global solutions to the one-dimensional navier-stokes-poission equation with large data
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高三英语自主学习效果评估2024.10第一部分听力(共两节,满分30分)第一节(共5小题;每小题1. 5分,满分7. 5分)听下面5段对话。
每段对话后有一个小题,从题中所给的A、B、C三个选项中选出最佳选项。
听完每段对话后,你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. What is the restaurant’s specialty?A. American food.B. Italian food.C. Thai food.2. Why is the man here?A. To have an interview.B. To make an inquiry.C. To visit the woman.3. What is the woman most excited about?A. Seeing sharks.B. Going to the beach.C. Staying with her relatives.4. Where are the speakers?A. At a bus stop.B. In a car.C. On a bus.5. What are the speakers talking about?A. Why the electricity bill went up.B. Where they can pay the electricity bill.C. How they can reduce the electricity usage.第二节(共15小题;每小题1 .5分,满分22.5分)听下面5段对话或独白。
每段对话或独白后有几个小题,从题中所给的A,B,C三个选项中选择最佳选项,并标在试卷的相应位置。
听每段对话或独白前,你将有时间阅读每个小题,每小题5秒钟,听完后,各小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
听第6段材料,回答第6至7题。
国际商务英语写作模板:商业计划书篇一:商业计划书模板---英文版精编资料商业计划书模板---英文版BUSINESS PLAN TEMPLATEBUSINESS PLAN[My Company]123 Main StreetAnytown, USA 10000123-4567[Your Name][DATE]TABLE OF CONTENTS...商业计划书商业计划书模板---英文版BUSINESS PLAN TEMPLATEBUSINESS PLAN[My Company]123 Main StreetAnytown, USA 10000123-45671[Your Name][DATE]2TABLE OF CONTENTSExecutive Summary ....................................................................................... (1)Management ................................................................................ (2)[Company] History ............................................................................................ . (5)[Product/Service] Description ................................................................................... .. (7)Objectives....................................................................................... . (9)Competitors ................................................................................. .. (10)Competitive Advantages ................................................................................... . (11)Innovation ..................................................................................... . (13)Pricing ............................................................................................ .. (14)Specific Markets .......................................................................................... . (15)Growth Strategy .......................................................................................... . (16)Market Size and Share ............................................................................................... . (17)Targeting New Markets .......................................................................................... .. (18)Location ......................................................................................... (19)Manufacturing Plan .................................................................................................. (20)Research &Development ............................................................................... (21)Historical Financial Data ................................................................................................. .. (22)Proforma Financial Data ................................................................................................. .. (23)Proforma Balance Sheet ............................................................................................... . (26)Cost Control ........................................................................................... (27)Effects of Loan or Investment .................................................................................... . (28)Attachments ................................................................................. . (29)3Executive Summary [My Company] was formed asa [proprietorship, partnership, corporation] in [Month, Year] in [City, State], by [John Doe] in response to the following market conditions:[Startup, growth] opportunities exist in [Product/Service].The need for use of efficient distribution (转载于: 小龙文档网:国际商务英语写作模板:商业计划书)and financial methods in these overlooked markets.[I/We] have several customers who are willing to place large [orders,contracts] within the next three months.Several other prospective [customers/clients] have expressed serious interest in doing business within six months. [I/We] previously owned a company that was active in the widget markets. Over the past few years I spent much time studying ways to improve overall performance and increase profits. This plan is a result of that study. The basic components of this plan are:1. Competitive pricing2. Expand the markets3. Increased advertising4. Lower our unit costs,5. Thereby achieving higher profits.1. Sign contracts2. Increased advertising3. Increase office staffTo this end, [I/we] need investment from private individuals and/or companies. A total of $XXX is being raised which will be used to finance working capital, plant and equipment. The company will be incorporated and common stock issued to investors. The company will be run as a [proprietorship, partnership, corporation].Financial Goals Sales Net Income Earnings pershareYear 1 $25,000 .01 Year 2 $250,000 .12 Year 3 $375,000 .141Management[Name] [Title]??[Experience]??Sales growth from zero to $1,000,000 in five years.??Led market in market share - 30%.Formulated advertising budgets & campaigns.Pioneered new distribution channels. Established national sales force.Established national repair & service centers.Brought new and innovative products to the market.Designed point-of-purchase materials.[Education}University of BostonBoston, MA- Computer SciencesPresidentJohn Q. Doe, Chief Executive Officer, and Director since February 1988 and President since January 1990. Mr. Doe was the founder and Chief Executive Officer of the original operating company known as Random Excess, Inc. He has had experience in the widget field with his own firm, John Doe Co., of Oshkosh (Wisconsin), from 1980 to 1987. This firm was sold to FatCat Widgets, Inc. in 1987.篇二:商务英语写作(商业计划书写作格式)商务英语写作:商业计划书写作格式XX-03-24 13:39:08 来源:爱词霸资讯官网封面(Title page)企业的名称和地址Name and address of business负责人的姓名和地址Name(s) and address(es) of principals企业的性质Nature of business报告机密性的陈述Statement of confidentiality目录(Table of contents)1. 概述/总结(Executive summary)2. 行业及市场分析(Industry analysis)对未来的展望和发展趋势(Future outlook and trends)竞争者分析(Analysis of competitors)市场划分(Market segmentation)行业预测(Industry forecasts)3. 企业的描述(The description of the venture)企业的宗旨和目标(Mission statement and objectives)产品或服务的描述(Description of the product or service)企业的规模(Size of business)产品的进一步开发(Future potential/product development)竞争优势(Competitive advantage)办公设备和人员(Office equipment and personnel)创业者的背景(Backgrounds of entrepreneurs)4. 生产计划(Production plan)制造进程/被分包的数量(Manufacturing process / amount subcontracted)选址(Location)厂房(Physical plant)机械和设备(Machinery and equipment)原材料的供给情况(Sources of raw materials to be supplied)生产能力和提高的可能性(Output limitations,if any,and scale-up possibilities)质量控制计划(Quality control plans)5. 营销计划(The marketing plan)定价(Pricing)分销(Distribution)促销(Promotion)产品预测(Product forecasts)预见的涨价(Anticipated mark-up)竞争对手的反映(Competitors’response)市场份额预测(Market share projection)控制(Controls)6. 组织计划(Organizational plan)所有权的形式(Form of ownership)合作者或主要股权所有人的身份(Identification of partners or principal shareholders)负责人的权利(Authority of principals)管理层成员的背景(Management team background)组织成员的角色和责任(Roles and responsibilities of members of organization)7. 风险与对策分析(Assessment of risks)企业弱点的评价(Evaluate weakness if business)新技术(New technologies)应急计划(Contingency plan)8. 财务计划(Financial plan)各类业绩比率和投资回报(Summary of performance ratios, ROI etc.)销售预测(Sales forecasts)财务预测的假设(Assumptions underpinning financial forecasts)损益表(Income statement / Profit and lossstatement)预测现金流量表(Cash flow projections)资产欠债预估表(Pro forma balance sheet)量本利分析(Break-even analysis)资金来源和运用(Sources and applications of funds)9. 融资需求(Financing requirements)融资前的活动小结(Summary of operations prior to financing)此刻的股东和未付债款(Current shareholders, loans outstanding)资金需要量及时间(Funds required and timing)投资回报(The deal on offer)资本欠债比率和盈利与利息比率(Anticipated gearing and interest cover)投资者退出方式(Exit routes for investors)附录(Appendix)1. 管理人员简历(Management team biographies)2. 职业咨询人员背景(Names and details of professional advisors)3. 技术参数和图纸(Technical data and drawings)4. 专利、版权、设计等(Details of patents,copyright, designs)5. 审计的报表(Audited accounts)6. 信件(Letters)7. 市场调研数据(Market research data)8. 租约或合同(Leaser or contracts)9. 供给商的报价单(Price lists from suppliers)10. 客户的定单(Orders from customers)篇三:英文商业计划书模板英语商业计划书(Business Plan)第一讲:概述第二讲:现状分析第三讲:目标肯定第四讲:组织结构第五讲:产品分析第六讲:市场分析第七讲:市场策略第八讲:生产分析第九讲:财务分析第十讲:附件第一讲:概述(executive summary)概述是整个商业计划的第一部份,相当于整个商业计划的浓缩,使整个商业计划的精华所在。
绿色物流可持续发展外文翻译(节选)中文2600字,1600单词,9500英文字符文献出处:Fransoo J C. Green Logistics: Enablers for Sustainable Development [J]. Supply chain management: an international journal, 2021, 8(2): 122-131.原文GREEN LOGISTICS: ENABLERS FOR SUSTAINABLEDEVELOPMENTJan C. Fransoo1 INTRODUCTIONLogistics is the backbone of industry and commerce. As a discipline, it describes the management and coordination of activities along supply chains. These activities include freight transport, storage, inventory management, materials handling and related information processing. A large part oflogistics activities are often outsourced to specialized providers thatprovide cost- effective services. Research has shown that, at least in high income economies, the value of services is not assessed in monetary andservice quality terms alone. In making decisions, logistics professionals are increasingly taking into consideration external effects such as emissions, pollution, noise, and accidents.The last LPI report release in 2021, for instance, pointed out that in shipments to OECD countries, environmentally friendly solutions are considered far more often than elsewhere. Mounting regulatory pressure, together with changes in customer preferences, are the main drivers of this phenomenon. Oneof the more widely used terms to describe this set of preferences is green Logistics, especially when the activities of logistics service providers are concerned.Research, including a recent book by Alan McKinnon, has established that green Logistics is an emerging concern of private operators and providers and users of logistics. From a policy standpoint, and especially for the global environment, green Logistics is potentially a major topic as well: estimates vary, but about 15% of global greenhouse gas emissions (GHG) can be traced to logistics activities.Green Logistics may not be an independent policy area. Rather, the supply chain perspective provides a framework to understand and deal with issues that are separate.but ultimately interrelated. Importantly, looking at supply chains helps policy makers understand the interests and actions of private sector operators. Green Logistics may therefore propose a number of tools and identify emerging sustainable solutions contributing to the overarching objective of green Growth.From a policy perspective, logistics cut across several areas and sectors. The performance of supply chains depends on areas or activities where government as regulator or catalyst of investment is critical, such as:Transport infrastructure: road and rail corridors, ports and airportsThe efficiencies of logistics services: services include not only modal freight transport, but also warehousing and intermediary services, such as brokers and forwarders, and related information-flow management. In modern economies, the trend is towards integration in multi-activity logistics providers (3PLs, 4PLs) to which industrial and commercial firms outsourcetheir supply chain activities. Understanding the regulatory dimension of services is becoming increasingly critical to the development of effective policies in areas such as:professional and operational standards, regulation of entry in market and professions, competition, enforcement.Procedures applying to the merchandise, such as trade procedures (customs and other controls).The soft infrastructure that supports information or financial flow associated with the physical movements along supply chains: IT infrastructure, payment systems.The concept of national logistics performance capturing the outcome of these policies is widely recognized by policy makers and the private sector worldwide as a critical contribution to national competitiveness. A key question for sustainable development is how to integrate supply chain participants concern with environmental sustainability with the concept of national logistics performance.Within logistics, transport creates the largest environmental footprint. But the volume of emissions can vary greatly, depending on the mode oftransport. The volume of emission per ton per km increases by an order of magnitude from maritime to land transportation and to air transportation. This is a key environmental aspect of logistics that is not taken into consideration by most supply chain operators. Logisticsexperts typically integrate freight modes and other related activities so that the transport and distribution network is used in the most efficient manner, which is important for keeping emissions in check, as well. Depending on the type of industry and geographical region, supply chain operators can place varying emphasis on the reliability of supply chains, as well. In summary, supply chain choices typically include multiple criteria and trade-offs, and this makes an analysis of their environmental impact complex; the most environmentally friendly choices do not only depend on mode of transportation, but also on other elements, such as efficiency and reliability.To reduce the environmental footprint of a supply chain, the focus should be on several dimensions and should select the best mode of transport,efficient movements, and innovation. Comprehensive work on greening individual modes of transportation is already available. Here, the key drivers have been energy efficiency and the urge to diminish various types of emission. Given the integrated nature of supply chains, however, the manner in which price signals and incentives catalyze supply chain structure is a rather intricate problem: lower- emission modes of transport (maritime, e.g.) are typically also less reliable or have other limitations (such as maritime access to a landlocked country). Such limitations may include the cost of such technologies, the temperature range within which they can be used or the availability of certain types of fuel. It is therefore critical to complement the current knowledge about emissions produced by different modes of transportation with an understanding of what drives the demand for Green Logistics within supply chains.The emerging response is likely to take the form of top-down policy, such as measures in the form of standards or taxes addressing emissions (GHG, SO2, NOx) by mode of freight. For instance, a cap on SO2 emissions on major maritime routes will go into effect at the end of 20212. At least as important is the response from the bottom up. These are supply-chain strategies coming from the private sector in response to policy or price changes, but also demand from consumers, clients and stake-holders. Green Supply Chain management has to be taken seriously by policy makers.An exclusive focus on price mechanism (including taxes), as is the current tendency, may miss some of the major driver of changes in supply chain management. Another complication, at least in the context of international trade, is that the focus on the impact on international logistics does not capture the footprint of production processes. These processes may have different impact than the supply chain itself, as in the case of food production.There is also evidence that much of the environmental footprint of logistics operations is tied to short distances and distribution. Green Logistics is intimately linked with concerns such as urban congestion, and innovations in Logistics are critical to sustainable supply chains. Grassroots innovations in Logistics have recently flourished, often producing win-win solutions in terms of jobs and the environment. More generally, there is increasing awareness that green supply chains can be also competitive, either because the awareness of the environment helps productivity or because consumers expect it, particularly in wealthy countries.A concrete case in point is also the so-called sculpture emission regulation by IMO that enters into force on January 1, 2021 in most of North Sea, Baltic Sea and along west and east coasts of US & Canada (bar Alaska). Ships have to go over from fuel with 1.5 % sculpture to 0.1 % sculpture or invest in so-called scrubbers, that absorb the sculpture from exhaust gases; technology that is still nascent in the maritime context. Scrubber investment per cargo ship is USD 2 million and no with multiples as the ship engine size increases, with annual maintenance cost approx..7-10 % of investment. This seemingly innocent and rather technical change is going to have a huge impact on shipping and the spillover effect to other modes & Supply chains are going to be significant Green Logistics also encompasses potentially longer-term concerns. A green focus within logistics analysis could examine a supply chain vulnerability to climate events or to large swings in the price of transport inputs, for instance. A recent volcanic episode in Iceland showed the vulnerability of one specific supply chain that relies heavily on air freight fresh produce coming from Africa spoiled when flights were cancelled because of the volcanic ash. Resilience concerns and other form of uncertainty are likely to shape supply chain choices by regional and global operators.Given the importance of trade in components and intra-firm trade, how large operators develop green supply chain strategies will have profound economic impact. Resilient and greener supply chains are likely to be lessextended and leaner, for example, though the consequences for trade and integration of low income economies cannot be treated fully here.Policy makers should be concerned by both the supply and demand aspects of logistics environmental dimensions. So far, the policy focus has been on modal footprint and has not taken into account a supply chain perspective. There have not been major initiatives in Green Logistics, even in the countries most sensitive to the issue, such as those in Northern Europe. Rather the most important changes have occurred as a combination of largely uncoordinated public and private initiatives: voluntary behavior by shippers, innovation in terms of technology, information (environmental logistics dashboard) or services, or common public-private objectives such as in modal shifts.2 DEFINING GREEN LOGISTICS AND GREEN SUPPLY CHAIN MANAGEMENTThere are many variations in the terminology regarding green logistics and green supply chain management. This section aims at providing a brief overview on some of the key terms used in the literature.Green logistics refers mainly to environmental issues related to transportation, material handling and storage, inventory control, warehousing, packaging, and facility location allocation decisions (Min & Kim, 2021). Gonzalez-Benito and Gonzalez-Benito (2021) use the term environmentallogistics to describe logistics practices that are divided intosupply/purchasing, transportation, warehousing and distribution, and reverse logistics and waste management. Although distribution is considered to be one of the interrelated areas of supply chain management, the term green distribution has also been used to describe the whole process of integrating environmental concerns into transportation, packaging, labeling and reverse logistics (Shi et al., 2021).Reverse logistics is often used as a synonym to efforts to reduce the environmental impact of the supply chain by recycling, reusing and remanufacturing.译文绿色物流:促进可持续发展贾恩. 法兰斯1. 引言物流是工商业的支柱。
E-VAC EP Series Medium Voltage Vacuum Circuit BreakerAutomotiveAerospaceTruckHydraulicsAutomotive Aerospace Truck Hydraulics Poweringbusiness worldwideEaton delivers the power inside hundreds of products that are answering the demands of today’s fast changing world. We help our customers worldwide manage the power they need for buildings, aircraft, trucks, cars, machinery and entire businesses. And we do it in a way that consumes fewer resources.Next generationtransportationEaton is driving the development of newtechnologies – from hybriddrivetrains and emission control systems to advanced engine components – that reduce fuel consumption and emissions in trucks and cars. Higher expectationsWe continue to expand our aerospace solutions andservices to meet the needs of new aviation platforms,including the high-flying light jet and very light jet markets. Building on our strengths Our hydraulics businesscombines localised service and support with an innovative portfolio of fluid powersolutions to answer the needs of global infrastructure projects, including locks, canals and dams.Powering Greener Buildings and BusinessesEaton’s Electrical Group is a leading provider of powerquality, distribution and control solutions that increase energy efficiency and improve power quality, safety and reliability. Our solutions offer a growing portfolio of “green” products and services, such as energy audits and real-time energy consumption monitoring.Eaton’s Uninterruptible Power Supplies (UPS), variable-speed drives and lighting controls help conserve energy and increase efficiency.ElectricalElectrical E-VAC EP Series Medium Voltage Vacuum Circuit Breaker 1Eaton Corporation is a worldwide leader in thedesign, manufacture, and sale of safe, reliableand high-performance medium voltage power distribution equipment in accordance with IEC,GB and ANSI standards.Complete Global Medium Voltage Switchgear Solutions Eaton, a premier leader in designing and manufacturing power distribution and protection equipment in the electrical industry, offers a comprehensive range of medium voltage (MV) solutionsto meet the needs of virtually every application. From productsthat feature cutting-edge design that allow for easy access, maintenance and space savings, to arc-resistant products that enhance safety, Eaton’s medium voltage solutions provide avariety of products for every need. Additionally, Eaton’s global service network provides maximum customer support in allregions of the world.As one of the few completely vertically integrated and diversified industrial manufacturers in the world, Eaton designs not only MV assemblies, but also the key components that comprise the MV solutions – from steel housing and circuit breaker compartmentsto vacuum interrupters, circuit breakers, bus systems and fuses. Eaton’s MV heritage, strengthened by acquisitions such as Westinghouse DCBU, Cutler Hammer, MEM and Holec, has resulted in breakthrough MV technologies and numerous international patents over the years.Part of Eaton’s complete electrical PowerChain Solutions– which help businesses minimize risks while realizing greater reliability, cost efficiencies, capital utilization and safety –Eaton’s medium voltage equipment meets all applicablestandards and certifications such as IEC, NEMA / ANSI, GB,UL, IEEE, KEMA and CSA.When it comes to medium voltage solutions, you can trust theone name with a long history of proven performance: Eaton.E-VAC EP Series Medium Voltage VacuE-VAC EP Series Medium Voltage Vacuum Circuit BreakerE-VAC EP Series medium voltage Ideal contact material and E-VAC EP Vacuum Circuit Breakervacuum circuit breakers from geometry ensure low Eaton Electrical combine our chopping current andexcellent vacuum technology reliable contact resistance . with decades of experience in designing and manufacturing A few components and power distribution system. They compact and reasonable offer high reliability, ease of structure ensure morehandling and maintenance, high reliable and safer operation. cost efficiency for Chinese users. Enable ideal cutoff and close Meet GB and DL standards. of resistance, inductance load and capacitive load. E-VAC equipped with new generation vacuum Secondary plug, chassis,interrupter, suited formoving contact and grounding technologies and operation methods are speciallycondition of power system. designed to Chinese users, completely compatible with E-VAC utilizes solid-enveloped domestically dominantpole of Eaton Electrical, offers medium voltage switchgear superior and reliable solid KYN28.enveloping insulation performance, passescondensation test, suitable for safely operating in harsh environment. It offers better creepage distance and clearance compared to the requirements in GB standards.Product modelsE -VAC -12 / T □ -□GB StandardEaton breaker seriesVoltage ratings kVRated current ARated short circuit breakingcurrent kASpring operation mechanismE-VAC EP Series Medium Voltage Vacuum Circuit Breaker3Application condition Technical features Temperature condition Ambient air temperature not E-VAC utilizes mature spring Product assembly utilizes The average of relative exceeding 40℃, and the operating mechanism, offers tooling method to ensure humidity measured within 24 average value measured within reliable and stable dimension consistency. All hours not exceeding 95%.24 hours not exceeding 35℃. performance, long service life, products have been subject toThe minimum ambient air ease of operating, excellent the push panel test for The average vapor pressure temperature is -15℃.corrosion protection and low standard panel, ensuring measured within 24 hours notmaintenance within the lifetime product interchangeability and exceeding 2.2kPa.The effect by solar radiation universality.can be ignored. E-VAC EP series 12kV vacuum The average of relativecircuit breaker adopts mature All products have been subject humidity measured within one The ambient air is not obviously APG process to enclose to hundreds of mechanical month not exceeding 90%.polluted by dust, smoke, vacuum interrupter and main operation running-in testscorrosive or flammable gases, conductive circuit in a before leaving the factory, The average vapor pressure vapor or salt mist. insulation tube, thoroughly ensuring the product measured within one montheliminating the environmental performance in the most stable not exceeding 1.8kPa.Seismic intensity not impact on insulated parts phase.exceeding 8 degree. which weakens the voltagewithstanding capacity, ensuring Utilize advanced importedAmplitude of electromagnetic the vacuum interrupter suitable testing equipment, exactlyinterference induced in for harsh environment. record no-load mechanicalsecondary system not characteristics of each product,exceeding 1.6kV. E2 level electrical life extended and provide users with theseand M2 level mechanical life characteristic curves, ensureextended as per GB1984-2003, product reliability.capacitive current breaking andlowre-breakdown probability C2level, having completed thetype test.Outline dimension anddistribution panel interlockingmethod completely compatiblewith domestically dominantmedium voltage switchgearKYN28, high universality,significantly reduce design cost4E-VAC EP Series Medium Voltage Vacuum Circuit BreakerE-VAC EP Series Medium Voltage Vacuum Circuit BreakerApplication areasChemical industry Substation Oil industry Cement industry Piping industry Automotive industry Offshore mining Power plantShipbuildingTextile and food industries Paper making industry Metallurgical industryOpencast coal mineT echnology creation historyAs the manufacturer of the world’s first vacuum interrupter, the pioneer of vacuum technology, Eaton Electrical has been committed to the research, development andmanufacturing of vacuum interrupters for over 70 years, and gathered plenty of experience. Westinghouse has become the synonym of quality and reliability.We own the world’s largest and globally leading vacuum interrupter plant and the only vacuum interrupter plant that is equipped with large capacity high voltage laboratories.Our manufacturing capacity and design and development always maintain a leadership position.E-VAC vacuum circuit breaker requires almost no relevant maintenanceSimple structure design of E-VAC vacuum circuit breaker further minimizes fault occurrence, simplifies daily maintenance. With the indicator on the circuit breaker panel, no detection instrument isrequired, facilitating the judgment of working state of circuit breaker. The circuit breaker utilizes the world’s first class Eaton Electrical’s vacuum interrupter with vacuum degree up to 10-6Pa, low air leakage, and ensure 50-year life with no maintenance required.Optional accessoriesCharging handle Trolley handle LifterIdeal for control and protection in medium voltage power supply and distribution systemThe circuit breaker is equipped with superior spring chargingmechanism, utilizes modular design, offering optimized mechanism main part distribution, simpler structure and more reliable performance. The whole mechanism is composed by three modules: charging,closing, opening. Assembly and maintenance of these three parts are very simple. The spring charging mechanism composed by ratchet wheel mechanism, oscillator and closing spring is compact and smart. The operating mechanism is usually equipped with manual charging device and electric charging device, enabling automatic reclosing function.The circuit for manual charging operating mechanism is provided with manual opening and closing operation buttons, circuit breaker position indicator and spring mechanism charging status indicator, switch operations counter, shunt release auxiliary switch, position and fault signals, etc..The circuit breaker of electric charging operating mechanism: added with spring charging motor, shunt release, trip free relay, and auxiliary switch for spring charging motor release.The following accessories can also be provided as needed: undervoltage release, overcurrent relay, etc..E-VAC EP Series Medium Voltage Vacuum Circuit Breaker5E-VAC EP Series Medium Voltage Vacuum Circuit BreakerMain specification and technical parametersItem Unit ValueRated voltage kV 12Rated short-time power frequency withstand voltage (1 min) 42 (phase to ground, phase to phase) 48 (gap)Rated lightning impulse withstand voltage (peak) 75 (phase to ground, phase to phase) 85 (gap)Rated frequency Hz 50Rated current A 630 630 1250 1250 1600 1250 16001250 1600 2000 2000 2500 2000 250040002500 2500 3150 3150 (1)4000 3150 (1) Rated short-circuit breaking current kA 25 31.5 40 50Rated short-time withstand current (4s) 25 31.5 40 50125Rated peak withstand current kA 63 80 100 (2)125Rated short circuit making current 63 80 100 (2) Secondary circuit power frequency withstand voltage (1 min) V 2000Opening time ms 20~50Closing time 35~70Mechanical endurance time 30000 (1600A/31.5kA and below), 20000 (2000A and above, 40kA), 10000(50kA) Rated current breaking endurance 30000 (1600A/31.5kA and below), 20000 (2000A and above, 40kA), 10000(50kA) Rated short circuit current breaking endurance time 50 (1600A/31.5kA and below), 30 (2000A and above, 40~50kA)Allowable accumulated wearingthickness of moving/fixed contact mm 3Rated closing operating voltage V AC 110/220 DC 110/220Rated opening operating voltageRated voltage of spring charging motor V AC 110/220 DC 110/220Rated power of spring charging motor W 55~90Charging duration s ≤15Rated operating sequence O-0.3s-CO-180s-CO (40kA and below), O-180s-CO-180s-CO (50kA)Note:(1) Forced air cooling is required at 4000A; (2) For higher parameters, please contact the Eaton Corp.T echnical parameters for trip/close coilsName ParameterRated operating voltage (V) AC, DC110 AC, DC220Rated operating current of close coil (A) 2.0 1.0Rated operating current of trip coil (A) 1.8 (40kA and above is 2.6) 0.9 (40kA and above is 1.6)Normal operating voltage range Closing: 80%~110% of rated operating voltageOpening: 65%~120% of rated operating voltage, opening will not occur when thenormal operating voltage is less than 30% of rated operating voltageE-VAC EP Series Medium Voltage Vacuum Circuit Breaker 6E-VAC EP Series Medium Voltage Vacuum Circuit BreakerOutline and dimension of E-VAC EP circuit breaker (drawout type)Distribution Rated Rated short panelcurrent circuit breaking width (mm) (A) current (kA)P H A B C D E G J K L M N R S T W Q 800 630 25~31.5 210 275 638 652 640 650 433 Φ35 280 598 76 78 637 508 277 40 23 / 800 1250 25~40 210 275 638 652 640 650 433 Φ49 280 598 76 78 637 508 277 40 23 550* 800 1600 31.5 210 275 638 652 640 650 433 Φ55 280 598 76 78 637 508 277 40 23 / 800 2000 40 210 310 638 652 640 650 361 Φ79 295 586 77 88 698 536 277 0 23 550 800 1250~2000 50 210 310 638 652 640 650 361Φ79295 586 77 88 698 536 277 0 19 550 1000 2500 31.5 275 310 838 852 838 850 361 Φ109 295 586 77 88 698 536 377 0 31 / 1000 3150 31.5 275 310 838 852 838 850 361 Φ109 295 586 77 88 725 536 377 0 31 / 10002500~400040~50275310 838 852838 850361 Φ109295586 77 88 725 53637731750**Note:Forced air cooling is required at 4000A. * 40kA only. ** 50kA only.E-VAC EP Series Medium Voltage Vacuum Circuit Breaker7E-VAC EP Series Medium Voltage Vacuum Circuit BreakerOutline and dimension of E-VAC EP circuit breaker (fixed type)E-VAC fixed type vacuum circuit breaker (210 phase space)Rated Rated shortcurrent circuit breaking(A) current (kA) H J E K B N Y1\Y2630~125025~31.527523771.54370555I 12504027523771.54370551II160031.5~4027523771.54370551II 200040310252804493614III1250~200050310252804493614IIIE-VAC EP Series Medium Voltage Vacuum Circuit Breaker 8E-VAC EP Series Medium Voltage Vacuum Circuit BreakerOutline and dimension of E-VAC EP circuit breaker (fixed type)E-VAC fixed type vacuum circuit breaker (275 phase space)Rated Rated short current circuit breaking (A) current (kA)M Z1\Z2 2500 31.5 628 IV 3150 31.5 678 V 2500~400040~50678VE-VAC EP Series Medium Voltage Vacuum Circuit Breaker9E-VAC EP Series Medium Voltage Vacuum Circuit BreakerSecondary control connection diagram of E-VAC EP series vacuum circuit breaker (drawout type) The diagram shows the circuit breaker in test position, opening, discharged statesE-VAC EP Series Medium Voltage Vacuum Circuit Breaker 10E-VAC EP Series Medium Voltage Vacuum Circuit BreakerSecondary control connection diagram of E-VAC EP series vacuum circuit breaker (fixed type) The diagram shows the circuit breaker in opening, discharged states11E-VAC EP Series Medium Voltage Vacuum Circuit BreakerE-VAC EP Series Medium Voltage Vacuum Circuit BreakerE-VAC EP series vacuum circuit breaker selection table1. Circuit breaker models□E-VAC (drawout type)□ E-VAC (fixe d type)2. Parameters of E-VAC EP series vacuum circuit breaker Panel width (mm) Breaker phase Rated short circuit Rated working current (A)spacing(mm) breaking current (kA) □630 □1250 80021025 □630□1250□ 160031.5 □1250 □ 1600 □ 2000 40 □1250 □ 1600□ 2000 501000 275 25 □2500 31.5 □2000□ 2500□ 315040 □1250 □ 1600 □ 2000 □ 2500 □ 3150 □ 4000* □□□ □□□1250 1600 2000 2500 31504000*50* Forced air cooling is required at 4000A.* * The specifications such as the need to purchase, please contact Eaton. 3. Technical parameters of spring operating mechanism Opening power supply (V) □DC110 □ AC110 □ DC220 □ AC220 Closing power supply (V)□DC110 □ AC110 □ DC220 □AC220 Spring charging motor power supply (V)□DC110 □ AC110 □ DC220 □AC2204. Optional configuration (standard option includes trip free device. Please note if the trip free device has to been canceled)□ Overcurrent release □ 2 Overcurrent □ 3 Overcurrent□A□ Closing latch □ V □ Position latch □ V□ Trip free relay □ V □ Undervoltage release □V□ Operating handle□ Quantity neededNote: Technical parameters of products will be changed without notice. Please confirm withEaton corporation before ordering.E-VAC EP Series Medium Voltage Vacuum Circuit Breaker 12•Electrical solutions that use less energy, improve power reliability andmake the places we live and work safer and more comfortable•Hydraulic and electrical solutions that enable machines to delivermore productivity without wasting powerWe deliver:Discover today’s Eaton.•Aerospace solutions that make aircraft lighter, safer and less costly tooperate, and help airports operate more effciently•Vehicle drivetrain and powertrain solutions that deliver morepower to cars, trucks and buses, while reducing fuel consumption and emissionsPowering business worldwideAs a global diversif ed power management company, We provide integrated solutions that help make we help customers worldwide manage the power energy, in all its forms, more practical and accessible. needed for buildings, aircraft, trucks, cars, machinery and businesses.With 2014 sales of $22.6 billion, Eaton has approxi-mately 99,000 employees around the world and sells Eaton’s innovative technologies help customers manage products in more than 175 countries.electrical, hydraulic and mechanical power more reliably, eff ciently, safely and sustainably.Eaton is a power management company with approximately 97,000 employees. The company provides energy-efficient solutions that help our customers effectively manage electrical, hydraulic and mechanical power more efficiently, safely and sustainably. Eaton sells products to customers in more than 175 countries. For more information, visit . Electrical Sector Asia PacificNo. 3 280 Nong Linhong RoadChangning DistrictShanghai, China 200335© 2016 Eaton Corporation Eaton is a registered trademarkAll Rights Reserved of Eaton Corporation.Printed in ChinaE-VAC EP-EN All trademarks are property of theirMay 2016 respective owners.。
一类带logistic源项的趋化方程组解的整体存在性和有界性林静秋;何璞;侯智博【摘要】本文研究了一类具有logistic源项的趋化方程组解的性质.利用先验估计并结合Neumann热半群的衰减性质,本文证明:当logistic源项中的二次项系数足够大时,方程组的齐次Neumann初边值问题的经典解在边界光滑的三维有界区域上整体存在且一致有界.【期刊名称】《四川大学学报(自然科学版)》【年(卷),期】2018(055)005【总页数】8页(P897-904)【关键词】趋化方程组;Logistic源;整体存在;一致有界【作者】林静秋;何璞;侯智博【作者单位】西华大学理学院,成都610039;西华大学理学院,成都610039;西华大学理学院,成都610039【正文语种】中文【中图分类】O175.291 IntroductionIn past decades, the nonlinear parabolic system have been widely studied[1-6]. Particularly, in 1970, Keller and Segel proposed the following chemotaxis Keller-Segel model[5]:whereuis the cell density,vis the density of the chemoattrctant,H(u,v)andK(u,v) are model source terms related to interactions,Du(u,v) andDv(u,v) are the diffusivity of the cells and chemoattactant, respectively.WhenDu(u,v)=Dv(u,v)=1,χ=1 andH(u,v)=0,K(u,v)=-v+u,the model recovers the classical minimal model[6]:The solution of the Neumann boundary value problem of this system in bounded domain Ω⊂RNwill blow up whenN≥3 orN=2 andis large[7]. WhenN=1, Osaki and Yagi[8]established the existence of global bounded classical solutions for any sufficiently smooth initial value.WhenN=2,Nagai[9]proved the solution is bounded ifN≥3,Winkler[10]obtained the same conclusion ifIn view of various biological phenomena and environment for cells, many variants of Keller-Segel model have been developed and investigated (see Refs.[6,11] and references therein). Among them, some recent works qualitatively study the effects of interplay between self-diffusion and cross-diffusion[12,13], between self-diffusion and logistic damping[14], or between nonlinear signal production and logistic growth[15]. In order to address the dependence of dynamical behaviors of solutions on the interactions between nonlinear cross-diffusion and logistic source, the following model:are exentisively considered.WhenN≥2,solutions with the logistictermf(u)=0 may blow up in finite time[16,17]. Ifτ=1,N=2 andf(u)=γu-μu2, whereμ>0 is arbitrarily small, all of solutions are global and bounded[8]. In the caseN≤2, even for arbitrarily smallμ>0 are sufficient to rule out any explosion by guaranteeing global existence of bounded classical solutions for all reasonably smooth initial data[18]. Whereas in the caseN≥3,the same conclusion holds provided th atμ>0 is suitably large[19]. Note that the additional logistic term destroys the energy structure of corresponding free Keller-Segel system obtained in the limit caseγ=μ=0[9]apparently. Another common type is to considerτ=0 that reflects and takes to a lim it the physically reasonable model assumption that chemicals diffuse much faster than cells move, we can accordingly obtained initial-boundary value problem for the parabolic-elliptic system. The solutions are global and bounded wheneverμ>0 satisfiesfor anyμ>0 one can at least construct globally existing weak solutions. The existence of weak solutions and a bounded absorbing set inL∞(Ω) are proved under more general conditions.In Ref.[20], it is shown that in another related model:the blow-up may occur for space-dimensionN≥5 andIn short, the logistic source exerts a certain growth-inhibiting influence which may keep the solution bounded and rule out blow-up. Currently,most scholars have studiedK(u,v)=-v+uin Keller-Segel model variants, and relatively few in terms ofK(u,v)=-uv.Therefore, in this paper, we assume thatK(u,v)=-uv.Particularily, we consider the following parabolic-parabolic chemotaxis-growth system with cross diffusion andconsumption terms:(1)where Ω⊂R3is a bounded domain with smooth boundary,ndenotes the outward normal vector field on ∂Ω,r∈R,μ>0,uandvrepresent the density of cells and the concentration of chemical substance.In order to specify the framework for our analysis, let us assume throughout the paper that the initial data satisfy(2)The goal of this paper is to build the existence of global bounded classical solutions for suitably largeμunder the influence of logistic term in three dimensional convex bounded domain. The main theorem of this paper can be stated as follows:Theorem 1.1 Suppose that (2) holds. Then wheneverμ≥(1) possesses a unique global classical solution (u,v)which is uniformly bounded in the sense that‖u(·,t)‖L∞(Ω)+‖v(·,t)‖W1,∞(Ω)≤Cfor allt∈(0,∞)(3)with some positive constantC.2 Global existence and some preliminariesWe first state the local solvability of System(1), which can by proved by a straightforward adaptation of the corresponding procedure in Lemma 3.1of Ref.[6] to our current setting.Lemma 2.1 Suppose that (2) holds. Then there existTmax∈(0,∞] and unique classical solution (u,v) of System (1) in Ω×(0,Tmax) such thatwe haveu≥0 andv≥0 inifTmax<∞,then‖u(·,t)‖L∞(Ω)+‖v(·,t)‖W1,∞(Ω)→∞ ast→Tmax.The following lemma is easily obtained but will be frequently used in the sequel.Lemma 2.2 If (2) holds, then the solution of (1) satisfies(4)for allt∈(0,Tmax).Proof The conclusion directly results from an integration of the first equation in (1) over Ω.As the consequence of the maximum principle and the nonnegativity of the solution, we have the following result.Lemma 2.3 If (2) holds, then the solution of (1) satisfies‖v(·,t)‖L∞(Ω)≤‖v0‖L∞(Ω)(5)for allt∈(0,Tmax).Lemma 2.4 There exists a positive constantMsuch that(6)for allt∈(0,Tmax).Proof Integration by parts and the Young inequality results in v·(Δv-uv)≤(7)On the other hand,(8)To sum up (7), (8), we obtain thatSince Lemma 2.2 shows thatfor allt∈(0,Tmax),a com-parison argument leads to3 Boundedness of u,vThis section contains the main step of our analysis by establishing an estimate for a combination ofandLet us first derive the following differential inequality forLemma 3.1(9)for allt∈(0,Tmax).Proof Testing the first equation in (1) againstu,we can obtainu·v+for allt∈(0,Tmax),which directly results in (9) by using the Young inequality to yieldu·Lemma 3.2(10)for allt∈(0,Tmax).Proof Using the factsv·(Δv-uv)=v·|v|2≤v·|v|2(11)Then an application of Young's inequality to the last two integralyields v·|v|2≤Inserting this inequality into (11) and rearranging it, we arrive at our conclusion.Lemma 3.3(12)for allt∈(0,Tmax).Proof A direct calculation shows thatv·(Δv-uv)(13)We can thereupon derive from integrating by parts and employing the identityv·thatu·|v|2+v·u·v=u·v·|v|2+u·v(14)for allt∈(0,Tmax).Then one can estimate by the Young inequality thatu·|v|2≤(15)v·|v|2≤(16)andu·(17)for allt∈(0,Tmax).In view of (15)~(17),the identity (14) readily implies (12). In view of Lemma 3.1~3.3,we can easily see the following result. Lemma 3.4(18)for allt∈(0,Tmax).Next we will show that ifμis suitably large, then all integrals on the right side in (18) can adequately be estimated in terms of the respective dissipated quantities on the left, in consequence implying theL2estimate ofuand the boundedness estimate for |v|.Lemma 3.5 Suppose thatμ≥Then there exists positive constantCsuch that(19)and(20)for allt∈(0,Tmax).Proof LetSinceμ≥(21)Using the Young inequality, we can assert that for anyδ>0,there exists someC1>0 such that the first three terms on the right hand side fulfilling(22)for allt∈(0,Tmax).Recalling the boundedness ofasserted in Lemma 2.4, we can apply the Gagliardo-Nirenberg inequality to estimatefor allt∈(0,Tmax) and some positive co nstantsC2,C3.Takingin (22),we arrive at(23)The boundary traceis continuously embedded intoL2(∂Ω),which guarantees the existence ofC4>0 such thatOn the other hand, sinceW1,2(Ω) is compactly embedded intoandis continuously embedded intoL1,then the Ehrling lemma entails that foranyε>0 we can pickC5(ε)>0 such thatfor allφ∈W1,2(Ω). This estimate and the one-sided pointwise inequality[22]for allx∈∂Ω andt∈(0,Tmax) with someC6>0 enables us to estimate the two rightmost summands in (21) as(24)f or allt∈(0,Tmax),wherewithM,mas in Lemma 2.2 and Lemma 2.4, respectively.Substituting (23),(24) into (21),we conclude thaty′(t)+y(t)≤C8for allt∈(0,Tmax)withimmediately leads tofor allt∈(0,Tmax) with some positive constantC9from the comparison argument.With the boundedness ofandat hand, we can derive theL∞estimate ofuby using the variation-of-constants formula now.Lemma 3.6 Ifμ≥then there existsC>0 such that‖u(·,t)‖L∞(Ω)≤C(25)for allt∈(0,Tmax)Proof We first use the variation-of-constants formula to representu(·,t) for eacht∈(0,Tmax) asu(·,t)=e(t-t0)Δu(·,t0)-e(t-s)Δ·(u(·,s)v(·,s))ds+e(t-s)Δ(ru(·,s)-μu2(·,s))ds(26)wheret0=(t-1)+.Then one can easily infer from the maximum principle that ‖e(t-t0)Δu(·,t0)‖L∞(Ω)≤‖u0‖L∞(Ω)(27)ift∈(0,1] and ift>1 the n theLp-Lqestimate for the Neumann heat semigroup yieldsC1>0 such that‖e(t-t0)Δu(·,t0)‖L∞(Ω)≤C2‖u(·,t0)‖L∞(Ω)≤C2m(28)Noticingfor allξ∈R,we can estimatee(t-s)Δ(ru(·,s)-μu2(·,s))ds≤(29)Finally, we will estimate the second integral on the right hand of (26).Fix an arbitraryp∈(3,4).The known smoothing properties of the Neumann heat semigroup (Ref.[10],Lemma 1.3) providesC3>0 fulfilling‖e(t-s)Δ·(u(·,s)v(·,s))ds‖L∞(Ω)≤(30)The Hölder inequality implies thatwhich yields positive constantC5fulfilling‖e(t-s)Δ·(u(·,s)v(·,s))ds‖L∞(Ω)≤(31)according to (4),(20) and (30).DenoteU(T):=supt∈(0,T)‖u(·,t)‖L∞(Ω)for anyT∈(0,Tmax).Noticing thatt-t0≤1,equality (31) shows that‖e(t-s)Δ·(u(·,s)v(·,s))ds‖L∞(Ω)≤(32)In view of (26)~(30),(32),we can obtainC6>0 such thatfor allT∈(0,Tmax),which directly yieldsfor allT∈(0,Tmax).This is our desired conclusion.Since the boundedness of ‖u‖L∞(Ω)has been verified, we can deduce the boundedness ofvas follows.Lemma 3.7 If the initial data condition (2) holds and ifμ≥t here exists a positive constantCsuch that the solution of (1) satisfies‖v(·,t)‖L∞(Ω)≤C(33)for allt∈(0,Tmax)Proof We use the standard estimate for Neumann heat semigroup to conclude that‖v(·,t)‖L∞(Ω)≤‖etΔv(·,0)‖L∞(Ω)+‖e(t-s)Δu(·,s)v(·,s)‖L∞(Ω)≤‖u(·,s)v(·,s)‖L∞(Ω),whereλ1denotes the first nonzero eigenvalue of -Δ in Ω under the homogeneous Neumann boundary conditions. Since ‖u(·,t)‖L∞(Ω)≤Cand (5) is valid, we can obtain our result immediately.Proof of Theorem 1.1 In combination with Lemma 2.3, Lemma 3.6, and Lemma 3.7,we can draw our conclusion.Remark The result of Theorem 1.1 can be extended to anyα≥2,that is to say, if the first equaion isut=Δu-·(uv)+ru-μuα(α≥2),then we still have Theorem 1.1. The proof for that is just a trival modification of the present one by making use of Young's inequality. References:【相关文献】[1] Li H F, Pang F Q, Wang Y L.Properties of a parabolic system with memory boundary condition [J]. J Sichuan Univ:Nat Sci Ed(四川大学学报:自然科学版), 2016, 53: 483.[2] Chen J Q, Wang Y L, Song X J.Blow-up for a parabolic equation with memory boundary condition [J]. J Sichuan Univ: Nat Sci Ed(四川大学学报:自然科学版), 2014, 51: 229.[3] Deng K, Dong Z.Blow up of a parabolic system with nonlinear memory [J]. Dynam Cont Discrete Impulsive Sys, 2012, 19: 729.[4] Deng K.The role of critical exponents in blow-up theorems: the seuel[J]. J Math Anal Appl, 2000, 243: 85.[5] Keller E F, Segel L A.Initiation of slime mold aggregation viewed as an instability [J]. J Theor Biol, 1970, 26:399.[6] Bellomo N, Bellouquid A, Tao Y,et al.Toward a mathematical theory of Keller-Segel models of pattern formation in biological tissues [J]. Math Methods Appl, 2015, 25: 1663.[7] Winkler M.Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system [J].J Math Pure Appl, 2013, 100: 748.[8] Osaki K, Tsujikawa T, Yagi A,et al.Exponenitial attactor for a chemotaxis-growth system of equations [J]. Nonlinear Anal:Theor, 2002, 51: 119.[9] Nagai T, Senba T, Yoshida K.Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis [J]. Funkc Ekvacioj:Ser I, 1997, 3: 411.[10] Winkler M.Aggregation vs global diffusive behavior in the higher-dimensional Keller-Segel model [J]. J Differ Equations, 2010, 248: 2889.[11] Hillen T, Painter K J.A user's guide to PDF models for chemotaxis [J]. J Math Biol, 2009, 58: 183.[12] Tao Y, Winkler M.Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity[J]. J Differ Equations, 2012, 252: 692.[13] Ishida S, Seki K, Yokota T.Boundedness in quasilinear Keller-Segel systems of parabolic-parabolic type on non-convex bounded domains [J]. J Differ Equations, 2014, 256: 2993.[14] Yang C, Cao X, Jiang Z, Zheng S.Boundedness in a quasilinear fully parabolic Keller-Segel system of higher dimension with logistic source [J].J Math Anal Appl, 2015, 430: 585.[15] Nakaguchi E, Osaki K.Global solutions and exponential attractors of a parabolic-parabolic system for chemotaxis with subquadratic degradation [J].Discrete Cont Dyn B, 2013, 18: 2627.[16] Herrero M A, Velzquez J J L.A blow-up mechanism for a chemotaxis model [J]. Annali Della Scuola Normale Superiore Di Pisa Classe Di Scienze, 1997, 24: 633.[17] Nagai T.Blow-up of nonradial solutions to parabolic-elliptic systems modeling chemotaxis in two-dimensional domains [J]. J Inequal Appl, 2001, 6: 37.[18] Osaki K, Yagi A.Finite dimensional attractors for one-dimensional Keller-Segel equations [J]. Funkc Ekvacioj-Ser I, 2001, 44: 441.[19] Winkler M.Boundedness in the higher-dimensional parabolic-parabolic chemotaxissystem with logistic source [J]. Commun Part Diff Eq, 2010, 35: 1516.[20] Winkler M.Blow-up in a higher-dimensional chemotaxis system despite logistic growth restriction [J]. J Math Anal Appl, 2011, 384: 261.[21] Haroske D D, Triebel H.Distributions, Sobolev spaces, elliptic equations[M]. Zurich:European Mathematical Society, 2008.[22] Mizoguchi N, Souplet P.Nondegeneracy of blow-up points for the parabolic Keller-Segel system[J]. Ann Inst H Poincaré Anal Non Linéai re, 2014, 31: 851.。
小学上册英语下册试卷(含答案)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.The symbol for molybdenum is _____.2.The cat loves to explore _____ new places.3.The chemical formula for silver bromide is _______.4.I like to ride my ________ (摩托车) on weekends.5.In a chemical reaction, the rearrangement of atoms leads to the formation of new_____.6.The moon is ___. (full)7.What is the name of the longest river in the world?A. AmazonB. NileC. YangtzeD. Mississippi8.What is the capital of Italy?A. RomeB. VeniceC. FlorenceD. Milan答案:A9.The ancient Romans used _____ to entertain their citizens.10.The _____ (火烈鸟) is a beautiful bird.11.The __________ is a large lake located in Canada. (安大略湖)12.The invention of the printing press revolutionized the spread of __________. (知识)13.I enjoy playing __________ with my family. (游戏)14.The ____ lives in the wild and is very fast.15.What is the name of the famous American singer known for "Ain't No Mountain High Enough"?A. Diana RossB. Aretha FranklinC. Tina TurnerD. Whitney Houston答案:A16. c Ocean is found near the ________ (北冰洋位于________附近). The Arct17. A solution that has a higher concentration of solute than the solvent is called a______ solution.18.The __________ (历史的记录者) document our journeys.19.I can ______ (solve) math problems quickly.20. e of Liberty was a gift from ________ to the United States. The Ston21.I enjoy _____ (购物).22.My cousin is a ______. She loves to help others succeed.23.What do you call a person who plays music?A. MusicianB. SingerC. PerformerD. All of the above答案:D24.What do we call a young guinea pig?A. PupB. KitC. CalfD. Baby答案:D Baby25. A _____ (植物历史) can provide context for their importance.26.What do we call the main character in a play or story?A. ProtagonistB. AntagonistC. Supporting characterD. Narrator27.Egypt is famous for its ancient ________ (埃及以其古老的________) and pyramids.28.Let’s go ________ to eat ice cream.29.I see a _______ (fox) in the distance.30.The process of ______ can change the landscape over time.31.The Earth's surface is constantly changing due to a variety of ______.32.The ________ is important for navigation on the seas.33.My aunt is a ______. She loves to teach children.34.My ________ (玩具名称) is a fantastic way to learn.35.The ________ was a major event that led to the founding of the United Nations.36.My ______ loves to explore new technologies.37.My mom always gives me __________ (鼓励) when I'm down.38.Which shape has three sides?A. SquareB. TriangleC. RectangleD. Circle答案:B39.The measure of how much space an object occupies is called ______.40.The __________ is part of the brain that controls movement.41. A __________ (化学职业) offers diverse opportunities in various fields.42.The __________ (非洲) has many diverse cultures and languages.43.I think technology is amazing, especially __________ because __________.44.What is the boiling point of water?A. 50°CB. 100°CC. 150°CD. 200°C答案:B45.What kind of animal is a frog?A. MammalB. ReptileC. AmphibianD. Fish答案:C46.What do we use to write on paper?A. PaintB. PencilC. GlueD. Tape47.There are many __________ in the garden.48. A _______ (小狼) learns to hunt from its parents.49.The ________ is a small, quiet creature.50.I like to watch the ______ at night.51.What do we call the place where we watch movies?A. TheaterB. ParkC. MallD. Playground52.My pet parrot can _________ (说话).53.What is the capital of Greece?A. AthensB. RomeC. IstanbulD. Cairo54.What is the primary color of a lime?A. YellowB. GreenC. RedD. Orange55.What do you call a baby dog?A. KittenB. PuppyC. CubD. Foal56.My cat loves to chase after ______ (光点).57.My best friend is _______ (funny/sad).58.The chemical formula for ammonia is ______.59.Which shape has three sides?A. SquareB. TriangleC. CircleD. Rectangle答案:B60.We hear ___ (birds/planes) flying.61.What do you call a large body of saltwater?A. LakeB. SeaC. OceanD. River62.The backbone protects the ______ in animals.63.What do you call the story of someone's life?A. NovelB. BiographyC. FantasyD. Poem答案:B64.What shape is a basketball?A. SquareB. TriangleC. CircleD. Oval答案:C65.We have a ______ (有趣的) discussion in class.66.I love to watch _____ (小动物) explore their surroundings.67.The chemical symbol for yttrium is ______.68.What do we call the warm-blooded animals that lay eggs?A. MammalsB. ReptilesC. BirdsD. Fish答案:C Birds69.The owl's exceptional hearing allows it to hunt effectively in ________________ (黑暗).70.We celebrate ________ (New Year) with fireworks.71. A lever can help lift a ______.72.What do we call a person who studies the past?A. HistorianB. ArchaeologistC. AnthropologistD. Sociologist73.Which animal is known for its long neck?A. ElephantB. GiraffeC. Polar BearD. Kangaroo答案:B74. A turtle can live for many ______ (年).75.The chemical symbol for bromine is ______.76.Which beverage is made from leaves?A. CoffeeB. TeaC. JuiceD. Soda77. A _____ (植物监测) program helps track plant health.78.What type of animal is a dolphin?A. FishB. MammalC. ReptileD. Bird79.The ancient Greeks held ________ in honor of their gods.80.What do we use to brush our teeth?A. ShampooB. ToothbrushC. SoapD. Comb答案:B81.I have a toy _______ that can change shapes and forms for fun.82.The __________ is the temperature at which a substance changes from a solid to a liquid.83.The ________ has a sharp smell.84.Bubbles forming in a solution may indicate a ________ reaction.85.The _______ of sound can be amplified with a speaker.86.I enjoy cooking ______ (传统) dishes from my culture.87.The ______ is a key part of the food chain.88.What is the name of the popular board game where you try to take over the world?A. RiskB. MonopolyC. Settlers of CatanD. Clue答案:A89.My toy ____ can play music and dance! (玩具名称)90.Astrobiology studies the possibility of ______ life in the universe.91.The children are _____ at the playground. (playing)92.I enjoy painting with ______ (水彩) because it creates beautiful ____________ (色彩).93.I enjoy _______ (参加) science clubs.94.What do you call the center of an atom?A. NeutronB. ProtonC. NucleusD. Electron答案:C95.canopy) of a forest is formed by the tops of trees. The ____96.What color is the sky?A. BlueB. GreenC. RedD. Yellow97.What is the color of snow?A. BlueB. YellowC. WhiteD. Green答案:C98.The chemical symbol for cobalt is __________.99.What is the name of the popular animated film about a girl who becomes a princess?A. MoanaB. CinderellaC. FrozenD. Snow White答案:C100.What do you call a young goat?A. KidB. CalfC. LambD. Puppy答案:A。
IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTA TION, VOL. 10, NO. 3, JUNE 2006281 Comprehensive Learning Particle Swarm Optimizerfor Global Optimization of Multimodal FunctionsJ. J. Liang, A. K. Qin, Student Member, IEEE, Ponnuthurai Nagaratnam Suganthan, Senior Member, IEEE, andS. BaskarAbstract—This paper presents a variant of particle swarmoptimizers (PSOs) that we call the comprehensive learning par- ticle swarm optimizer (CLPSO), which uses a novel learning strategy whereby all other particles’historical best information is used to update a particle’s velocity. This strategy enables the diversity of the swarm to be preserved to discourage premature convergence. Experiments were conducted (using codes available from .sg/home/epnsugan) on multimodal test functions such as Rosenbrock, Griewank, Rastrigin, Ackley,and Schwefel and composition functions both with and without coordinate rotation. The results demonstrate good performance of the CLPSO in solving multimodal problems when compared with eight other recent variants of the PSO.Index Terms—Composition benchmark functions, comprehen- sive learning particle swarm optimizer (CLPSO), global numerical optimization, particle swarm optimizer (PSO).I. I NTRODUCTIONPTIMIZATION has been an active area of researchfor several decades. As many real-world optimizationproblems become increasingly complex, better optimizationexperienc es of the swarm to search for the global optimum inthe-dimensional solution space.ThePSOalgorithmis easy toimplementand hasbeen empir-ically shown to perform well on many optimization problems.However, it may easily get trapped in a local optimum whensolving complex multimodal problems. In order to improvePSO’s performance on complex multimodal problems, wepresent the comprehensiv e learning particle swarm optimizer(CLPSO) utilizing a new learning strategy.Thispaper isorganizedas follows.Section IIintroducestheoriginal PSO and some current variants of the original PSO.Section III describes the comprehensive learning particle swarmoptimizer. Section IV presents the test functions, the experi-mental setting for each algorithm, the results, and discussions.Conclusions are given in Section V.II. P ARTICLE S WARM O PTIMIZERSA. Particle Swarm OptimizerPSO emulates the swarm behavior and the individuals repre-algorithms are always needed. Unconstrained optimization sentpoints in the problems can be formulated as a -dimensionalminimization problem as follows: the thdimension ofthe th particleare updated asfollows [1],[2]:whereis thenumber of theparameters tobe optimized.The particle swarm optimizer (PSO) [1], [2] is a relatively (2)new technique. Although PSO shares many similarities with evolutionary computation techniques, the standard PSO does not use evolution operators such as crossover and mutation.where ticle; .PSO emulates the swarm behavior of insects, animals herding, birds flocking, and fish schooling where these swarms searchposition yielding the best fitness value for the th particle; andfor food in a collaborative manner. Each member in the swarm coveredby the wholepopulation. adapts its search patterns by learning from its own experience tionconstantsreflecting theweighting ofOstochastic accelera-and other members ’ experiences. These phenomena are studiedtion terms that pull each particle towardand mathematical models are constructed. In PSO, a member tions, respectively.in the swarm, called a particle, represents a potential solutionbers in the range [0, 1]. A particle ’s velocity on eachdimensionwhich is a point in the search space. The global optimum is re-isclamped to a maximum magnitudegarded as the location of food. Each particle has a fitness value positive constant valueand a velocity to adjust its flying direction according to the bestlocity of thatdimension is assigned toWhen updating the velocity of a particle using (1), dif-Manuscript received May 3, 2005; revised July 15, 2005.ferent dimensions have differentThe authors are with the School of Electrical and Electronic Engi- neering, Nanyang Technological University, 639798 Singapore (e-mail:liangjing@.sg; qinkai@.sg; epnsugan@.sg; baskar_mani@).Digital Object Identi fier 10.1109/TEVC.2005.857610research ers use the following updating equation:1089-778X/$20.00 © 2006 IEEE282IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTA TION, VOL. 10, NO. 3, JUNE 2006A linearly decreasing inertia weight over the course of searchwas proposed by Shi and Eberhart [8]. Parameters in PSO arediscussed in [9]. Shi and Eberhart designed fuzzy methodsto nonlinearly change the inertia weight [10]. In [11], inertiaweight is set at zero, except at the time of reinitialization. In ad-dition to the time-varying inertia weight, a linearly decreasingis introduced in [12]. By analyzing the convergencebehavior of the PSO, a PSO variant with a constriction factorwas introduced by Clerc and Kennedy [13]. Constriction factorguarantees the convergence and improves the convergencevelocity.Improving PSO’s performance by designing different typesof topologies has been an active research direction. Kennedy[14], [15] claimed that PSO with a small neighborhood mightperform better on complex problems, while PSO with a largeneighborhood would perform better on simple problems.Suganthan [16] applied a dynamically adjusted neighborhoodwhere the neighborhood of a particle gradually increases untilit includes all particles. In [17], Hu and Eberhart also usedadynamicneighborhoodwhereclosest particles in theperformance space are selected to be its new neighborhoodin each generation. Parsopoulos and Vrahatis combined theglobal version and local version together to construct a unifiedparticle swarm optimizer (UPSO) [18]. Mendes and Kennedyintroduced a fully informed PSO in [19]. Instead of using theandpositions in the standard algorithm, all theneighbors of the particle are used to update the velocity. Theinfluence of each particle to its neighbors is weighted based onits fitness value and the neighborhood size. Veeramachaneni et Fig. 1. Flowchart of the conventional PSO.Comparing the two variants in (1) and (3), the former can have a larger search space due to independent updating of eachdimension, while the second is dimension-dependent and has a smaller search space due to the same random numbers being used for all dimensions. Equation (1) always yields better per- formance on unrotated problems than the rotated version of the problems. Equation (3) performs consistently on unrotated and rotated problems [3]. As the first updating strategy achieves alarger search space and always performs better, we use (1) inthis paper. The flowchart of the standard PSO employing (1)isgiven in Fig. 1.B. Some Variants PSOSince its introduction in 1995 by Kennedy and Eberhart[1],[2], PSO has attracted a high level of interest [4]–[7]. Manyre-searchers have worked on improving its performance invariousways, thereby deriving many interesting variants. One of thevelocity dimension, the FDR-PSO algorithm selects one otherparticle , which has a higher fitness value and is nearer tothe particle being updated.Some researchers investigated hybridization by combiningPSO with other search techniques to improve the performanceof the PSO. Evolutionary operators such as selection, crossover,and mutation have been introduced to the PSO to keep the bestparticles [21], to increase the diversity of the population, and toimprove the ability to escape local minima [22]. Mutation op-erators are also used to mutate parameters such as the inertiaweight [23]. Relocating the particles when they are too close toeach other [24] or using some collision-avoiding mechanisms[25] to prevent particles from moving too close to each other inorder to maintain the diversity and to escape from local optimahas also been used. In [22], the swarm is divided into subpopula-tions, and a breeding operator is used within a subpopulation orbetween the subpopulations to increase the diversity of the pop-ulation. Negative entropy is used to discourage premature con- variants [8] introduces a parameter called inertia weightthe original PSO algorithms as follows:into(4)The inertia weight is used to balance the global and localsearch abilities. A large inertia weight is more appropriate forglobal search, and a small inertia weight facilitates localsearch.the results of these searches are integrated by a global swarmto significantly improve the performance of the original PSO onmultimodal problems.LIANG et al.: COMPREHENSIVE LEARNING PARTICLE SW ARM OPTIMIZERIII. C OMPREHENSIVE L EARNING P ARTICLE S WARM O PTIMIZERAlthough there are numerous variants for the PSO, prema-ture convergence when solving multimodal problems is still themain deficiency of the PSO. In the original PSO, each par-283ticle learns from its andthe social learning aspect to only the makesthe original PSO converge fast. However, because all particles in the swarmlearn from the even ifthe current global optimum, particles may easily be attracted to theregion and get trapped in a local optimum if the search envi-ronment is complex with numerous local solutions. As, the fitness value of a particle is possiblydetermined by values of all parameters, and aparticle that has discovered the region corresponding to the global optimumin some dimensions may have a low fitness value because of thepoor solutions in the other dimensions. In order to make betteruse of the beneficial information, we proposed new learningstrategies to improve the original PSO [30]. In [30], all parti-cles’are usedto update thevelocity ofany oneparticle. This novel strategy ensures that the diversity of the swarm is pre-served to discourage premature convergence. Three versions ofPSO using the comprehensive learning strategy were discussedand demonstrated with significantly improved performances onsolving multimodal problems in comparison to several othervariants of the PSO. Among the three variants, the CLPSO isthe best, based on the results. Hence, we further investigate theCLPSO in this paper. Fig. 2.Selection ofexemplardimensions forparticle .A. Compehensive Learning StrategyAll theseIn this new learning strategy, we use the following velocity updating equation:(5)space using the information derived from different particles’historical best positions. To ensure that a particle learns fromgood exemplars and to minimize the time wasted on poor direc-tions, we allow the particle to learn from the exemplars until thewhere definesparticle ceases improving for a certain number of generationss the particle shouldfollow.responding dimension of any particle’s including its own, and the decision depends on probability ,referred to as the learning probability, which can take different values for 1)Instead ofusingparticle’s own different particles. For each dimension of particle , we generate exemplars, allparticles’a random number. If this random number is larger than corresponding dimension will learn from its own, the ; other-wise it will learn from another particle’s . Weemploy the tournament selection procedure when the particle’s dimension canlearn fromdifferent learns from another particle’s asfollows.1) We first randomly choose two particles out of the popu- aparticle maylearn from thecorrespondingdimension of lation which excludes the particle whose velocity is up- differentparticle’s dated. 3)Instead oflearning fromtwo exemplars(2) We compare the fitness values of these two particles’s and select the better one. In CLPSO, we define the fitness value the larger the better, which means that when solving minimization problems, we will use the negative function value as the fitness values.3) We use the winner’s as the exemplar to learn fromfor that dimension. If all exemplars of a particle are itsatthesametime ineverygeneration as intheoriginalPSO(1)and (3),eachdimension of aparticlelearnsfromjustoneexemplar for afewgenerations.B. CLPSO’s Search BehaviorThe above operations increase the swarm ’s diversity to yieldown, we will randomly choose one dimension tolearn from another particle ’s’scorresponding di-mension. The details of choosingare given in Fig. 2.284IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTA TION, VOL. 10, NO. 3, JUNE 2006Fig. 3.(b) The CLPSO’s and the original PSO’s possible search regions per variable in a swarm with five members.(a). (c)., theandever, the is more likely to provide a larger momentum, asis likely to be larger than the . Hence, themay influence the particle to move in its directioneven ifticle beit is in a local optimum region far from the global optimum. Ifand are on the same side of the particle’s current po-sition and if it points to a local optimum, the particle will movein that direction and it may be impossible to jump out of theranges for the th particle of PSO asand CLPSO, as shown in (9) at the bottom of the page.local optimum area once its falls into the same local op-timum region where the is. However, in our new learning strategy, the particle can fly in other directions by learningfromrespectively.other particles’when the particle’sinto the same local optimum region. Hence, our new learning strategy has the ability to jump out of local optimum via the co-operative behavior of the whole swarm.swarm. In order to compare the potential search spaces of PSO and CLPSO, both algorithms are run 20 times on a (unimodal) sphere function and a (multimodal) Rastrigin function defined inIn order to compare the original PSO’s and CLPSO’spoten-Section IV-A.tial search spaces, first we omit the old velocitycom-ponent. If we let , in the original PSO and in CLPSO allbe equal to one, the update equations of the original PSO andCLPSO reduce to the following equations:(6) Table I presents ’s mean value of the 20 runs. andand versus the iterations are plotted in Fig. 4.From Table I and Fig. 4, we observe that CLPSO’s updating strategy yields a larger potential search space than that of theoriginal PSO. The multimodal Rastrigin’s function’s meanis ten times larger than that of the unimodal sphere function. By increasing each particle’s potential search space,(7)the diversity is also increased. As each particle’spossibly a good area, the search of CLPSO is neither blind norLet us consider the fourth particle in a swarm with five members as an example. The potential search spaces of the original PSO and the CLPSO on one dimension are plotted as arandom. Compared to the original PSO, CLPSO searches more promising regions to find the global optimum. Experimental results in Section IV support this description.line in Fig. 3. For the fourth particle whose position isdifferent cases are illustrated in Fig. 3: (a), threeand(c) ,values yielded different results on the same problem if theample,is theis the ,(9)LIANG et al.: COMPREHENSIVE LEARNING PARTICLE SW ARM OPTIMIZER285Fig. 4. Comparison of PSO’s and CLPSO’s potential search space. (a)andsphere function. (d) forRastrigin’sfunction.TABLE I M EAN V ALUE OF FORS PHERE R ASTRIGIN F UNCTIONS IN 20 R UNSwhile on the rotated problems, differentvaluesyield the best performance for different problems. Different values yield similar results on simple unimodal problems while seri-ously affecting CLPSO’s performance on multimodal problems.In order to address this problem in a general manner, we pro-pose to set suchthat eachparticle has adifferent Therefore, particles have different levels of exploration and ex-ploitation ability in the population and are able to solve diverseproblems. We empirically developed the following expressionto set a valuefor eachparticle:(10)searchbounds, inmanypracticalproblems,there areboundson thevariables’ranges. Thesearch rangefor a problem Fig. 5 presents an example of assignedfor apopulationof 30. Each particle from 1 to 30 has a0.05 to 0.5.D. Implementation of Search Boundsvalueranging fromThough we have shown in [30] the CLPSO to be ro- fitnessvalue of aparticle andupdate its bust to initialization and independent of upper and lower theparticle is inthe range.Since allexemplars arewithin the286IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTA TION, VOL. 10, NO. 3, JUNE 2006Fi g . 7. C L P S O ’s r e s u l t s o n s i x t e s t f u n c t i o n s w i t h d i f f e r e n t r e f r e s h i n g ga p. Fig. 6.Flowchart of the CLPSO algorithm.range, the particle will eventually return to the search range. The complete flowchart of the CLPSO is given in Fig. 6.E. Adjusting the Refreshing GapThe refreshing gap parameterneeds be tuned. In this sec-tion, six different kinds of ten-dimensional (10-D) test functions are used to investigate the impact of this parameter. They are the sphere, Rosenbrock, Ackley, Griewank, Rastrigin, and ro-tated Rastrigin functions as de fined in Section IV . The CLPSOis run 20 times on each of these functions, and the mean valuesof the final results are plotted in Fig. 7. As all test functions areFig. 8. The landscape maps of Group D problems. (a) Composition function 1 (CF1). (b) Composition function 5 (CF5).and better results on the sphere function. For the other five testminimization problems, the smaller the final result, the better functions, better results were obtained whenit is. From Fig. 7, we can observe that can in fluence the re-sults. Whenis zero, we obtained a faster convergence velocityLIANG et al.: COMPREHENSIVE LEARNING PARTICLE SW ARM OPTIMIZER287 IV. E XPERIMENTAL R ESULTS AND D ISCUSSIONA. Test FunctionsAs we wish to test the CLPSO on diverse test functions andour main objective is to improve PSO’s performance on mul- timodal problems, we choose two unimodal functions and 14 multimodal benchmark functions [32]–[35]. All functions are tested on ten and 30 dimensions. According to their properties, these functions are divided into four groups: unimodal prob- lems, unrotated multimodal problems, rotated multimodal prob-lems, and composition problems. The properties and the for- mulas of these functions are presented below.Group A: Unimodal and Simple Multimodal Problems: 7)8)1) Sphere function(11)2)Rosenbrock’s functiondimensions than higherdimensions [36]. The Weierstrass function is continuous butdifferenti able only on aThe first problem is the sphere function and is easy to solve. The second problem is the Rosenbrock function. It can be treated as a multimodal problem. It has a narrow valley from the perceived local optima to the global optimum. In the experiments below, we find that the algorithms that perform well on sphere function also perform well on Rosenbrock function.Group B: Unrotated Multimodal Problems:3) Ackley’s functionis a complex multimodal problem with a large number oflocal optima. When attempting to solve Rastrigin’s function,algorithm s may easily fall into a local optimum. Hence, analgorithm capable of maintaining a larger diversity is likelyto yield better results. Noncontinuou s Rastrigin’s function isconstruct ed based on the Rastrigin’s function and has the samenumber of local optima as the continuous Rastrigin’s function.The complexity of Schwefel’s function is due to its deep localoptima being far from the global optimum. It will be hard tofind the global optimum if many particles fall into one of thedeep local optima.Grou p C: Rotated Multimod al Problems:In Group B, somefunctions are separable and can be solved by using 1-D(13) searches,wherein Group C, we have four rotated multimodal problems. Torotate a function, first an orthogonal matrix shouldbe gener-4) Griewanks’s functionmatrix to getthe newrotatedvariable5)Weierstrass function(15)Whenone dimensionin6) Rastrigin’s functionIn thispaper, we used Salomon ’s method [37] to generate the orthog- onal matrix.288IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTA TION, VOL. 10, NO. 3, JUNE 20069)Rotated Ackley’s function10) Rotated Griewanks’s function11) Rotated Weierstrass function (22)than CF1 since evenafter the global basin is found, the global optimum isnot easy to locate. The landscape maps of these two composition functions are illustrated in Fig. 8. T h e g l o b a l o p t i ma, the corresponding fitness value (23)the search ranges each function are given in Table II. Biased initializations are12) Rotated Rastrigin ’s function13) Rotated noncontinuous Rastrigin ’s function(24)··· PSO with inertia weight (PSO-w) [8]; PSO with constriction factor (PSO-cf) [13]; Local version of PSO with inertia weight (PSO-w-local); 14) Rotated Schwefel ’s function(25)CPSO-H [29]; CLPSO.Among these PSO local versions, PSO_w_local and PSO_cf_local were chosen as these versions yielded the best results [15] with von Neumann neighborhoods where(26)In rotated Schwefel ’s function, in order to keep the global op- timum in the search range after rotation, noting that the original global optimum of Schwefel ’s function is at [420.96, 420.96, , 420.96 ], andareused instead of ’s function has better solutions out of the search range , when ,, i.e. is set in portion to thesquare neighbors above, below, and one each side on a two-dimen- sional lattice were connected. FIPS with U-ring topology that achieved the highest success rate [19] is used. When solving the 10-D problems, the population size is set at ten and the maximum fitness evaluations (FEs) is set at 30 000. When solving the 30-dimensional (30-D) problems, the population size is set at 40 and the maximum FE is set at 200 000. All experiments were run 30 times. The mean values and standard deviation of the results are presented.distance between and the bound.Group D: Composition Problems: Composition functions are constructed using some basic benchmark functions to obtainmore challenging problems with a randomly located global optimum and several randomly located deep local optima. The1More composition functions can be found at .sg/home/EPNSugan/.LIANG et al.: COMPREHENSIVE LEARNING PARTICLE SW ARM OPTIMIZERTABLE IIG LOBAL O PTIMUM, S EARCH R ANGES AND I NITIALIZA TION R ANGES OF THE T EST F UNCTIONS 289When solving real-world problems, usually the fitness calcu- lation accounts for the most time as the PSO is highly compu- tation efficient. Hence, the algorithm-related computation times of these algorithms are not compared in this paper. Further, the main difference between the CLPSO and the original PSO is the modified velocity updating equation, which has been made simpler in the CPSO. The complexity of the new algorithm is similar to the original PSO. In the experiments, a serial imple- mentation is used, while it is easy to be modified to a parallel implementation. With a parallel form, the performance is likelyFromthe results,we observethat for theGroup Aunimodalproblems, since CLPSO has a large potential search space, itcould not converge as fast as the original PSO. CLPSO achievedbetter results on all three multimodal groups than the originalPSO. CLPSO surpasses all other algorithms on functions 4,5, 7, 8, 10, 12, 13, 14, 15, and 16, and especially significantlyimproves the results on functions 7 and 8. According to theresults of -tests, these results are different from the secondbest results. The CLPSO achieved the same best result as theCPSO-H on function 6, and they both are much better thanto be not affected much due to batch updating ofcomputational efficiency improves.whileC. Experimental Results and Discussions1) Results for the 10-D Problems: Table III presents the means and variances of the 30 runs of the nine algorithmsperform s better on more complex problemswhen the otheralgorithms miss the global optimum basin. The Schwefel’sfunction is a good example, as it traps all other algorithms inlocal optima. The CLPSO successfully avoids falling into theon the sixteen test functions with . Thebest resultsamong the nine algorithms are shown in bold. In order to deter- mine whether the results obtained by CLPSO are statistically different from the results generated by other algorithms, the nonparametric Wilcoxon rank sum tests are conducted between the CLPSO’s result and the best result achieved by the otherOn the two composition functions with randomly distributedlocal and global optima, CLPSO performs the best.Comparing theresults andtheconvergence graphs,amongthese nine PSO algorithms, FDR-PSO has good local searchability and converges fast. PSO with inertia weight (PSO-w)eight PSO versions for each problem. The valuespresentedin the last row of Tables III and IV are the results of -tests. An value of one indicates that the performances of the two al- gorithms are statistically different with 95% certainty, whereas value of zero implies that the performances are not statisti- cally different. Fig. 9 presents the convergence characteristics in terms of the best fitness value of the median run of each algorithm for each test function.versions where the whole population is the neighborhood. PSOwith constriction factor converges faster than the PSO withinertia weight. But PSO with inertia weight performs betteron multimodal problems. UPSO combines global PSO andlocal PSO together to yield abalanced performance betweenthe global and the local versions. PSO with inertia weight (PSO-w-local), PSO with constriction factor (PSO-cf-local)290IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTA TION, VOL. 10, NO. 3, JUNE 2006TABLE IIIR ESULTS FOR 10-D P ROBLEMSand FIPS with a U-ring topology are all local versions. Theyall perform better on multimodal problems than the globalversions. Among the three, FIPS yields a comparatively betterperformance. CPSO-H presents good performance on someunrotated multimodal problems and converges faster whencompared to CLPSO. However, its performance is seriouslyaffected after rotation. Although CLPSO’s performance is alsoaffected by the rotation, it still performs the best on four rotated problems. It can be observed that all PSO variants failed onthe rotated Schwefel’s function, as it becomes much harder to solve after applying rotation.2) Results for the 30-D Problems: The experiments con- ducted on 10-D problems are repeated on the 30-D problems and the results presented in Table IV. As the convergence graphs are similar to the 10-D problems, they are not presented. From the results in Table IV, we can observe that the algorithms。
2020年上海市紫竹园中学高三英语上学期期末考试试题及答案解析第一部分阅读(共两节,满分40分)第一节(共15小题;每小题2分,满分30分)阅读下列短文,从每题所给的A、B、C、D四个选项中选出最佳选项AIn his 402nd anniversary year, Shakespeare is still rightly celebrated as a great language master and writer. But he was not the only great master of play writing to die in 1616, and he is certainly not the only writer to have left a lasting influence on theater.While less known worldwide, Tang Xianzu is considered one of Chinas greatest playwrights and is highly spoken of in that country of ancient literary and dramatic traditions.Tang was born in 1550 inLinchuan,Jiangxiprovince. Unlike Shakespeare's large body of plays,poems and sonnets (十四行诗), Tang wrote only four major plays: The Purple Hairpin, Peony Pavilion (《牡丹亭》), A Dream under the Southern bough, and Dream of Handan. The latter three were constructed around a dream narrative, a way through which Tang unlocked the emotional dimension of human desires and ambitions and explored human nature beyond the social and political limits of that time.Similar to Shakespeare, Tang's success rode the wave of a renaissance (复兴) in theater as an artistic practice. As in Shakespeare'sEngland, Tang's works became hugely popular inChinatoo. During Tang'sChina, his plays were enjoyed performed, and changed. Kunqu Opera, a form of musical drama, spread from southernChinato the whole nation and became a symbol of Chinese culture. Combining northern tune and southern music, kunqu Opera was known for its poetic language, music, dance movements and gestures. Tang's works benefited greatly from the popularity of kunqu Opera, and his plays are considered classics of kunqu Opera.While Tang and Shakespeare lived in a world away from each other, there are many things they share in common, such e humanity of their drama, their heroic figures, their love for poetic language, a lasting popularity and the anniversary during which we still celebrate them.1. Why is Shakespeare mentioned in the first paragraph?A. To describe Shakespeare's anniversary.B. To introduce the existence of Tang Xianzu.C. To explain the importance of Shakespeare.D. To suggest the less popularity of Tang Xianzu.2. What's possibly one of the main theme of Tang's works?A. Social reality.B. Female dreams.C. Human emotions.D. Political environment.3. What does the author mainly tell us in Paragraph 4?A. The influence of Kunqu Opera on Tang's works.B. Tang's success in copying Shakespeare's styles.C. The way Kunqu Opera became a symbol of Chinese culture.D. Tang's popularity for his poetic language and music.BAt the World Economic Forum last month, President Trump drew claps when he announced the United States would respond to the forum's proposal to plant one trillion(万亿) trees to fight climate change. The trillion-tree idea won wide attention last summer after a study published in the journal Science concluded thatplanting so many trees was “the most effective climate change solution to date”.If only it were true. But it isn't. Planting trees would slow down the planet's warming, but the only thing that will save us and future generations from paying a huge price in dollars, lives and damage to nature is rapid and considerable reductions in carbon release from fossil fuels, to net zero by 2050.Focusing on trees as the big solution to climate change is a dangerous diversion(偏离). Worse still, it takes attention away from those responsible for the carbon release that are pushing us toward disaster. For example, in the Netherlands, you can pay Shell an additional 1 euro cent for each liter of regular gasoline you put in your tank, to plant trees to balance the carbon release from your driving. That's clearly no more than disaster slightly delayed. The only way to stop this planet from overheating is through political, economic, technological and social solutions that end the use of fossil fuels.There is no way that planting trees, even across a global area the size of theUnited States, can absorb the huge amounts of fossil carbon released from industrial societies. Trees do take up carbon from the atmosphere as they grow. But this uptake merely replaces carbon lost when forests were cleared in the first place, usually long ago. Regrowing forests where they once grew can undo some damage done in the past, but even a trillion trees can't store enough carbon to head off dramatic climate changes this century.In a sharp counter argument to last summer's Paper in Science, Justin Gillis wrote in the same journal in October that the study's findings were inconsistent with the dynamics of the global carbon cycle. He warned that “the claimthat global tree restoration(复原) is our most effective climate solution is simply scientifically incorrect and dangerously misleading”.4. What do we know about the trillion-tree idea?A. It was published in a journal.B. It was proposed last summer.C. It was put forward by Trump.D. It drew lots of public attention.5. What is paragraph 3 mainly about?A. A drawback of the tree planting strategy.B. An example of balancing carbon release.C. An anecdote of making a purchase at Shell.D. A responsibility for politicians and economists.6. What was Justin Gillis's attitude towards global tree restoration?A. Indifferent.B. Opposed.C. Hesitant.D. Supportive.7. What is the best title for the text?A. Contradictory Ideas on Tree Planting.B. A Trillion Trees Come to the Rescue.C. Planting Trees Won't Save the World.D. The Best Solution to Climate Change.CIn order to develop the pandemic-stricken economy, China recovered the street vendors(商贩)in a new nation-wide method known as “street stall economy'', allowing residents to set up open-air shops on the sidewalks or other available public spaces.Street vendors were once an important part ofChina's economy and urban landscape. However, sinceChina's economy took off in the last decade, street vendors have gradually disappeared from the streets and many of them opened shops of their own.Fast forward to today, street vendors have come into our sight again after cities such asChengduand Yantai succeeded in creating hundreds of thousands of jobs by giving street stalls permission to operate.China's tech industry was quick to jump on the street vendor trend, with tech giants including Alibaba, Tencent, Meituan and flocking todish outcheap loans, offer support and payment solutions to millions of owners of newly established small businesses.Ant Financial, Alibaba's fintech arm, promised its mobile wallet app Alipay will give interest-free loans to 30 million vendors, and 70 billion RMB of interest-free credit line to consumers to make purchases everywhere, including street vendors. provided 50 billion RMB worth of quality goods for street vendors, and provided each one of them with a maximum 100,000 RMB interest-free loan to stock up.Tencent's WeChat announced to offer payment solutions, marketing supports and even training for up to 50 million street vendors, with the end goal of digitally transforming them to increase their income.Guangzhoucity partnered with WeChat this month to hold a live streaming shopping festival to improve sales of local produce. In attempts to promote various live streaming platforms, many tech CEOs also made their own live streamed e-commerce debuts(首次亮相)selling goods coming from all over the country.8. What does the underlined part “dish out" in Paragraph 3 mean?A. turn down.B. provide with.C. pay off.D. apply for.9. Compared with and Tencent, what unique measure did Ant Financial take?A. It provides interest-free loans for vendors.B. It offers interest-free credit line to customers.C. It provides quality goods for street vendors.D. It offers marketing support to businessmen.10. What's the purpose of the cooperation between WeChat andGuangzhoucity?A. To volunteer to train street vendors.B. To give away free goods to the poor.C. To promote to develop the local economy.D. To help CEOs make their own streaming platforms.11. What can be the best title for the text?A. Chengdu and Yantai Succeeded in Creating Job OpportunitiesB. "Street Vendor Economy” Greatly Increases People's IncomeC. The Whole Nation Are Involved in a New Economy ModelD.China's Major Tech Companies Are Helping With "Street Vendor Economy”DIt is essential that students have a category of school-related activities they can participate in. These activitiescan range from activities during normal school hours to after-school activities. No matter the time, these activities should be available to every student, and at Victory Pioneers International Schools (V.P.I.S) it is encouraged that every student participate in at least one activity, educational and recreational.One of the primary reasons school activities are important at V.P.I.S. is because it gives students the exercise they might not normally receive. Most popularly, these types of activities include major sports such as football, basketball, baseball, tennis, track and field and soccer but also might include gymnasium games and other games.Activities during V.P.I.S. also make a good impression on colleges if students are planning to pursue more education. Colleges look for students who do not just go to school and go home after school. These activities range from participating in clubs and sports to volunteering after school at a recreation center or having a part-time job. If a college sees you maintained good grades while participating in these activities, it will be impressed.V.P.I.S. activities also allow students to be creative. Gifted-and-talented activities allow gifted students to participate in what they otherwise would never have experienced in the classroom. They are a great way to allow students to be creative. Additionally, participating in clubs such as drama that appeal to students’ interest also allows them to expand their knowledge and be creative.Students also can have their interests expanded by participating in activities. These activities could consist of anything, such as joining the Future Business Leaders, the school’s debate team and the chess team, to name a few. By participating in these activities, a student might realize he is interested in something he never knew he was interested in before.12. What can we learn about activities at V.P.I.S.?A. Not every student has access to them.B. Students are required to take part in them after school.C. They give students exercise that might not be got in other schools.D. Educational activities are more popular with the students.13. What benefits can the students get from the activities?A. They can get extra grades when applying for colleges.B. They will become more gifted and talented .C. They may expand their knowledge in drama.D. They may better know their own interests.14. Which of the following is a suitable title for the passage?A. The Benefits of V.P.I.S. ActivitiesB. School-related Activities at V.P.I.S.C. Colleges Need Creative StudentsD. Activities Make You Creative15. Where is the passage probably from?A. A scientific magazine.B. A college application guideline.C. A club introduction.D. The website of V.P.I.S.第二节(共5小题;每小题2分,满分10分)阅读下面短文,从短文后的选项中选出可以填入空白处的最佳选项。
Technical PublicationRelated Support and Learning Opportunities Offered by the CommScope Infrastructure Academy The insights and expertise contained in this manual represent just one small part of Andrew Solutions global learning initiative. Few industries are evolving as quickly as wireless communications. Every technological innovation impacts what happens in the field. Our customers look to the CommScope Infrastructure Academy to make sure their technicians and installers are well trained, well-prepared, and well-educated to take advantage of opportunities as they evolve. To access a course, go to /coursecatalog.php, course #6107.Field Engineering Services (FES)Support services, such as our Field Engineering Services (FES) Group gives Andrew Solutions’ customers access to technical support where and when it is needed the most — in the field. The FES team is staffed by an expert team of technicians who, in turn, are supported by some of the brightest and most experienced product line managers. With all of this knowledge and support the FES offers our customers access to hands-on, specialized training classes.Section 1: System Components ......................................................................................................02Section 2: General Specifications ..................................................................................................03Section 3: HELIAX ® FiberFeed ® Trunk Cables .........................................................................................04Section 4: HELIAX ® FiberFeed ® Jumpers ..............................................................................................05Section 5: Breakout Procedure / LC Connection Considerations ........................................................06Section 6: All-in-One Cleaner / Inspecting ................................................................................................07Section 7: OVP Identification / Gland Installation .................................................................................08Section 8: Color Code ...............................................................................................................................09Section 9: Grounding .................................................................................................................................10Section 10: Excess Cable Management .................................................................................................11Section 11: Inspection Check list . (12)For more information, Contact Customer Service Center United States and Mexico 1-800-255-1479 or 1-888-235-5732 International: +1-779-435-8579Installation Guidelines - – HELIAX ® FiberFeed ® SolutionsFiber/Copper Cables: HFT1206 │ HFT806 │ HFT406 │ HFT412!HELIAX ® FiberFeed ®Verizon System ComponentsOVP/Fiber Junction BoxOVP/Fiber Junction Box Hoisting GripsFeed Thru GlandsFiber HELIAX ® FiberFeed Hybrid JumpersHELIAX FiberFeed ® Hybrid JumpersHELIAX ®FiberFeedHybrid CableWARNING: CommScope Hybrid FiberFeed cables require the use of approved installation accessories.6 Circuit Rack Mount OVPHFT1206-24S49-XXX UL Type TC-OF-ER 6 AWG 12 24Corrugated aluminum Bend insensitive singlemode 18 │ 18 AWG1.78 lb/ft 1.56 in 39 in 29 in 39 in 29 in31 in 15.6 in 450 lbf 1500 lbfGeneral SpecificationsCable Type RatingCenter Conductor Gauge Conductors, quantity Total Fiber Quantity Shielding Type Fiber TypeAlarm Wire (Qty │ Gauge)DimensionsCable Weight Diameter Over Jacket Breakout Length, Fiber, end 1Breakout Length, Power, end 1 Breakout Length, Fiber, end 2Breakout Length, Power, end 2Physical SpecificationsMinimum Bend Radius, loaded Minimum Bend Radius, unloaded Tensile Load, long term, maximum Tensile Load, short term, maximumHFT806-16S48-XXX UL Type TC-OF-ER 6 AWG 8 16Corrugated aluminum Bend insensitive singlemode 14 │ 18 AWG1.24 lb/ft 1.3 in 39 in 29 in 39 in 29 in26 in 13 in 240 lbf 800 lbfHFT406-8S48-XXX UL Type TC-OF-ER 6 AWG 4 8Corrugated aluminum Bend insensitive singlemode 10 │ 18 AWG.772 lb/ft 1.12 in 23 in 23 in 23 in 23 in22 in 11 in 180 lbf 600 lbfGeneral SpecificationsCable Type RatingCenter Conductor Gauge Conductors, quantity Total Fiber Quantity Shielding Type Fiber TypeDimensionsCable Weight Diameter Over Jacket Breakout Length, Fiber, end 1Breakout Length, Power, end 1 Breakout Length, Fiber, end 2Breakout Length, Power, end 2Physical SpecificationsMinimum Bend Radius, loaded Minimum Bend Radius, unloaded Tensile Load, long term, maximum Tensile Load, short term, maximumHFT412-2SXX-XX UL Type TC-OF-ER 12 AWG 4 2Corrugated aluminum Bend insensitive singlemode.220 lb/ft .62 in various various various various12.4 in 6.2 in 90 lbf 300 lbfHFT412-4SXX-XX UL Type TC-OF-ER 12 AWG 4 4Corrugated aluminum Bend insensitive singlemode.220 lb/ft .62 in various various various various12.4 in 6.2 in 90 lbf 300 lbfTrunk Fiber FeederHoisting RecommendationsReminder: Plan grip location by measuring distance (D) from Fiber Enclosure Box to tower support member.• In general this cable will handle similarly to coaxial cable, and similar installation techniques apply. All cables are individually serialized, be sure to write down the cable serial number for future reference.• The terminated fiber ends (the broken out fibers plus connectors) however are fragile, and these must be protected during the installation process.• Leave the protective tube and sock around the fiber tails and connectors in place during hoisting and securing the cable. Remove this only just prior to making the final connections to the Junction box.• DO NOT BEND THE FIBER ENDS (in the furcation tubes) TIGHTER THAN 1.2" (30mm) BEND RADIUS ELSE THEREIS A RISK OF BREAKING THE GLASS FIBERS.• Be sure that the lace up ends and fiber connectors are not damaged by attachment of a hoisting grip or during the hoisting process. Attach a hoisting grip on the jacketed cable no less than 6" below the fiber breakout point. If a hoisting grip is not easily attached, use a simple line attached below the fiber break-out point (i.e. at the cable outer jacket). Prevent the fiber tails (in protective tube) at the cable end from undue movement during hoisting by securing the protective tube (with outer sock) to the hoisting line.• During hoisting ensure that there is a free path and that the cable, and especially the fiber ends, will not be snagged on tower members or other obstacles.• Installation temperature range is -22F to 158F• Minimum cable bend radii can be found in this document or on-line.• Maximum cable tensile load can be found in this document or on-line.• CommScope Lace-Up Hoisting Grip 19256B-C required for 406 and 806 installations.• CommScope Lace-Up Hoisting Grip 29961-Crequired for 1206 installations.•Maximum hanger spacing 3ft (0.9m) - 4ft (1.2m)Hybrid Fiber Cables weigh more than traditional coaxial cables. Be sure to follow proper hoisting and attachment procedures.!• In general this cable will handle similarly to a coaxial cable.• The terminated fiber ends however are fragile and must be protected during installation. Leave the packaging around the fiber ends in place until ready to connect the jumper between OVP box and RRU or BBU.• DO NOT BEND THE FIBER ENDS (in the furcation tubes) TIGHTER THAN 1.2" (30mm) BEND RADIUS ELSE THERE IS A RISK OF BREAKING THE GLASS FIBERS.• Attach the main cable securely to the structure or equipment using hangers and/or cable ties to preventstrain on connections from movement in wind or snow/ice conditions.• Ensure the LC fiber connectors are seated firmly in the OVP box, RRU or in BBU equipment.• Ensure the weatherproof boots for both fiber and power connections and seated firmly in the RRU. • Heat shrink tube of the jumper should be 1" (25.40mm) inside of the OVP box.• Installation temperature range is -22F to 158F (-30C to 70C).• Minimum cable bend radii can be found in this document or on-line.• Standard lengths available are 3-6-9-12-15-30 foot.•All jumpers are individually serialized, for immediate access to test results visit /webtrak/• Power connector is supplied with the RRU • Blue power conductor is -48V • Black power conductor is 0V (return)•RRU/BBU connectivity per OEM instructionJumper AssembliesPower ConductorsEND 1 (RRU)END 2 (Junction box)Power ConductorsPower ConductorsLC Duplex ConnectorsEND 1 (BBU)END 2 (Junction box)HFT412-2S28 Hybrid tails, 2 Fiber - RRU to 2-OVP Box HFT412-2S29 Hybrid tails, 2 Fiber - RRU to 6-OVP BoxHFT412-2S27 Hybrid tails, 2 Fiber - BBU to 2-OVP Boxisopropyl alcohol), and by applying medium pressure, first wipe against wet area and then onto dry area to clean potential residue from end face. Clean connector ferrule inside adapter by inserting lightly moistened cleaning stick with fiber optic cleaning solution (or >91% isopropyl alcohol) inside the adapter until contact is made with connector on opposite end. Rotate cleaning stick with medium pressure in one circular motion as it is pulled away from the adapter. Repeat process using dry cleaning stick.Caution: Signal strength will be affected if end and sides of ferrule are not thoroughly cleaned. Discard cleaningsticks after each use. Do not turn cleaning sticks back and forth pressing against connector end face. This may cause Clean adapter by inserting adapter cleaning stick (or fiber adapter sleeve brush) moistened with fiber optic cleaning solution (or >91% isopropyl alcohol) inside the adapter and gently pull out with twisting motion. Repeat process with a dry cleaning stick.Caution: Do not try to clean adapter with a standard pipe cleaner. The sleeve inner diameter of LC adapters is too small. Do not try to clean the adapter with cleaning stick if a connector is mounted in one side. Discard cleaning sticks Clean Tip of FerruleWhile holding the protection tube straight pull the tube away from cable.Device designed for cleaning the ferrule end faces of LC connectorsOpen guide cap, insert LC connector into guide, push the outer shell to start cleaning the LC connector interface, a "click" sound indicates end of a cleaning process, repeat, close cap immediately after use.Caution: Be careful not to slant LC connector while inserting into the Guide cap. Do not overly exert force during insertion as this may cause damage to both the connector and the cleaner.All in one cleanerLC ConnectorCapPart Number: FCCT - LThere are 3 basic principles that are critical to achieving an efficient fiber optic connection: 1. Perfect Core Alignment 2. Physical Contact3. Pristine Connector InterfaceToday’s connector design and production techniques have eliminated most of the challenges to achieving core alignment and physical contact. What remains challenging is maintaining a pristine end-face. As a result, CONTAMINATION is the #1 reason for troubleshooting optical networks.Implementing the process of cleaning and inspecting before mating can reduce the time spent troubleshooting, optimize signal performance and prevent damage.InspectingScan to view videoOVP IdentificationPart NumberDescriptionExcess Fiber StorageRC3DC-3315-PF-48*Distribution box with 6 Strikesorb modules 55 ft RC3DC-4750-PF-48*Distribution box with out Strikesorb modules55 ft RC3DC-1064-PF-48*Sector box with 2 Strikesorb modules45 ft RCMDC-2260-RM-48* 6 circuit rack mount OVPN/ANote: *Twisted Pair Alarm Conductors8 pair FiberColor coding (6 X 12 shown)Conductors Return Power Conductors12 pair FiberGroundingGround kits required at the top and bottombefore entering the shelter / cabinetGround Kit UG12158-15B4-T is a universalsolution for all HFF trunk cables.Only use Tin Plated grounding kitsRemoving Jacketing for Grounding Kit installation1. Score the jacketing 360º2. Measure 2 inches (51 mm) and repeat3. Identify where the aluminum shielding overlaps, this will feel like a flat spot in the cable4. With a knife flat on the cable remove a section of jacketing between score marks5. Lift edge of jacketing with knife tip6. Grab lifted edge of jacketing with a pair of pliers and roll on the cable7. Remove excess adhesive with a piece of emery clothScan to view videoExcess Cable ManagementIf length of cable installed needs to be adjusted you can split the cable at the BBU end using the process below and then coiling the excess fiber subunits in a storage box. Fiber management trays are available to manage any excess fiber length in the breakouts at the BBU.1. Mark cutback length2. Notch Armor using flush cutter in-line with Kevlarstrings3. Place Rip Cord in Notches'4.Pull Rip Cord Parallel to Cable (while supportingbreakout)5. Stop at Length Marker6. Separate Armor7. Cut Armor Using Side Cutter 8. Remove Water Blocking Tape9. Remove Excess Rip Cord 10. Apply Electrical Tape to Protect BreakoutExcess Fiber storage Box Part Number: FE-14126-EFiber management tray, Part Number:FE-14192-IRScan to view videoCable Splitter tool Part Number: FA-RCRT-PDNOTE:Remember to slide identifier labels down the power conductors before trimming the cable to it’s final lengthClick here for videoNotice: CommScope disclaims any liability or responsibility for the results of improper or unsafe installation, inspection, maintenance, or removal practices.Aviso: CommScope no acepta ninguna obligación ni responsabilidad como resultado de prácticas incorrectas o peligrosas de instalación, inspección, mantenimiento o retiro.Avis : CommScope décline toute responsabilité pour les conséquences de procédures d’installation, d’inspection, d’entretien ou de retrait incorrectes ou dangereuses.Hinweis: CommScope lehnt jede Haftung oder Verantwortung für Schäden ab, die aufgrund unsachgemäßer Installation, Überprüfung, Wartung oder Demontage auftreten.Atenção: A CommScope abdica do direito de toda responsabilidade pelos resultados de práticas inadequadas e sem segurança de instalação, inspeção, manutenção ou remoção.Avvertenza: CommScope declina eventuali responsabilità derivanti dell’esecuzione di procedure di installazione, ispezione, manutenzione e smontaggio improprie o poco sicure.CommScope 1100 CommScope Place SE P .O. Box 339, Hickory, NC 28603-0339(828) 324-2200 (800) /andrew Customer Service 24 hoursNorth America: +1-800-255-1479 (toll free)Any country: +1-779-435-6500email:**************************************Jumpers are properly support to prevent strain on fiber during severe weather Bend radius minimums haven't been exceededCommScope FiberFeed ® approved installation accessories are used Maximum hanger spacing of 0.9 m (3 ft) - 1.2 m (4 ft) is maintained Visually inspected end face for residual dirt and damageAvoid migration of contaminations from one connector to anotherCheck continuity by using LED or lazer light source from one end face and look for light from other end to identify any broken fiber (Do not look directly at cable with laser source)Fiber Connections are engaged and the sectors are consistent with requirementsCable serial number has been documented in the closeout paperwork and a copy has been left on-siteInstallation Check List。
The future we want –and decisions we needMaking headwayTime for change is hereUNEA – reconciling the needs ofpeople and planet The First United Nations Environment AssemblyUnited Nations Environment ProgrammeT able of ContentsPage 12Angela MerkelThe future we want–and decisions we need Page 6Ban Ki-moonUNEA – reconciling the needs ofpeople and planetFeaturesPage 14Zhou ShengxianFacing environmental challenges–promoting green solutionsPage 8Michelle Bachelet Jeria Time for change is here Page 22Michael Bloomberg Making headwayPage 34Paul Polman Step change in ambitionPage 28Pekka Haavisto Stronger UNEP forstronger post-2015 goalsPage 24Juan José Guerra Abud Challenge aheadReflections IPCC Bacteria in soil The road to UNEA World Environment Day Car manufacturer goes solar PublicationsRegional Seas Programme Making trash a home Goodwill ambassadorsPage 4Page 10Page 18Page 20Page 30Page 32Page 36Page 42Page 54Page 56Page 38Rachel KyteBreak from the pastPage 48Mary Robinson Opening a worldof opportunityPage 44Trevor ManuelJosé María Figueres David Miliband Reckoning on thehigh seas Page 52Ashok KhoslaErnst Ulrich von Weizsäcker Sustaining ourresources – by choice or by chance?.Page 50Carlos López Powering Africa’s industrialization andagricultural revolution withrenewable energiesAchim Steiner: ReflectionsAchim SteinerUN Under- Secretary-General and UN Environment Programme ExecutiveDirectordetermine policy and catalyse internationalaction, UNEA represents th e world’s pol-icy forum and th e new global environmentalauthority.At this first UNEA, fittingly meeting in Nairobi,th e h ome of UNEP, ministers responsible forth e environment, benefitting from contribu-tions from civil society and other stakeholders,will start providing the design and architecturefor th e next ch apter of th e environment pro-gramme of th e United Nations and inputs toimportant global policy ch allenges. Th is willhappen in a new configuration, with all memberstates of the United Nations being representedin the Assembly – the most significant changeto UNEP and international environmentalgovernance in the UN since its creation at theStockholm conference of 1972.But UNEA is about much more th an anenlarged governing council. Th is new body is inaugural meeting of th e UnitedNations Environment Assembly (UNEA)is a truly historic event. It is the culminationof more than four decades of ground-breakingwork by UNEP to tackle and provide responsesto the environmental challenges of our age andplaces these firmly at the centre of the broaderjourney towards sustainable development.UNEP h as indeed come a long way since th etimes wh en th e environmental agenda wasfrequently ch aracterized as th e “preoccupa-tion of the few at the expense of the many” or“th e luxury of th e rich at th e expense of th epoor”. In June 2012, at Rio+20 – held exactly20 years after th e transformative Rio EarthSummit – world leaders provided for UNEP’sstrengthening and upgrading and it is in thiscontext that UNEA has been designed to takeus furth er along th at road, to a world wh ereseven billion people can live with dignity andin h armony withour planet. Mandated toT4Mandated to determine policy and catalyse international action, UNEA represents the world’s policy forum and the new global environmental authority.bestows a new level of legitimacy and author-ity on the decisions that will be taken, which in turn can translate into a more effective service that UNEP and the UN family can pro-vide to th e international community and to ministers responsible for the environment.At i ts f irst session, UNEA is expected to provide leadership on global environmental policy and to continue to keep th e world environment under review, a mandate first conferred upon UNEP’s Governing Council by the 1972 United Nations General Assembly resolution 2997 and subsequently enhanced through Rio+20’s outcome, The Future We Want.One of th e main th emes of UNEA’s first ses-sion will be “Sustainable Development Goals (SDGs) and t h e Post-2015 Development Agenda, including sustainable consumption and production”. Ministers will also have the opportunity to address th e illegal trade in wildlife, a complex, multi-faceted issue that isgenerating increasing global attention givenits alarming scale and its global inter-linkagesand implications.UNEA will additionally provide a forum forexamining crucial processes in environmen-tal action such as the science-policy interfaceand th e strength ened engagement of majorgroups and other key stakeholders as well asa dedicated gender forum.A set of unprecedented symposia will alsobe organized on th is h istoric occasion tobroaden the scope for key actors in the sus-tainable development arena to participate inUNEA. A symposium on the EnvironmentalRule of Law will bring togeth er lawmakersand decision makers, along with key civilsociety organizations in lively debates onrecent developments linked to internationalenvironmental governance.Th e second symposium will focus on th equestions of h ow th e global finance systemcan contribute to th e green economy andwh at makes th e green economy work forth e financial systems. It will bring togeth erprofessionals of th e finance sector, pol-icy makers and environmental economistswith th e expectation to identify opportuni-ties and bottlenecks for green, sustainableinvestments.For th e UN system, th e United NationsEnvironment Assembly of UNEP embodiesthe notion that challenges are best addressedand opportunities realized wh en th e com-munity of nations and citizens of th e worldjoin forces to promote economic prosperity,social equity, and environmental sustainabil-ity in a holistic manner. ▲5e h ave come a long way since th e UN General Assembly established UNEP in the wake of the 1972UN Conference on the Human Environment in Stockholm. Four decades of growing awareness backed by science have eroded th e once widespread belief th at environmental concerns are secondary to economic development. Th e principle of common but differentiated responsibility h as established that wealthy nations should bear the burden of repairing historic environmental ills, but recognizes that all governments have a role in environmental stewardship. We are now ready to embark on the crucial next phase of human development – a universal post-2015 sustainable develop-ment agenda that reconciles the needs of people and planet.Today, th ere is common acceptance among governments that a healthy environment is necessary for eradicating pov-erty and supporting equitable economic growth and social progress. That is why the 2012 Rio+20 UN Conference on Sustainable Development agreed to strength en UNEP as the leading global environmental authority by establishing universal membership in its Governing Council. The United Nations Environmental Assembly (UNEA) represents a coming-of-age for UNEP and its governing body. For th e first time, all 193 United Nations member states are repre-sented along with major stakeholders. The message is clear: protecting humanity’s life support system is a duty for all, for the benefit of all.With its augmented role as a subsidiary of the UN General Assembly, UNEA h as th e mandate and capacity to posi-tion the environment within the sustainable development debate alongside peace and security, poverty reduction, global health, trade and sustainable economic growth as an issue of crucial importance to every government. As of this year, UNEP is better placed than ever to help governments and other key actors incorporate the environment into the mainstream of all policymaking.The timing could not be better. Next year marks the dead-line for the Millennium Development Goals; it is when we will launch a post-2015 sustainable development agenda; and it is when member states have pledged to sign a mean-ingful new global climate agreement. The decisions that will be made over the coming months will have profound rami-fications for this generation and many to come. UNEP and UNEA have a central role to play – beginning now.Th is first session of UNEA will address some weigh ty and contentious issues. Th e formulation of Sustainable Development Goals with th e core purpose of eradicating extreme poverty and improving h uman well-being acrossth e board must h ave a solid environmental dimension. Yet policies must also factor in many other considerations. The closely interlinked global financial system is a source of great opportunity but also risk, as we have seen through a series of food, fuel and financial crises. UNEA will bring togeth er policy-makers, economists, financiers and civil society groups to examine how green economy principles can help in designing a more sustainable and equitable system.Ban Ki-moon:UNEA – reconciling the needs ofpeople and planetWBan Ki-moonSecretary-General of the United NationsUNEA shows how far we have come: all governments have a role in environmental stewardship.6The decisions that will be made over the coming months will have profound ramifications for this generation and many to come. UNEP and the UNEA have a central role to play – beginning now.Th e illegal trade in wildlife will provide th e focus for anoth er symposium. Only international cooperation and multilateral agreement can prevail against wildlife crime, wh ich th reatens so many of our endangered species and ecosystems, to the ultimate detriment of local communities and national governments. UNEA will also provide a forum for member states to advance environmental governance through the Rule of Law by facilitating knowledge exchange and formulating policy. Th e responsibilities of th is new body are considerable. Under UNEA’s stewardsh ip, UNEP should now finally have the resources to match its mission to carry the environmental message of the United Nations with clarity, authority and vigour to all countries and sectors of society. Development cannot be sustainable with out its environmental dimension. Th e institutional framework h as been establish ed. Wh at remains is for all 193 member states and th eir multi-stakeh older partners to seize th is opportunity by acting decisively to transform h umanity’s relationship with our planet. ▲7ext year will be a decisive year for sustainable devel-opment. First, we h ave a concrete opportunity to advance towards a global sustainable development agenda under the Sustainable Development Goals set by Rio+20. Second, it is imperative to reach a binding, ambitious agreement on climate change.About 15 years ago, we set the Millennium Development Goals, which served as guidelines for countries struggling to eradicate poverty and improve th e standard of living in the developing world. Although some goals are still to be accomplished, we learnt that in order to combat pov-erty more efficiently we need to incorporate development considerations.Experience h as sh own th at rapid progress in a world showing significant weaknesses in some areas may impact negatively. For example, countries with h igh economic growth sustained h ealth crises due to pollution or social conflicts arising from differences in income. In this regard, failure to match progress in different areas may h inder development itself since costs deriving from environmental degradation or social inequality impair ach ievements in economic growth.A development agenda incorporating social, environmen-tal and economic dimensions not only bridges the gap in the Millennium Development Goals, but also ensures more comprehensive well-being for society as it favours the cre-ation of decent jobs, equal access to opportunities and a healthier environment.Ch ile is a good example. In past decades, our country quadrupled per capita income, reduced poverty, consol-idated democratic institutions and gained a reputation as an emerging country with an open market economy and macroeconomic soundness. However, in order to maintain development, it is crucial to reduce economic inequality and increase the economy’s sustainability. At present this depends primarily on the exploitation of raw materials.We are a small, narrow country extending for 4,000 km between th e Pacific Ocean and th e Andean Mountains, with diverse geograph y, climates, soils and ecosystems, particularly vulnerable to climate ch ange. Indeed, gla-ciers – which feed our rivers, lakes, wetlands, aquifers and underground reservoirs and supply water to th e popula-tion – are receding.In addition, temperate valleys – the cradle of our renowned Chilean wine – are increasingly threatened by desertifica-tion. To think that these issues are just local is a mistake.NMichelle Bachelet:Time forchange is hereMichelle BacheletPresident of ChileSustainability is not only a requirement for economic development, but also a condition for peace and international security.8Consequently, sustainability is not only a requirement for economic development, but also a condition of social peace and international security. In th e case of Ch ilean glaciers, th ey must be treated as a global water reserve, since th eir disappearance or retreat will h ave a global impact.Th is commonality demands a global political agreement uniting all of us and requiring an increased commitment by present – and past – stakeholders responsible for factors leading to climate change. Scientific evidence collected is eloquent: we cannot continue to defer a solution. We are now at a critical scenario for each and every nation, which will make realpolitik – where each country sees to its own interests – obsolete.Chile undertakes this commitment with the international community by setting an ambitious emission control goal. Therefore, we hope that high-polluting countries will notattempt to define a set of goals and their indicators, whilst facing up to the challenges posed by integrated and inte-grating development, and tailored to the particular needs of each country or region. These goals should allow us to measure advances and shortcomings and mobilize inter-national cooperation. This will force us, as leaders, to focus our efforts on designing and laying the foundations of com-mon goals contributing to an inclusive, environmentally friendly growth.Great results are obtained by leaders with ambition and ch allenging visions. We are now at th e crossroads. We need to have integrated development, which incorporates neglected populations and diversity. This will protect and maintain the natural base on which our lives, coexistence and future depend. The evidence is on the table. As lead-ers, we are now compelled to seek solutions demanded by the international community. ▲The scientific evidence collected is eloquent: we cannot continue to defer a solution. We are now at a critical scenario for each and every nation.On the contrary, sustainability issues are of global impor-tance. Chile has 75 per cent of the total area of glaciers in South America, making it a country rich in an ever-shrink-ing resource. According to estimates, by 2050 water demand will have increased by 50 per cent in developing countries and 18 per cent in developed countries. P h o t o : S h u t t e r s t o c kBy 2050 water demand will have increased by 50% in developing countries and 18% in developedcountries.only assume their responsibility, but will also play a lead-ing role in managing wh at will be a difficult process, but wh ich will lead towards a global agreement. Let us not forget th at global ch ange will impact h arder on th e most vulnerable communities. Th e Sustainable Development Goals afford us an opportunity to make progress. We willP h o t o : S h u t t e r s t o c khat do we, the human race, see as the future we want? What can and what must we do today to ensure thatwe really are moving in the right direction? These questions are relevant to all of us, in all regions of the world. We all want peace, security and prosperity – today and tomorrow. That, however, requires a fundamental rethink, because we cannot live and work as if the resources of our environment are inexhaustible. Planetary boundaries exist and we cannot exceed th em if we want to avoid diminish ing th e resources younger and future generations need to live their lives.Only recently, th e Intergovernmental Panel on Climate Ch ange (IPCC) reiterated just h ow vulnerable h umans and nature are to th e effects of unch ecked climate ch ange.Therefore we must finally make the shift to climate-friendly development, something that is in fact very compatible with increasing prosperity. It is not a question of limiting economic development in the poorest regions of the world. On the con-trary, many new development prospects need to be opened up to them. This can succeed if around the world we learn how to generate prosperity differently from how we do today. Despite all the encouraging progress of recent years, around 1.3 billion people worldwide still suffer abject poverty. In view of this, it is very tempting to strive solely for quantita-tive growth whilst disregarding the limits set by nature in terms of water, land, raw materials and biodiversity. Yet an increasing depletion of resources vital for people’s liveli-hoods would inevitably undermine long-term development prospects, exacerbate hunger and poverty and, as a result of this, increase the risk of conflicts. Security and stability, on the other hand, are vital prerequisites for developing suc-cessful economies.Th e relationsh ip between economic performance and th e protection of th e natural resource base is symbiotic. Th erefore we cannot avoid th inking about th em togeth er and indeed bringing them together. The key is sustainable development. Th e international community reiterated its commitment to this at the 2012 United Nations Conference on Sustainable Development in Rio de Janeiro. We agree th at our existing economy needs to be developed into a “green economy”. This means above all investing in renew-able energy, boosting resource efficiency in production andconsumption and establish ing effective instruments for th e protection and sustainable management of forests and oceans. For th is, we need strong and capable international orga-nizations and so it was very important th at Rio 2012 succeeded in boosting UNEP’s clout as a voice of interna-tional environmental protection, thus enabling it to make itself permanently heard. The establishment of the United Nations Environment Assembly (UNEA) is a visible sign of this enhanced status. For the first time, all 193 members ofAngela Merkel: The future we want – and the decisions we needWAngela MerkelChancellor of theFederalRepublic of GermanyThe future we all want requires afundamental rethink of how we live and work.We need strong and capable international organizationsand so it was very important that Rio 2012 succeeded in boosting UNEP’s clout as a voice of international environmental protection.the United Nations will debate and make decisions on global challenges together. I see this as a great opportunity for us to reach a joint consensual understanding on what needs to be done in the coming years and on how it can be achieved.Experience h as sh own us th at we make th e best progress in sustainable development wh en we define clear and universally valid rules. An impressive example of th is is th e 1987 Montreal Protocol on Substances th at Deplete the Ozone Layer. For instance, until the 90s it was normal for ozone-damaging CFCs to be used in fridges. Since then the global production and use of such chemicals has beenreduced by 97 per cent. Th is determined action is now bearing fruit, as th e latest research sh ows th at th e ozone layer is slowly starting to recover. Here in Germany and also amongst EU member states we take this very seriously. This is evident, for instance, in three national targets that we aim to meet by 2050. By then, we want to reduce our greenh ouse gas emissions by 80 to 95 per cent compared to 1990 levels. We want 80 per cent of ourelectricity to come from renewable energy – above all wind and solar – and we want to reduce our primary energy con-sumption by 50 per cent. Germany’s shift to green energy will show that it is not only possible but indeed economi-cally beneficial to decouple economic growth from energy consumption. 2015 will be an important year in setting the course for the future, with th e UN Climate Ch ange Conference in Paris and the UN summit on the Post-2015 Development Agendain New York. Germany is working to facilitate the adoption of a legally binding climate change agreement, with the par-ticipation of all states, which would enter into force in 2020. In our view, it must include ambitious goals, fair rules for more transparency, sh ould initiate cooperation between industrial and developing countries and boost investment in climate protection in all parts of the world whilst at the same time taking into consideration legitimate interests when it comes to adaptation and the protection against risk.We are also striving to incorporate ambitious goals th at apply to all states into the Post-2015 Development Agenda. Each country will be responsible for implementing the goals but support will be available in th e form of international monitoring. I consider there to be four main strategic areas – eradicating extreme poverty and h unger, preserving th e natural resource base and ensuring its sustainable use, thecreation of decent jobs and adequate income through eco-logically sound growth, and good governance. Shared goals are contingent upon joint understanding for sustainable development. Germany th erefore supports a new global partnership as proposed last year by the high-level panel of eminent persons on th e Post-2015 Development Agenda. Such a partnership must involve business, science and soci-ety in equal measure.A path of sustainable development th at benefits everyone requires us to go the extra mile time and again and to thinknot only about what is happening today, but also about what tomorrow will bring. If we succeed in doing this then I amsure we will succeed in building the future we want. ▲A furth er example is th e Nagoya Protocol on Access and Benefit Sh aring, wh ich regulates access to genetic resources, such as medicinal plants, and aims to fairly and equitably share the benefits of their use between countries of origin and countries utilizing th ese resources. It also provides economic incentives to preserve biodiversity in countries of origin. Generally funding is a key factor in the global protection of biodiversity. That is why Germany is standing by its pledge to make an annual sum of 500 millioneuros available for this.Joint action in no way diminishes national and local obli-gations, everyone must assume responsibility to the extent that their circumstances permit.In 2050 we want 80% ofour electricity to come from renewable energy – above all wind and solar.uman society h as been ch allenged by overpopula-tion, unbalanced development, resource depletion, and environmental degradation, wh ile creating unprec-edented material wealth since the industrial revolution. For th is consideration, th e international community has been seeking a global solution to environmental and development issues, from the United Nations Conference on the Human Environment in Stockholm to Rio+20 and from the Declaration on the Human Environment to The Future We Want.China, the world's largest developing country, is also expe-riencing unprecedented environmental ch allenges during its fast economic expansion. Environmental issues th at occurred in developed countries during industrialization over 100–200 years h ave exposed th emselves in Ch ina in 30 years and sh ow remarkable structural, compres-sion, and complex features. New environmental issues become increasingly prominent before old ones are solved. Generally, the country faces more complex and difficult envi-ronmental issues than any other in the world.As a responsible country, Ch ina h as always followed th e national strategy of sustainable development. It h as inte-grated into its development, ecological, economic, political, social, and cultural aspects, which envision a beautiful coun-try. Ecological civilization philosophy and strategy is a major achievement of the Chinese Government and responds cre-atively to th e relationsh ip between economic development and environmental issues, and also th e localization and escalation of sustainable development. To push ahead with ecological progress, the Chinese Prime Minister highlighted in the Government Work Report this year that the Chinese Government will resolutely declare war against pollution and fight it with the same determination as it battles poverty.In China, the newly revised Environmental Protection Law marks a milestone in environmental protection with its adoption by the legislature on April 24, 2014. It maximizes the cohesion and absorption of consensus in all aspects and breaks th rough difficulties in promoting th e green devel-opment model based on environmental carrying capacity and promoting th e modern multi-party environmental governance system. For example, th e law clearly defines th e concepts of ecological civilization construction and sustainable development, and requires th e establish ment of environmental and public h ealth monitoring and eval-uation system and the rights of citizens to have access to environmental information, participation and supervi-sion. Meanwh ile, to address outstanding environmental problems threatening human health and improve environ-mental quality as soon as possible, the Chinese GovernmentHZhouShengxian:Facing environmental challenges – promotinggreen solutionsZhou ShengxianMinister of Environmental Protection, People’s Republic of ChinaIn a shorter time frame, China has experienced similar unprecedentedenvironmental challenges as the rest of the world.directs attention to air, water and soil pollution prevention and control in the "resolute war against pollution". It has formulated and implemented in depth the Action Plan for th e Prevention and Control of Air Pollution and is step-ping up th e preparation of Clean Water Action Plan and th e Action Plan for th e Prevention and Control of Soil Pollution, which highlight the firm determination to con-trol pollution, improve environmental quality, and protect the health of the people.Looking back, th e international community h as exerted massive efforts to address environmental issues, but except for a few cases, the overall situation is deteriorating. Biodiversity loss, climate ch ange, water crises, ch emical pollution, and land degradation have not been effectively resolved. In most developing countries, the deterioration of environmental quality is exacerbated by population expan-sion, industrialization, and urbanization, as well as transfer of pollution from developed countries, adding difficulty in control.Looking ahead, we expect a green and prosperous world that is free from excessive requests and ravages of humans and strikes a harmonious balance between economic, social and environmental development. It sh ould be our long-term vision to face environmental challenges and promote green development. It necessitates a sound system for interna-tional environmental governance with the concerted efforts。
SIAM J.M ATH.A NAL .c 2013Society for Industrial and Applied Mathematics Vol.45,No.2,pp.547–571GLOBAL SOLUTIONS TO THE ONE-DIMENSIONAL COMPRESSIBLE NA VIER–STOKES–POISSON EQUATIONS WITH LARGE DATA ∗ZHONG TAN †,TONG YANG ‡,HUIJIANG ZHAO §,AND QINGYANG ZOU ¶Abstract.In this paper,we study the global solutions with large data away from vacuum to the Cauchy problem of the one-dimensional compressible Navier–Stokes–Poisson system with density-dependent viscosity coefficient and density-and temperature-dependent heat-conductivity coefficient.The proof is based on some detailed analysis on the bounds on the density and temper-ature functions.Key words.Navier–Stokes–Poisson equations,global solutions with large data,viscosity and heat-conductivity coefficients AMS subject classifications.35Q35,35D35,76D05DOI.10.1137/1208761741.Introduction.The compressible Navier–Stokes–Poisson (NSP)system con-sisting of the compressible Navier–Stokes equations coupled with the Poisson equation models the viscous fluid under the influence of the self-induced electric force:⎧⎪⎪⎪⎨⎪⎪⎪⎩ρτ+∇ξ·(ρu )=0,(ρu )τ+∇ξ·(ρu ⊗u )+∇ξp =ρ∇ξΦ+∇ξ·T ,(ρE )τ+∇ξ·(ρu E +up )=ρu ·∇ξΦ+∇ξ·(u T )+∇ξ·(κ(v,θ)∇ξθ),ΔξΦ=ρ−ρ(ξ),lim |ξ|→+∞Φ(τ,ξ)=0.Here,ρ>0,u =(u 1,u 2,u 3),θ>0,p =p (ρ,θ),e ,and Φdenote the density,ve-locity,absolute temperature,pressure,internal energy,and the electrostatic potential function,respectively.Also the total energy E =12|u |2+e and the stress tensor T =μ(ρ,θ)(∇ξu +(∇ξu )t )+ν(ρ,θ)(∇ξ·u )I with I being the identity matrix.The viscosity coefficients μ(ρ,θ)>0and ν(ρ,θ)satisfy μ(ρ,θ)+23ν(ρ,θ)>0.The ther-modynamic variables p ,ρ,and e are related by Gibbs equation de =θds −pdρ−1with s being the specific entropy.κ(ρ,θ)>0denotes the heat-conductivity coefficient and ρ(ξ)>0is the background doping profile;see [30].To explain the purpose of this paper,we first give the following remarks on the viscosity and heat-conductivity coefficients:∗Received by the editors May 7,2012;accepted for publication November 7,2012;published electronically March 14,2013./journals/sima/45-2/87617.html †School of Mathematical Sciences,Xiamen University,Xiamen 361005,Fujian,China (tan85@).The first author was supported by the grant from the National Natural Science Foundation of China under contract 10976026.‡Department of Mathematics,City University of Hong Kong,Kowloon,Hong Kong,China (matyang@.hk).The second author was supported by the General Research Fund of Hong Kong,CityU 104310and the Croucher Foundation.§Corresponding author:School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China (zgyheda@).The third author was supported by two grants from the National Natural Science Foundation of China under contracts 10925103and 11271160.This work was also supported by the Fundamental Research Funds for the Central Universities.¶School of Mathematics and Statistics,Wuhan University,Wuhan 430072,China (qy zou@).This work was also supported by the Fundamental Research Funds for the Central Universities.547D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h p548Z.TAN,T.YANG,H.ZHAO,AND Q.ZOU •When the viscosity coefficients μ(ρ,θ)>0,ν(ρ,θ),and the heat-conductivity coefficient κ(ρ,θ)>0are constants,(1.1)is used in semiconductor theory tomodel the transport of charged particles under the influence of self-induced electric field;see [30].•In the kinetic theory,the time evolution of the particle distribution func-tion for the charged particles in a dilute gas can be modeled by the Vlasov–Poisson–Boltzmann system;see [4],[3],[34].When we derive the NSP (1.1)from the Vlasov–Poisson–Boltzmann system by using the Chapman–Enskog expansion,see [4],[12],[34],the viscosity coefficients μ,ν,and the heat-conductivity coefficient κdepend on the absolute temperature θand ν=−23μfor the monatomic gas.If the intermolecular potential is proportional to r −αwith α>1,where r represents the intermolecular distance,then μ,ν,and κare proportional to the temperature to some power:μ,−ν,κ∝θα+42α.In particular,for the Maxwellian molecule (α=4),such dependence is lin-ear,while for the hard sphere model and alsothe case when α→+∞,the dependence is in the form of √θ.This paper is concerned with the global existence oflarge-data solutions when the viscosity coefficients μ,ν,and the heat-conductivity coefficient κdepend on ρand θ.Unlike the small perturbation solutions,such dependence has a strong influence on the solution behavior and thus leads to difficulties in analysis but not for the case of constant coefficients.In fact,for the one-dimensional compressible Navier–Stokes equations,there are a lot of recent papers on the construction of nonvacuum solutions to the one-dimensional compressible Navier–Stokes equations with density-and temperature-dependent transportation coefficients in various forms;see [1],[5],[18],[19],[21],[22],[23],[24],[25],and the references therein.However,there is a gap between the physical models and the satisfactory existence theory.The main purpose of this paper is the construction of globally smooth,non-vacuum solutions to the one-dimensional nonisentropic compressible NSP with density dependent viscous coefficient and density-and temperature-dependent heat-conducti-vity coefficient for arbitrarily large data.We hope that the analysis here can shed some light on the construction of global classical solutions to the fluid model derived from the Vlasov–Poisson–Boltzmann system with large data.Let x be the Lagrangian space variable,t be the time variable,and v =1ρdenote the specific volume.Then the one-dimensional compressible NSP system (1.1)with viscous coefficient μ(v )and heat-conductivity coefficient κ(v,θ)becomes⎧⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎩v t −u x =0,u t +p (v,θ)x = μ(v )u x v x +Φx v ,e t +p (v,θ)u x =μ(v )u 2x v + κ(v,θ)θx v x , Φx v x =1−v,lim |x |→+∞Φ(t,x )=0.(1.1)Throughout this paper,we will concentrate on the ideal,polytropic gases:(1.2)p (v,θ)=Rθv =Av −γexp γ−1R s ,e =C v θ=Rθγ−1,D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h pCOMPRESSIBLE NAVIER–STOKES–POISSON EQUATIONS 549where the specific gas constant R and the specific heat at constant volume C v arepositive constants and γ>1is the adiabatic constant.Moreover,to simplify the presentation,we will only consider the case when the background doping profile ρis a positive constant which is normalized to 1as in (1.1)4.Take the initial data (v (0,x ),u (0,x ),θ(0,x ))=(v 0(x ),u 0(x ),θ0(x )),(1.3)lim x →±∞(v 0(x ),u 0(x ),θ0(x ))=(v ±,u ±,θ±),satisfying v −=v +,u −=u +,θ−=θ+.Without loss of generality,we assume v −=v +=1,u −=u +=0,θ−=θ+=1.The first result is concerned with the case (1.4)μ(v )=v −a ,κ(v,θ)=θb ,which is stated as follows.Theorem 1.1.Suppose•(v 0(x )−1,u 0(x ),θ0(x )−1,Φ0x (x ))∈H 1(R ),and there exist positive constants V ,V ,Θ,Θsuch that (1.5)V ≤v 0(x )≤V ,Θ≤θ0(x )≤Θ;•13<a <12;•b satisfies one of the following conditions:(i)1≤b <2a 1−a ,(ii)0<b <1,2−b 2+(a 2−a +2)(1−b )(1−2a )(3a −1)<1,(1−b )(3+a −2a 2)(3a −1)(1−2a )<1.Then the Cauchy problem (1.1),(1.3)with μ(v )and κ(v,θ)given by (1.4)admits aunique global solution (v (t,x ),u (t,x ),θ(t,x ))satisfying (1.6)(v (t,x )−1,u (t,x ),θ(t,x )−1)∈C 0 0,T ;H 1(R ) ,(u x (t,x ),θx (t,x ))∈L 2 0,T ;H 1(R ) ,Φx (t,x )∈C 0 0,T ;H 2(R ) ,0<V −10≤v (t,x )≤V 0,0<Θ−10≤θ(t,x )≤Θ0∀(t,x )∈[0,T ]×R .Here T >0is any given positive constant and V 0,Θ0are some positive constants which may depend on T .Note that the assumptions imposed on a and b in Theorem 1.1exclude the casewhen the viscous coefficient μand the heat-conductivity coefficient κare positive constants.The next result will recover this in another setting.The main idea is to use the smallness of γ−1to deduce uniform lower and upper bounds on the absolute temperature.This can be achieved by showing that (v 0(x )−1,u 0(x ),s 0(x )−s )∈H 1(R )are bounded in H 1(R )independent of γ−1so that θ0(x )−1 L ∞(R )can bechosen to be small when γis close to 1.Here s =R γ−1ln R A is the far field of the initial entropy s 0(x ),that is,lim |x |→+∞s 0(x )=lim |x |→+∞R γ−1ln Rθ0(x )v 0(x )γ−1A=s.Taking (v,u,s )as the unknown functions,the second global existence theorem canbe stated as follows.D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h p550Z.TAN,T.YANG,H.ZHAO,AND Q.ZOU Theorem 1.2.Suppose we ahve the following:• (v 0(x )−1,u 0(x ),s 0(x )−s,Φ0x (x )) H 1(R )is bounded by some positive con-stant independent of γ−1and (1.5)holds for some (γ−1)-independent positive constants V ,V ,Θ,Θ.•(γ−1) s 0(x ) L ∞(R )is bounded by some constant independent of γ−1.•The smooth function μ(v )satisfies μ(v )>0for all v >0and(1.7)lim v →0+Ψ(v )=−∞,lim v →+∞Ψ(v )=+∞.Here,(1.8)Ψ(v )= v 1√z −ln z −1z μ(z )dz.•For the heat-conductivity coefficient,there are two cases.If κ(v,θ)=κ(θ)depends only on θ,we only assume κ(θ)>0for θ>0with some smoothnesscondition.If it depends on both v and θ,thenin addition to κ(v,θ)>0for all v >0,θ>0,we also assume the following.Set κ1(v )=min Θ≤θ≤Θκ(v,θ)and assume (1.9)κθθ(v,θ)<0∀v >0,θ>0and (1.10)lim v →0+μ(v )κ1(v )|Ψ(v )|2=lim v →+∞μ(v )κ1(v )|Ψ(v )|2=0.•γ−1is sufficiently small.Then the Cauchy problem (1.1),(1.3)admits a unique global solution (v (t,x ),u (t,x ),θ(t,x ))satisfying (1.6)and (1.11)lim t →+∞sup x ∈R (v (t,x )−1,u (t,x ),θ(t,x )−1) =0.Remark 1.1.We give the following remarks on Theorems 1.1and 1.2.•From the proof of Theorem 1.2,one will notice that the assumption (1.10)can be replaced by the following weaker assumption:(1.12)lim v →0+μ(v )κ1(v )|Ψ(v )|2≤ε0,lim v →+∞μ(v )κ1(v )|Ψ(v )|2≤ε0.Here ε0>0is a suitably chosen sufficiently small positive constant.•Under the assumptions in Theorem 1.2,when γ−1is sufficiently small,although θ0−1 H 1(R )is small, (v 0−1,u 0,s 0−s ) H 1(R )can be large.•When μ(v )satisfies certain growth conditions when v →0+and v →+∞,for example,μ(v )∼v a as v →0+and μ(v )∼v b as v →+∞with a <0,b >−12,then a similar result to Theorem 1.2also holds even when (v 0−1,u 0,s 0−s ) H 1(R ),V ,and V depend on 1γ−1with certaingrowth conditions as γ→1+.•The same arguments for Theorems 1.1and 1.2can be applied directly to the compressible Navier–Stokes equations which generalize the previous re-sults [18]and [23],where the viscosity coefficient is assumed to be a positiveconstant.D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h pCOMPRESSIBLE NAVIER–STOKES–POISSON EQUATIONS 551•It is worth pointing out that since (1.13) μ(v )u x v x = μ(v )v t v x = μ(v )v x v t plays an important role in the following analysis,we can only treat the case when μ(v )is a smooth function of v .Hence,it is interesting to study the case when μdepends on θ.We now review some related results.First,there are some recent results on the construction of nonvacuum,large solutions to the one-dimensional compress-ible Navier–Stokes equations with constant viscosity coefficient μand density-and temperature-dependent heat-conductivity coefficient κ;see [18],[23].A key ingredi-ent in these works is the pointwise a priori estimates on the specific volume which guarantees that no vacuum or concentration of mass occurs.This together with the standard maximum principle deduce a lower-bound estimate on the absolute tempera-ture θ(t,x )and,consequently,the main effort in [18],[23]is to obtain the upper-boundestimate on θ(t,x ).The strategy to prove Theoerem 1.1can be stated as follows.We note that,however,for the compressible NSP system (1.1),even when the viscosity coefficient μ(v )is a positive constant,the argument in [25]does not give bounds on v (t,x )because of the nonlocal term Φx v .For this,to prove Theorem 1.1,we will first apply the maximum principle for second-order parabolic equations to obtain a lower-bound estimate on θ(t,x )in terms of the lower bound on v (t,x )in Lemma 2.4.And thenby combining the arguments used in [21]and [25],we can deduce a lower bound and an upper bound on v (t,x )in terms of θ1−b L ∞([0,T ]×R ),that is,the estimates (2.35)and (2.36).These two estimates together with the L ∞([0,T ]×R )estimate on θ(t,x )given in Lemma 2.9then yield the desired lower and upper bound on v (t,x )and θ(t,x )provided that the parameters a and b satisfy certain conditions.To prove Theorem 1.2,the main idea is to assume the following a priori assumption on the absolute temperature θ(t,x ):(1.14)12Θ≤θ(t,x )≤2Θfor (t,x )∈[0,T ]×R .Then by some delicate energy-type estimates and by using the argument initiated in [21],we can deduce a uniform (with respect to the time variable t )lower and upper bound on v (t,x )and some uniform-energy estimates on v −1,u,(θ−1)/√γ−1 (t ) H 1(R )in terms of v 0−1,u 0,(θ0−1)/√γ−1 H 1(R ),inf x ∈R v 0(x ),and sup x ∈R v 0(x ).At the end,to extend the solution globally in time,we only need to close the a priori assumption (1.14)where we need the smallness of γ−1.Before concluding the introduction,we point out that there are many results on the construction of global solutions to the NSP system (1.1).In particular,the global existence of smooth small perturbative solutions away from vacuum with the optimal time-decay estimates was recently obtained in [26]for the isentropic flow,and in [37],[16]for the nonisentropic flow.There,it is observed that the electric field affects the large time behavior of the solution so that the momentum decays at the rate (1+t )−14which is slower than the rate (1+t )−34for the compressible Navier–Stokes system,while the density tends to its asymptotic state at the rate (1+t )−34just like the compressible Navier–Stokes system.Moreover,the global existence of a strong solution in Besov-type space was obtained in [15].On the other hand,it is D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h p552Z.TAN,T.YANG,H.ZHAO,AND Q.ZOU quite different for the compressible Euler–Poisson system.In fact,it was shown in [14]that the long time convergence rate of the global irrotational solution is enhanced by the dispersion effect due to the coupling of the electric field,namely,both density and velocity tend to the equilibrium constant state at the rate (1+t )−p for any p ∈(1,32).Note that even though most of the results for the small perturbative solutions are considered for the case when μ,ν,and κare constants,it is straightforward to show that they hold when μ,ν,and κare smooth functions of density and temperature.Finally,for the results with large initial data,the existence of renormalized solu-tions to the NSP system are obtained in [6],[33],[38].Note that for the compressible NSP system related to the dynamics of self-gravitating gases in stars,some existence results on the weak solution (renormalized solution)were given in [8],[9],[38].Since the analysis in these works is based on the weak-convergence argument,only isen-tropic polytropic gas was studied with a special requirement on the range of adiabatic exponent,i.e.,γ>32with constant viscosity coefficient.For the nonisentropic case,even for the compressible Navier–Stokes system,the only available global existence theory for large data is the construction of the so called “variational solution”;see [11].The rest of the paper is organized as follows.The proofs of Theorems 1.1and 1.2will be given in sections 2and 3,respectively.Notations.O(1)or C i (i ∈N )stands for a generic positive constant which is independent of t and x ,while C i (·,···,·)(i ∈N )is used to denote some positive constant depending on the arguments listed in the parenthesis.Note that all these constants may vary from line to line. · s represents the norm in H s (R )with · = · 0and for 1≤p ≤+∞,L p (R )denotes the standard Lebesgue space.2.The proof of Theorem 1.1.To prove Theorem 1.1,we first define the following function space for the solution to the Cauchy problem (1.1),(1.3):X (0,T ;M 0,M 1;N 0,N 1)(2.1)=⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩(v,u,θ,Φ)(t,x ) (v −1,u,θ−1)(t,x )∈C 0 0,T ;H 1(R ) (u x ,θx )(t,x )∈L 2 0,T ;H 1(R ) Φx (t,x )∈C 0 0,T ;H 2(R ) M 0≤v (t,x )≤M 1,N 0≤θ(t,x )≤N 1⎫⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎭.Here T >0,M 1≥M 0>0,N 1≥N 0>0are some positive constants.Under the assumptions given in either Theorems 1.1or 1.2,we can get the fol-lowing local existence result.Lemma 2.1(local existence ).Under the assumptions in either Theorems 1.1or 1.2,there exists a sufficiently small positive constant t 1,which depends only on V ,V ,Θ,Θ,and (v 0−1,u 0,θ0−1) 1,such that the Cauchy problem (1.1),(1.3)admits a unique smooth solution (v (t,x ),u (t,x ),θ(t,x ),Φ(t,x ))∈X 0,t 1;12V ,2V ;12Θ,2Θ and (v (t,x ),u (t,x ),θ(t,x ),Φ(t,x ))satisfy ⎧⎨⎩0<V 2≤v (t,x )≤2V ,0<Θ2≤θ(t,x )≤2Θ,(2.2)sup [0,t 1]( (v −1,u,θ−1,Φx )(t ) 1)≤2 (v 0−1,u 0,θ0−1,Φ0) 1,(2.3)and D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h pCOMPRESSIBLE NAVIER–STOKES–POISSON EQUATIONS 553(2.4)lim |x |→∞(v (t,x )−1,u (t,x ),θ(t,x )−1,Φx (t,x ))=(0,0,0,0).Lemma 2.1can be proved by the standard iteration argument as in [32]for the one-dimensional compressible Navier–Stokes system;we thus omit the details for brevity.Now we give some properties on the local solution (v (t,x ),u (t,x ),θ(t,x ),Φ(t,x ))constructed above.Noticing that u + Φx v t x =u x + Φx v x t =u x +(1−v )t =u x −v t =0,we have the following lemma from (2.4).Lemma 2.2.Under the conditions in Lemma 2.1,we have(2.5)u (t,x )=− Φx (t,x )v (t,x ) t .Now we turn to prove Theorem 1.1.Recall that μ(v )=v −a ,κ(v,θ)=θb ,and the constitutive equations (1.2),and thus the Cauchy problem (1.1),(1.3)can be rewritten as ⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩v t −u x =0,u t +p (v,θ)x = u x v 1+a x +Φx v ,C v θt +p (v,θ)u x =u 2x v 1+a + θb θx v x , Φx v x =1−v,lim |x |→+∞Φ(t,x )=0,(2.6)(v (0,x ),u (0,x ),θ(0,x ))=(v 0(x ),u 0(x ),θ0(x )),lim |x |→+∞(v 0(x ),u 0(x ),θ0(x ))=(1,0,1).(2.7)Suppose that the local solution (v (t,x ),u (t,x ),θ(t,x ),Φ(t,x ))constructed in Lemma 2.1has been extended to t =T ≥t 1and satisfies the a priori assumption (H 1)V 0≤v (t,x )≤V 1,Θ0≤θ(t,x )≤Θ1for all x ∈R ,0≤t ≤T,and some positive constants 0<Θ0≤Θ1,0<V 0≤V 1;we now deduce certain a priori estimates on (v (t,x ),u (t,x ),θ(t,x ),Φ(t,x ))which are independent of Θ0,Θ1,V 0,V 1but may depend on T .The first one is concerned with the basic energy estimate.For this,note that η(v,u,θ)=Rφ(v )+u 22+Rφ(θ)γ−1with φ(x )=x −ln x −1is a convex entropy to (2.6)which satisfies (2.8)η(v,u,θ)t + Rθv −R u x − uu x v 1+a +(θ−1)θx vθ1−b x + u 2x v 1+a θ+θ2x vθ2−b =u Φx v .With (2.8),since u Φx v = u Φv +Φv Φx v t x −12 Φx v 2 t +Φv x v 2 u + Φx v t ,D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h p554Z.TAN,T.YANG,H.ZHAO,AND Q.ZOU we can deduce the following lemma by integrating (2.8)with respect to t and x over[0,T ]×R and from (2.5).Lemma 2.3(basic energy estimates ).Let the conditions in Lemma 2.1hold andsuppose that the local solution (v (t,x ),u (t,x ),θ(t,x ),Φ(t,x ))constructed in Lemma 2.1satisfies the a priori assumption (H 1),then we have for 0≤t ≤T that R η(v,u,θ)+12 Φx v 2 (t,x )dx + t 0 R u 2x v 1+a θ+θ2x vθ2−b (τ,x )dxdτ= R η(v 0,u 0,θ0)+12 Φ0x v 0 2 (x )dx.(2.9)The next estimate is concerned with a lower-bound estimate on θ(t,x )in termsof the lower bound on v (t,x ).Lemma 2.4.Under the assumptions in Lemma 2.3,we have for a <1that(2.10)1θ(t,x )≤O (1)+O (1) 1v 1−a L ∞T,x ,x ∈R ,0≤t ≤T.Proof .First of all,(2.6)3implies C v 1θ t =−u 2x θ2v 1+a +Ru x vθ−2θ1+b v 1θ x 2+ θb v 1θ x x = θb v 1θ x x − 2θ1+b v 1θ x 2+1v 1+a θ2 u x −Rθv a 2 2 (2.11)+R 24v 1−a .Set h (t,x )=1θ−R 2t 4C v 1v 1−a L ∞T,x and we can deduce that h (t,x )satisfies ⎧⎨⎩C v h t ≤ θb v h x x ,x ∈R ,0≤t ≤T,h (0,x )=1θ0(x )≤1Θ,(2.12)and the standard maximum principle for parabolic equations implies that h (t,x )≤1Θholds for all (t,x )∈[0,T ]×R .That is,for x ∈R ,0≤t ≤T ,(2.13)1θ−R 2t 4C v 1v 1−a L ∞T,x ≤1Θ.This is (2.10)and the proof of Lemma 2.4is completed.To use Kanel’s method to deduce a lower bound and an upper bound on v (t,x ),we need to deduce an estimate on v x v 1+a ,which is the main concern of our next lemma.D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h pCOMPRESSIBLE NAVIER–STOKES–POISSON EQUATIONS 555It is worth pointing out that it is in this step that we ask the viscous coefficient μdepend only on v .Lemma 2.5.Under the assumptions in Lemma 2.3,we have v x v 1+a 2+ t 0 R θv 2x v 3+a +g (v )(v −1) dxds (2.14)≤ v 0x 2+ (v 0−1,u 0,θ0−1,Φ0x ) 2+ t 0 R u 2x v 1+a dxds +O (1) t 0 R θ2x v 1+a θdxds and g (v )= v 1dz z 1+a =1−v −a a .Proof .Notice that v x v 1+a t = v t v 1+a x = u x v 1+a x =u t +p (v,θ)x −Φx v .We have by multiplying the above identity by v x v 1+a and integrating the resultingequation with respect to t and x over [0,T ]×R that 12 v x v 1+a 2+ t 0 R Rθv 2x v 3+a dxds (2.15)≤O (1) v 0x 2+ t 0 R Rθx v x v 2+a dxds I 1+ t 0 R u t v x v 1+a dxds I 2− t 0 R v x v 1+a Φx v dxds I 3.Now we estimate I 1,I 2,and I 3term by term.First,we have from (2.6)4and the Cauchy–Schwarz inequality that I 3= t 0 R g (v )x Φx v dxds =− t 0 R g (v ) Φx v x dxds (2.16)=− t 0 R g (v )(1−v )dxds ≥0and (2.17)I 1≤12 t 0 R Rθv 2x v 3+a dxds +O (1) t 0 R θ2x v 1+a θdxds.As to I 2,we have from (2.9)that I 2= R uv x v 1+a dx t 0− t 0 R u v x v 1+a t dxds (2.18)≤ R uv x v 1+a dx +O (1) (u 0,v 0x ) 2− t 0 R u u x v 1+a x dxds ≤12 v x v 1+a 2+O (1) (v 0−1,v 0x ,u 0,θ0−1,Φ0x ) 2+ t 0 R u 2x v1+a dxds.D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h p556Z.TAN,T.YANG,H.ZHAO,AND Q.ZOU Inserting (2.16)–(2.18)into (2.15),we can deduce (2.14)immediately.This com-pletes the proof of Lemma 2.5.To bound the two terms on the right-hand side of (2.14),we now estimate t 0 R u 2x v 1+a dxds in the following lemma.Lemma 2.6.Under the assumptions in Lemma 2.3,we have(2.19) u (t ) 2+ t 0 R u 2x v 1+a dxds ≤O (1) (v 0−1,u 0,θ0−1,Φ0x ) 2+O (1) t 0 R (θ−1)2v 1−a dxds.Proof .Multiplying (2.6)2by u ,we have by integrating the resulting equation with respect to t and x over [0,T ]×R that 12 u (t ) 2+ t 0 R u 2x v 1+a dxds (2.20)≤O (1) u 0 2+ t 0 R R (θ−1)u x v dxds I 4+ t 0 R R 1−1v u x dxds I 5+ t 0 R u Φx v dxds I 6.From the basic energy estimate (2.9)and the Cauchy–Schwarz inequality,we can bound I j (j =4,5,6)as follows:I 6≤ t 0 u (s ) Φx v (s ) ds ≤C (T ) (u 0,v 0−1,θ0−1,Φ0x ) 2,I 5= t 0 R R 1−1v v t dxds =R R φ(v )dx t 0=R R φ(v )dx − R φ(v 0)dx ≤O (1) (u 0,v 0−1,θ0−1,Φ0x ) 2,I 4≤12 t 0 R u 2x v 1+a dxds +O (1) t 0 R (θ−1)2v 1−a dxds.Substituting the above estimates into (2.20),we can deduce (2.19)and complete the proof of the lemma.To bound the terms appearing on the right-hand side of (2.19)and (2.14),weneed the following lemma.Lemma 2.7.Under the assumptions in Lemma 2.3,we have for b =0,−1that t 0max x ∈R |θ(s,x )|b ds ≤C (T ),(2.21) t 0max x ∈R |θ(s,x )|b +1ds ≤C (T ) 1+ θ L ∞T,x ,(2.22)and (2.23) t 0max x ∈R |θ(s,x )|b +1ds ≤C (T ) 1+ v L ∞T,x .D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h pProof .We only prove (2.22)because (2.21)and (2.23)can be proved similarly.From the argument used in [25]we have,from the basic energy estimate (2.9),theJenssen inequality that for each i ∈Z ,there are positive constants A 0>0,A 1>0which are independent of i such that(2.24)A 0≤ i +1i v (t,x )dx, i +1i θ(t,x )dx ≤A 1∀t ∈[0,T ].Hence,there exist a i (t )∈[i,i +1],b i (t )∈[i,i +1]such that(2.25)A 0≤v (t,a i (t )),θ(t,b i (t ))≤A 1.Define g 1(θ)=θ1s b −12ds =2b +1 θb +12−1 ;for each x ∈R ,there exists an integer i ∈Z such that x ∈[i,i +1]and we can assume without loss of generality that x ≥b i (t ).Thus g 1(θ(t,x ))=g 1(θ(t,b i (t )))+xb i (t )g 1(θ(t,y ))y dy ≤O (1)+ i +1iθb −12θx dx ≤O (1)+ Rθ2x vθ2−b dx 12i +1i vθdx 12≤O (1)+ θ 12L ∞T,x R θ2x vθ2−b dx 12.The above estimate and (2.9)give (2.22)and thus completes the proof of the lemma.As a direct corollary of (2.21)–(2.23),we have the following corollary.Corollary 2.1.Under the conditions in Lemma 2.3,we have (2.26) t 0R(θ−1)2dxds ≤O (1) θ1−b L ∞T,x.Proof .In fact,(2.9)together with (2.21)imply that t 0 R (θ−1)2dxdτ≤O (1) t 0 R (θ+1)φ(θ)dxdτ≤O (1) t0max x ∈R θ(τ,x )dτ+O (1)=O (1)t0max x ∈Rθ1−b θb dτ+O (1)≤O (1) θ1−b L ∞T,xt 0max x ∈Rθb (τ,x )dτ+O (1)≤O (1) θ1−b L ∞T,x+O (1),and this completes the proof of the corollary.D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h pHaving obtained (2.26),we can deduce that (2.27) t 0 R (θ−1)2v 1−a dxdτ≤ 1v 1−a L ∞T,x t 0 R (θ−1)2dxdτ≤O (1) θ1−b L ∞T,x 1v 1−a L ∞T,x .On the other hand,from (2.9),we have t 0 R θ2x θv 1+a dxdτ= t 0 R θ2x vθ2−b 1v a θb −1dxdτ≤ 1v a L ∞T,xθ1−b L ∞T,x t 0 R θ2xvθ2−b dxdτ≤O (1) (v 0−1,u 0,θ0−1,Φ0x ) 2 1v a L ∞T,xθ1−b L ∞T,x .(2.28)Substituting (2.27)and (2.28)into (2.19)and (2.14),we have the followingcorollary.Corollary 2.2.Under the assumptions in Lemma 2.3,we have u (t ) 2+ t 0 Ru 2x v 1+a dxdτ(2.29)≤O (1) (v 0−1,u 0,θ0−1,Φ0x ) 2+O (1) 1v a L ∞T,x θ1−b L ∞T,x, v x v 1+a 2+ t 0 Rθv 2xv 3+a +g (v )(v −1) dxdτ(2.30)≤O (1) (v 0−1,u 0,θ0−1,Φ0x ) 2+O (1) 1v a L ∞T,x 1v 1−a L ∞T,xθ1−b L ∞T,x .Now we apply Kanel’s approach to deduce a lower bound and an upper bound on v (t,x )in terms of θ1−b L ∞T,x.To this end,set(2.31)Ψ(v )= v 1φ(z )z 1+a dz.Note that there exist positive constants A 2,A 3such that (2.32)|Ψ(v )|≥A 2 v −a +v 12−a −A 3.Since|Ψ(v )|= x −∞Ψ(v (t,y ))y dy ≤ R φ(v )v1+a v x dx ≤φ(v ) v x v 1+a (2.33)≤O (1) 1+ 1v a 2L ∞T,x +1v 1−a 2L ∞T,xθ1−b 12L ∞T,x ,D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h pwe have from (2.32)and (2.33)that (2.34) 1v a L ∞T,x + v 12−a L ∞T,x ≤O (1) 1+ 1v a 2L ∞T,x + 1v 1−a 2L ∞T,xθ1−b 12L ∞T,x .Thus if 13<a <12,we can deduce from (2.34)the following corollary.Corollary 2.3.Under the conditions in Lemma 2.3,if we assume further that 13<a <12,then we have(2.35)1v (t,x )≤O (1) 1+ θ1−b 13a −1L∞T,xand (2.36)v (t,x )≤O (1) 1+ θ1−b 2a (3a −1)(1−2a )L ∞T,x hold for any (t,x )∈[0,T ]×R .Consequently,(2.29)and (2.30)can be rewritten as u (t ) 2+ t 0 R u 2x v1+a dxdτ≤O (1) 1+ θ1−b 2a 3a −1L ∞T,x ,(2.37) v x v 1+a 2+ t 0 Rθv 2x v 3+a +g (v )(v −1) dxdτ≤O (1) 1+ θ1−b 2a 3a−1L ∞T,x .(2.38)To get an upper bound on θ(t,x ),we need also the estimate on u x (t ) which is given in the following lemma.Lemma 2.8.Under the conditions listed in Lemma 2.3,we have for 0≤t ≤T that u x (t ) 2+ v (t ) 2+ t 0 R u 2xxv 1+adxdτ(2.39)≤O (1) (v 0−1,u 0,θ0−1,Φ0x ) 2+O (1) θ2−b L ∞T,x 1+ θ1−b 2a 2(3a −1)(1−2a )L ∞T,x +O (1) 1+ θ1−b 2(2a −2a 2+1)(3a −1)(1−2a )L ∞T,x.Proof .By differentiating (2.6)2with respect to x ,multiplying the resulting iden-tity by u x ,and integrating the result with respect to t and x over [0,T ]×R ,we have u x (t ) 2+ t 0 R u 2xx v 1+adxdτ+ v −1 2(2.40)≤O (1) u 0x 2+2 t 0 R u xx p (v,θ)x dxdτ I 7+2(1+a ) t 0Ru x v x u xx v 2+a dxdτ I 8.D o w n l o a d e d 09/30/13 t o 202.121.182.203. R e d i s t r i b u t i o n s u b j e c t t o S I A M l i c e n s e o r c o p y r i g h t ; s e e h t t p ://w w w .s i a m .o r g /j o u r n a l s /o j s a .p h p。