sequences and Series- Arithmetic Sequences- Geometric Sequences- Arithmetic Series- Geometric Series- Infinite SeriesChapter 9: Logarithmic and Exponential Functions- Exponential Functions- Logarithmic Functions- Properties of Logarithms- Solving Exponential Equations with Logarithms- Exponential Growth and DecayChapter 10: Matrices and Determinants- Introduction to Matrices- Matrix Operations- Matrix Inverses- Determinants- Solving Systems of Linear Equations with Matrices Chapter 11: Complex Numbers- Introduction to Complex Numbers- Operations with Complex Numbers- Complex Conjugates- Complex Plane- Complex Roots of Quadratic EquationsChapter 12: Conic Sections- Introduction to Conic Sections- Circles- Parabolas- Ellipses- HyperbolasChapter 13: Word Problems and Applications- Age Problems- Mixture Problems- Distance, Rate, and Time Problems - Interest Problems- Work Problems。
THE RIEMANN HYPOTHESISMICHAEL ATIYAH1.IntroductionIn my Abel lecture [1] at the ICM in Rio de Janeiro 2018, I explained how to solve a long-standing mathematical problem that had emerged from physics. The problem was to understand the fine structure constant α.The full details are contained in [2] which has been submitted to proceedings A of the Royal Society. The techniques developed in [2] are a novel fusion of ideas of von Neumann and Hirzebruch. They are sophisticated and powerful, based on an infinite iteration of exponentials, while having an inherent simplicity.Attacking the mystery of α was the motivation, but the power and universality of the methods indicated that they should solve other hard problems, or at least shed new light on them if they are insoluble. In expanding my Abel Lecture for the ICM Proceedings I speculated that the techniques of [2] might lead to the new subject of Arithmetic Physics.The Riemann Hypothesis RH is the assertion that ζ(s) has no zeros in the critical strip 0 < Re(s) < 1 , off the critical line Re(s) = 1/2. It is one of the most famous unsolved problems in mathematics and a formidable challenge for the programme envisaged in [1]. I believe it will live up to this challenge, and this paper will provide the proof.The proof depends on a new function T (s), the Todd function, named by Hirzebruch after my teacher J.A.Todd. Its definition and properties are all in [2] but, in section 2, I will review and clarify them. In section 3 I will use the function T (s) to prove RH. In section 4, entitled Deus ex Machina, I will try to explain the mystery of this simple proof of RH. Finally, in section 5, I will place this paper in the broader context of Arithmetic Physics as envisaged in [1].2.The Todd functionIn this section I summarize the properties of the Todd function T (s), constructed in [2].T is what I will call a weakly analytic function meaning that it is a weak limit of a family of analytic functions. So, on any compact set K in C, T is analytic. If K is convex, T is actually a polynomial of some degree k(K). For example a step function is weakly analytic and, for any closed interval K on the line, the degree is 0. This shows that a weakly analytic function can have compact support, in contrast to an analytic function. Weakly14analytic functions are weakly dense in L 2 and in their weak duals. They are well adapted for Fourier transforms on all L p spaces. They are also composable: a weakly analytic function of a weakly analytic function is weekly analytic.Define K [a ] to be the closed rectangle(2.1)|Re (s − 1/2)| ≤ 1 , |Im (s )| ≤ a. Then, on K [a ], T is a polynomial of degree k{a} = k (K [a ]).This terminology is formally equivalent to that of Hirzebruch [3], with his Todd polynomials. But Hirzebruch worked with formal power series and did not require convergence. That was adequate for his applications which were essentially algebraic and arithmetic, as the appearance of the Bernoulli numbers later showed.However, to relate to von Neumann’s analytical theory it is necessary to take weak limits as h as just been done. This provides the c rucial link between a lgebra/arithmetic a nd a nalysis which is at the heart of the ζ function.This makes it reasonable to expect that RH might emerge naturally from the fusion of the different techniques in [2].I return now to other properties of T (s ) explained in [2]:2.2 T is real i.e. T (s ¯) = T (¯s ). 2.3 T (1) = 12.4 T maps the critical strip into the critical strip and the critical line into the critical line. (This is not explicitly stated in [2] but it is included in the mimicry principle 7.6, which asserts that T is compatible with any analytic formula, so in particular Im (T (s − 1/2)= T (Im (s − 1/2)).)The main result of [2], identifying α with 1/Ж, was2.5 on Re (s ) = 1/2, Im (s ) > 0, T is a monotone increasing function of Im (s ) whose limit, as Im (s ) tends to infinity, is Ж.As was noted above, on a given compact convex set, the Todd polynomials stabilize as the degree increases. In [3] Hirzebruch expressed this stability in the form of an equation:2 { } | − |2.6 if f and g are power series with no constant term, thenT {[1 + f (s )] · [1 + g (s )]} = T {1 + f (s ) + g (s )}.Remark. Weakly analytic functions have a formal expansion as a power series near the origin. F orm ula 2.6 is just the linear appro ximation of this exp a √n s ion (more precisely this is on the branched double cover of the complex s -plane given by 2.6 T (√s ) = √T (s ) or2.7 √T (1 + s ) = T (1 + s/2)s ). This implieswhich gives us the uniform constant 1/2 needed in 3.3 of section 3.3. The proof of RHIn this section I will use the Todd function T (s ) to prove RH. The proof will be by contradiction : assume there is a zero b inside the critical strip but off the critical line. To prove RH, it is then sufficient to show that the existence of b leads to a contradiction. Given b , take a = b in 2.1 then, on the rectangle K [a ], T is a polynomial of degree k a . Consider the composite function of s , given by(3.1) F (s ) = T {1 + ζ(s + b )} − 1From its construction, and the hypothesis that ζ(b ) = 0, it follows that3.2 F is analytic at s = 0 and F (0) = 0.Now take f = g = F in 2.6 and we deduce the identity3.3 F (s ) = 2F (s ).Since C is not of characteristic 2, it follows that F (s ) is identically zero. 2.3 ensures that T is not the zero polynomial and so it is invertible in the field of meromorphic functions of s . The identity F (s ) = 0 then implies the identity ζ(s ) = 0. This is clearly not the case and gives the required contradiction.This completes the proof of RH.The proof of RH that has just been given is sometimes referred to as the search for the first Siegel zero . The idea is to assume there is a counterexample to RH, study the first such zero b , and hope to derive a contradiction.This is exactly what we did. Using the composite function F (s ) of 3.1 with a zero at b , offthe critical line, we found another zero b j which halves the distance s 1 to the critical line. Continuing this process gives an infinite sequence o f distinct zeros, c onverging t o a p oint (onthe critical line).But an analytic function which vanishes on such an infinite sequence must be identically zero. Applying this to F (s) (using 2.8 now instead of 2.6) shows that F (s) is identically zero and this then leads to a contradiction as argued in the last few lines after 3.3.Remark. This Siegel version of the proof can be viewed as a renormalized version of Fermat’s proof of infinite descent. As is well known, the Fermat descent may not improve on the hypothetical solution. But our use of the Hirzebruch/von Neumann process of infinite ascent cancels the Fermat descent and enables us to derive a contradiction. What is crucial to make this work is establishing a uniform inequality. In our case the uniform factor is the 1/2 that appears in 2.8.4.Deux ex machinaThe proof of RH in section 3 looks deceptively easy, even magical, so in this section I will look behind the scenes and explain the magic. Clearly the function T is the secret key that unlocks the doors, so I must explain its secret.In [1] I fused together the algebraic work of Hirzebruch, as summarized above, and the analytical work of von Neumann, enabling me to get the best of both worlds. In brief the merits of the two worlds are:4.1Hirzebruch worked with explicit polynomials T4.2von Neumann worked with the unique hyperfinite factor A.Von N eumann’s w ork i s c learly d eep s ince A i s c onstructed b y a n i nfinite l imit o f e xponential operations. Hirzebruch’s work is deceptively simple, like that of all good magicians. But look carefully behind the scenes and it becomes clear that here too there is an infinite limit of exponentials. This time the limit is given by a sequence of discrete steps and the process is formal and algebraic. There is more detail in section 4 of [1].The fusion between the work of Hirzebruch and that of von Neumann involves a passage from the discrete to the continuous, the transition from algebra to analysis. Although explained in [2], the new presentation in section 2 of this paper makes it clearer. The notion of a weakly analytic function captures the essence of the fusion.I hope this brief explanation shows why the new technique is both powerful and natural. It should also have removed the mystery behind the short proof of RH.In the final section 5 I will put this paper into the general context of Arithmetic Physics envisaged in [1].5.Final CommentsIn this final section I will comment on possible future developments in Arithmetic Physics. These comments are on two levels.At the first level there are firm expectations. At the second level there are speculations.Starting with the first level, some comments on RH. Using our new machinery, RH and the mystery of α, were solved. But RH was a problem over the rational field Q, and there are many generalizations to other fields or algebras. I firmly anticipate much work in this direction.There are also logical issues that will emerge. To be explicit, the proof of RH in this paper is by contradiction and this is not accepted as valid in ZF, it does require choice. I fully expect that the most general version of the Riemann Hypothesis will be an undecidable problem in the Gödel sense.RH should be the bench mark for other famous problems in mathematics, such as the Birch-Swinnerton Dyer conjectures. I expect most cases will be undecidable.I now pass to the second level. Following the example of α, and the more difficult case of the Gravitational constant G (see 2.6 in [2]), I expect that mathematical physics will face issues where logical undecidability will get entangled with the notion of randomness.In 4-dimensional smooth geometry I expect the famous 11/8 conjecture of Donaldson theory will prove to be undecidable, as will the smooth Poincare conjecture.References[1]M.F.Atiyah Arithmetic Physics. Proceedings of ICM Rio de Janeiro 2018[2]M.F.Atiyah The Fine Structure Constant. submitted to Proc.Roy. Soc A 2018[3]F.Hirzebruch Topological methods in algebraic geometry (with appendices by R.L.E.Schwarzenberger,and A.Borel). Springer 1966。
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All force-related specifications are established using dead weight or compliant force.2. The range of voltage excitation which can be supplied to the product to produce an output which isproportional to force but due to ratiometricity errors may not remain within the specified performance limits. Non-compensated force sensors, excited by constant current (1.5 mA) instead of voltage, exhibit partial temperature compensation of span.3. The output signal obtained when the zero force is applied to the sensor. Also known as "null" or "zero".4. The change in the null resulting from a change in temperature. It is not a predictable error as it can shift upand down from unit to unit. Change in temperature causes the entire output curve to shift up or down along the voltage axis.5. The algebraic difference between output signals measured at the upper and lower limits of the operating forcerange. Also known as "full scale output" or simply "span".6. The maximum deviation of product output from a straight line fitted to output measured over the operatingforce range. T he straight line through a set of points which minimizes the sum of the square of the deviations of each of the points from the straight line.7. The ratio of output signal change to the corresponding input force change. Sensitivity is determined bycomputing the ratio of span to the specified operating force range multiplied by the supply voltage being used.8. The maximum deviation in sensitivity due to changes in temperature over the operating temperaturerange, relative to sensitivity measured at 25 °C.9. The maximum difference between output readings when the same force is applied consecutively, underthe same operating conditions, with force approaching from the same direction within the operating force range.10. The maximum force which may safely be applied to the product for it to remain in specification once force isreturned to the operating force range. Exposure to higher forces may cause permanent damage to theproduct. Unless otherwise specified, this applies to all temperatures within the operating temperature range.1. The temperature range over which the product may safely be exposed without excitation or force applied. Under these conditions theproduct will remain in specification after excursion to any temperatures in this range. Exposure to temperatures beyond this range may cause permanent damage to the product.2. MCTF is a basic measure of reliability for a non-repairable device. It is the mean number of cycles to maximum operating force over whicha sensor can be expected to operate until failure. The mean value is determined statistically from a probability distribution for failures based upon test data. MCTF may vary depending on the specific application in which a sensor is utilized.Low Profile Force SensorHoneywell Sensing and Control311. Absolute maximum ratings are the extreme limits that the product can withstand without damage to the product.2. The temperature range over which the product may safely be exposed without excitation or force applied. Under these conditions, theproduct will remain in the specification after excursions to any temperature in this range. Exposure to temperatures beyond this range may cause permanent damage to the product.3. The maximum temperature and time to which the product may be exposed for processing of solder electrical connections.Figure 3. Packaging Dimensions (For reference only.) Short Tube: 43,9 mm [1.73 in] long, 5 units/tubeStandard Tube: 584 mm [22.99 in] long, 100 units/ tubeTape and Reel (mm)2.∙∙Sensing and Control Honeywell1985 Douglas Drive NorthGolden Valley, MN 55422 080809-2-ENFebruary 2013© 2013 Honeywell International Inc. 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计算数学研究方向网上摘抄：计算数学研究方向及网上资料计算数学目的为物理学和工程学作计算。
主要研究方向包括：数值泛函分析；连续计算复杂性理论；数值偏微与有限元；非线性数值代数及复动力系统；非线性方程组的数值解法；数值逼近论；计算机模拟与信息处理等；工程问题数学建模与计算等等。
目前发展最好的方向已经与应用数学的CAGD 方向合二为一。
现在最热的方向应该是微分方程的数值求解、数值代数和流形学习，数值计算名校：西安交通大学、北京大学、大连理工大学从计算数学的字面来看，应该与计算机有密切的联系，也强调了实践对于计算数学的重要性。
也许Parlett 教授的一段话能最好地说明这个问题：How could someone as brilliant as von Neumann think hard about a subject as mundane as triangular factoriz-ation of an invertible matrix and notperceive that, with suitable pivoting, the results are impressively good? Partial answers can be suggested-lack of hands-on experience, concentration on the inverse rather than on the solution of Ax = b -but I do not find them adequate. Why did Wilkinson keep the QR algorithm as a backup to a Laguerre-based method for the unsymmetric eigenproblem for at least two years after the appearance of QR? Why did more than 20 years pass before the properties of the Lanczos algorithm were understood? I believe that the explanation must involve the impediments to comprehension of the effects of finite-precision arithmetic.( 引自/siamnews/11-03/matrix.pdf)既然是计算数学专业的学生，就不能对自己领域内的专家不有所了解。
艺术与数学的关联英语作文Art and mathematics, seemingly disparate disciplines, are in fact deeply intertwined. While art is often associated with creativity and expression, mathematics is hailed for its logic and structure. However, these two fields share fundamental principles that have shaped human understanding and innovation throughout history.To begin with, both art and mathematics involve patterns and structures. In art, patterns manifest in various forms—geometric designs, repetitions in motifs, or rhythmic arrangements of elements. These patterns evoke a sense of harmony and aesthetic pleasure, resonating with the mathematical concept of symmetry. Mathematics, on the other hand, studies patterns through numerical sequences, geometric shapes, and algebraic equations, aiming to uncover underlying rules and relationships.Furthermore, both disciplines require a meticulous attention to detail. Artists meticulously blend colors, refine textures, and manipulate light and shadow to convey their intended messages or emotions. Similarly, mathematicians delve into intricate proofs, scrutinize calculations, and analyze data with precision to derive meaningful insights and conclusions.Moreover, art and mathematics share a common quest for abstraction and representation. Artists often strive to depict abstract concepts, emotions, or philosophical ideas through symbolic imagery or unconventional forms. This parallels the mathematical pursuit of abstract concepts such as infinity, prime numbers, or complex geometries that transcend physical reality yet hold profound significance in theoretical frameworks.Beyond abstraction, both disciplines are integral to technological advancements and scientific breakthroughs.Mathematics provides the theoretical foundation for physics, engineering, and computer science, enabling the development of sophisticated algorithms, simulations, and models. In parallel, art inspires innovation in design, architecture, and visual communication, pushing boundaries of creativity and aesthetics in the digital age.Moreover, interdisciplinary collaborations between artists and mathematicians have led to groundbreaking discoveries and innovations. From the Renaissance period, when artists like Leonardo da Vinci explored anatomy and perspective using mathematical principles, to contemporary digital art and fractal geometry, these collaborations have enriched both fields by fostering new perspectives and methodologies.In conclusion, the relationship between art and mathematics transcends mere parallels; it represents a symbiotic fusion of creativity and logic, imagination, andanalysis. By understanding and appreciating their interconnectedness, we can cultivate a holistic approach to education, innovation, and human expression, bridging the perceived gap between the arts and sciences for a more enriched and interconnected future.。
