外文翻译原文.
外文文献翻译(图片版)
本科毕业论文外文参考文献译文及原文学院经济与贸易学院专业经济学（贸易方向）年级班别2007级 1 班学号3207004154学生姓名欧阳倩指导教师童雪晖2010 年 6 月 3 日目录1 外文文献译文（一）中国银行业的改革和盈利能力（第1、2、4部分） (1)2 外文文献原文（一）CHINA’S BANKING REFORM AND PROFITABILITY（Part 1、2、4） (9)1概述世界银行（1997年）曾声称，中国的金融业是其经济的软肋。
当一国的经济增长的可持续性岌岌可危的时候，金融业的改革一直被认为是提高资金使用效率和消费型经济增长重新走向平衡的必要（Lardy，1998年，Prasad，2007年）。
事实上，不久前，中国的国有银行被视为“技术上破产”，它们的生存需要依靠充裕的国家流动资金。
但是，在银行改革开展以来，最近，强劲的盈利能力已恢复到国有商业银行的水平。
但自从中国的国有银行在不久之前已经走上了改革的道路，它可能过早宣布银行业的改革尚未取得完全的胜利。
此外，其坚实的财务表现虽然强劲，但不可持续增长。
随着经济增长在2008年全球经济衰退得带动下已经开始软化，银行预计将在一个比以前更加困难的经济形势下探索。
本文的目的不是要评价银行业改革对银行业绩的影响，这在一个完整的信贷周期后更好解决。
相反，我们的目标是通过审查改革的进展和银行改革战略，并分析其近期改革后的强劲的财务表现，但是这不能完全从迄今所进行的改革努力分离。
本文有三个部分。
在第二节中，我们回顾了中国的大型国有银行改革的战略，以及其执行情况，这是中国银行业改革的主要目标。
第三节中分析了2007年的财务表现集中在那些在市场上拥有浮动股份的四大国有商业银行：中国工商银行（工商银行），中国建设银行（建行），对中国银行（中银）和交通银行（交通银行）。
引人注目的是中国农业银行，它仍然处于重组上市过程中得适当时候的后期。
第四节总结一个对银行绩效评估。
外文文献翻译译稿和原文
外文文献翻译译稿1卡尔曼滤波的一个典型实例是从一组有限的，包含噪声的，通过对物体位置的观察序列（可能有偏差）预测出物体的位置的坐标及速度。
在很多工程应用（如雷达、计算机视觉）中都可以找到它的身影。
同时，卡尔曼滤波也是控制理论以及控制系统工程中的一个重要课题。
例如，对于雷达来说，人们感兴趣的是其能够跟踪目标。
但目标的位置、速度、加速度的测量值往往在任何时候都有噪声。
卡尔曼滤波利用目标的动态信息，设法去掉噪声的影响，得到一个关于目标位置的好的估计。
这个估计可以是对当前目标位置的估计（滤波），也可以是对于将来位置的估计（预测），也可以是对过去位置的估计（插值或平滑）。
命名[编辑]这种滤波方法以它的发明者鲁道夫.E.卡尔曼（Rudolph E. Kalman）命名，但是根据文献可知实际上Peter Swerling在更早之前就提出了一种类似的算法。
斯坦利。
施密特（Stanley Schmidt）首次实现了卡尔曼滤波器。
卡尔曼在NASA埃姆斯研究中心访问时，发现他的方法对于解决阿波罗计划的轨道预测很有用，后来阿波罗飞船的导航电脑便使用了这种滤波器。
关于这种滤波器的论文由Swerling（1958）、Kalman (1960)与Kalman and Bucy（1961）发表。
目前，卡尔曼滤波已经有很多不同的实现。
卡尔曼最初提出的形式现在一般称为简单卡尔曼滤波器。
除此以外，还有施密特扩展滤波器、信息滤波器以及很多Bierman, Thornton开发的平方根滤波器的变种。
也许最常见的卡尔曼滤波器是锁相环，它在收音机、计算机和几乎任何视频或通讯设备中广泛存在。
以下的讨论需要线性代数以及概率论的一般知识。
卡尔曼滤波建立在线性代数和隐马尔可夫模型（hidden Markov model）上。
其基本动态系统可以用一个马尔可夫链表示，该马尔可夫链建立在一个被高斯噪声（即正态分布的噪声）干扰的线性算子上的。
系统的状态可以用一个元素为实数的向量表示。
国际贸易对碳排放的影响外文文献翻译中英文
外文文献翻译(含：英文原文及中文译文)英文原文The effects of international trade on Chinese carbon emissionsB Wei ，X Fang ，Y WangAbstractInternational trade is an important impact factor to the carbon emissions of a country. As the rapid development of Chinese foreign trade since its entry into the WTO in 2002, the effects of international trade on carbon emissions of China are more and more significant. Using the recent available input-output tables of China and energy consumption data, this study estimated the effects of Chinese foreign trade on carbon emissions and the changes of the effects by analyzing the emissions embodied in trade between 2002 and 2007. The results showed a more and more significant exporting behavior of embodied carbon emissions in Chinese international trade. From 2002 to 2007, the proportion of net exported emissions and domestic exported emissions in domestic emissions increased from 18.32% to 29.79% and from 23.97% to 34.76%, respectively. In addition, about 22.10% and 32.29% of the total imported emissions were generated in processing trade in 2002 and 2007, respectively, which were imported and later exported emissions. Although, most of the sectors showed a growth trend in imported and exportedemissions, sectors of electrical machinery and communication electronic equipment, chemical industry, and textile were still the biggest emission exporters, the net exported emissions of which were also the largest. For China and other developing countries, technology improvement may be the most favorable and acceptable ways to reduce carbon emissions at present stage. In the future negotiations on emissions reduction, it would be more fair and reasonable to include the carbon emissions embodied in international trade when accounting the total emissions of an economy. Keywords: input-output analysis, carbon emissions, international trade, ChinaIntroductionGlobal warming has been considered an indisputable fact. The main reason is that the warming of the global climate system is due to the continuous increase in the concentration of greenhouse gases in the atmosphere, the result of human activities (IPCC, 2007). In order to avoid the possible negative impact on human society's global warming, a series of measures have been taken to reduce global greenhouse gas emissions to slow down global warming. However, around the CO2 emission reduction and the future allocation of carbon emission rights, the game plays a different interest group.With the development of globalization, the impact on the international trade of the environment is becoming more and moresignificant, including the potential impact of carbon emissions from geographical relocation. Many researchers estimate that it is reflected in international trade in certain countries as well as in the world economy (Wykoff and Rupp, carbon emissions in 1994; Schaefer and Lealdesa, 1996, Machado et al., 2001 Year; Munksgaard, Peder and Sen, 2001; Ahmed and Wykov, 2003; Sanchez-Chóliz and Duarte, 2004; Peters and Hess, 2006, 2008; Mäenpää et al, 2007; Keman et al., 2007). The general conclusion is that in a more open economy, the impact of large foreign trade on the carbon emissions of a country. In addition, all these studies have pointed out that import and export trade cannot ignore a relatively open economy; otherwise, energy and carbon emissions figures may be seriously distorted by this economy (Machado et al., 2001). In terms of total volume, the value of China’s trade surplus increased from US$30.43 billion in 2002 to US$261.83 billion in 2007 (National Bureau of Statistics, 2008). The rapid growth of China’s foreign trade will have a significant effect on China’s carbon emissions.As one of the countries with the highest carbon emissions, China is facing increasing pressure to reduce emissions. However, China is also a big country in international trade. The rapid development of China’s economy has led to steady growth in foreign trade. From 1997 to 2002, China’s total import and export value increased by an average annual growth rate of 14.35%. Since joining the World Trade Organization, theaverage annual growth rate of China’s trade has jumped to 28.64%. From 2002 to 2007, the value of exports compared with 2002, it increased by 2.7 times in 2007 to reach US$1.2177.8 billion. Imports also soared to US$955.95 billion in 2007, which was 2.2 times higher than the 2002 imports. In terms of total volume, the value of China’s trade surplus increased from US$30.43 billion in 2002 to US$261.83 billion in 2007 (National Bureau of Statistics, 2008). The rapid growth of China’s foreign trade will have a significant effect on China’s carbon emissions.However, quantitative assessment of the impact of China's international trade in energy use and carbon emissions has only recently begun. Estimates from the IEA (2007) show that China's domestic production and export of energy-related carbon dioxide emissions account for 34% of total emissions, and if it is used in 2004, the weighted average carbon intensity of commodity countries imported from China is estimated. China's net exports of EM-rich CO2 may be more than 17% of total emissions in 2004 (Levin, 2008). Using a single-area input-output model, Pan et al. (2008) estimated that their production of energy and emissions in 2002 accounted for 16% and 19% of China’s net exports of primary energy consumption, respectively, in 2002. In the input-output analysis, China reported that the discharge volume of pre-grid discharges to the United States accounted for about 5%. Weber et al. (2008), ESTI mating production exported from China's carbon dioxide emissions from1987 to 2005. In 2005, about one-third of China's emissions were due to production exports, and this proportion has risen from 12% in 1987 to 21% in 2002. In developed countries, consumption is driving this trend. Wei et al.'s estimation (2009a) also found that the presence of emissions in China's economy in 2002 reflected significant export behavior; in addition, subsequent exports (processing trade played by EMIS--) were total imports of 20 %the above. In addition, using a multi-area input-output model, Peters and Hewei (2008) also found that export emissions represented 24.4% of China's domestic emissions, and the proportion of imports in 2001 was only 6.6%. A similar study by Atkinson et al. (2009) also shows that China is a net exporter of carbon emissions in international trade. In recent years, using ecological input-output based on physical access programs, MOD-Y eling, Chen and Chen (2010) estimated that in 2007 China's export of carbon dioxide emissions and total energy were respectively 32.31% and 33.65% of total emissions.Both the United States and European countries are major importers of China’s export carbon emissions. Using the economic input-output life cycle assessment software, Ruihe Harris (2006) found that about 7% of China’s carbon dioxide emissions from exports to the United States during the period of 1997-2003 were produced by 14% of the total; the US’s CO2 emissions will At 3%-6%, if increased imports from Chinahave been produced in the United States. AP-walking a similar approach, Lee Hewitt found that bilateral trade between the United Kingdom and China (2008) produced about 4% of CO2 emissions. In 2004, China's CO2 emissions were for the UK market to produce goods and the UK trade decreased. About 11%. Weber et al. (2008) also found that most of China’s recent export emissions went to developed countries, approximately 27% of the United States, 19% of the EU-27, and 14% of the remaining Annex B countries, mainly Japan and Australia. And New Zealand. Recently, Xu et al. (2009) studied the impact of energy consumption and exhaust emissions on the environment. From 2002 to 2007, the use of environmental input-output analysis and adjustment of bilateral trade data reflected trade in the East (from China to the United States). Zhang (2009) has also obtained similar results. Energy and CO2 account for about 12% and 17% of China's energy consumption, and China's CO2 emissions are 8% and 12%, respectively.Although China's international trade is a meaningful research on carbon emissions, further related research is necessary because of the rapid development of China's foreign trade, especially the development of processing trade. According to statistics (National Bureau of Statistics, 2008), the export share of processing trade has been more than 50% of total exports since 1996. In 2002 and 2007, the share of processing trade reached 55.26% and 50.71%, which will be processing trade. Thenecessary distinction between the impact of general trade and China's carbon emissions.Since China's input-output table is only 5 years, we have chosen from 2002 (entry to the WTO) to 2007 (the latest issue), and China's international trade input-output table has impact on carbon emissions with the view of the last requirement of this paper. Influence changes. In addition, we distinguish between domestic processing trade and import investment in the assessment of production processes (import emissions and re-exports), which will help us to further understand the impact of international trade on emissions status. In this study, we tried to answer three questions: 1) What is the net emissions generated by foreign trade in China as a big country's foreign trade? 2) China from 2002 to 2007, International How does trade affect carbon emissions? 3) From 2002 to 2007, which departments were the major emitters of China's import and export trade and their roles?Uncertainty in the calculation of carbon emissionsThe calculation of emissions from China's trade reflects a certain degree of uncertainty. One is that the input-output analysis itself has many inherent uncertainties (more discussion in Lenzen, 2001). Based on an input-output table for China's single region, it allows us to obtain a relatively accurate assessment of the emissions that are reflected in China's exports, but this error may be more pronounced when estimatingthe emissions of goods and services exported to China. (Lenzen , 2001; Lenzen et al., 2004). Another important factor of uncertainty is that the calculations come from different regions, which may underestimate the method of importing the carbon intensity factor that is reflected in the import of larger proportion of finished product producing countries and tertiary industries, and the smaller proportion of secondary industries. In addition, the method of pro-grade introduction of the column will inevitably result in some errors in order to obtain a matrix from the inlet of the original import and export table.At present, for reasons of data availability, we cannot fully quantify the accuracy of our calculations, but preliminary estimates suggest that the use of more accurate data results from research will not significantly change the conclusions of this analysis. These restrictions will be improved through the use of multi-zone import and export tables and out-of-zone more detailed industry carbon intensity and sector-to-sector production processes in the future for detailed analysis.Understand the impact of international trade on carbon emissions in ChinaFrom 2002 to 2007, the impact of foreign trade on China’s carbon emissions has greatly expanded. It may be largely related to two factors. The first is the coal-based energy consumption structure. The secondary industry-based production structure will maintain high domestic energyintensity. In 2002, the coal consumption exchange was only 66.3% of the total energy consumption. The 44.8% of China's gross domestic product (GDP) is due to the secondary industry in 2002 (National Bureau of Statistics, 2008). In 2007, related stock prices rose as high as 69.5% and 48.6%, respectively, which will lead to the fact that the unit exports are higher than the carbon emissions reflected in unit imports. The second factor, which may be a more important factor, is the rapid growth of export trade. From 2002 to 2007, China’s exports increased by 246.80%, while imports increased by 199.97% (National Bureau of Statistics, 2008). Export growth is significantly higher than imports, which may lead to a sharp increase in net exports. Decomposition analysis using input and output structures, Liu et al. (2010) also found that the total export expansion of export and energy-intensive products tends to expand, reflecting the export of energy from 1992 to 2005, but the improvement and change of energy efficiency in the primary energy consumption structure can offset part of the impact on export energy. The above driving force is implemented.Although, based on the coal-based energy consumption structure, the carbon dioxide emissions produced by the secondary industry-based production structure, the more important role, it may be difficult for China to adjust because of its endowment characteristics, and in a very short time Its structural characteristics and its current economicdevelop ment stage. In addition, the expansion of China’s foreign trade, including the expansion of the trade surplus, is mainly the result of the market economy’s maximizing its comparative advantage. The development-replacement of China's economy not only provided many of the world's goods and services, but also reduced the nation's production-based relative costs in developed countries. China’s foreign trade has always played an important role in the development of the world economy, due to its huge market, stable government system and abundant cheap labor. Therefore, it can be argued that at the current stage, for China's better methods to reduce the impact of international trade on national or global CO2 emissions should be to improve its production technology, reduce the intensity of energy consumption as a whole, not only to control China The amount of foreign trade. In addition, the imported goods from China should take part in China's carbon emission responsibilities, because the CON-consumer demand of foreign consumers has generated a large amount of China's carbon emissions, especially for consumers in developed countries.ConclusionDespite some uncertainties in this study, most areas produced from the details of the data, we can conclude that international trade has a significant impact on China's carbon emissions, and changed the impact of time on going. Compared with 2002 emissions, domestic exportemissions in 2007 increased from 267.07 MTC to 718.31 MTC, with a speed increase of over 160%; net exports also increased correspondingly, from 204.08 MTC up to 615.65 MTC, over 200% growth rate Now. From 23.97% in 2002, the share of domestic emissions from domestic emissions jumped to 34.76% in 2007. The share of pre-net transplants that exceeded domestic emissions also rose from 18.32% in 2002 to 29.79% in 2007. The results show that more and more significant net export behaviors of implied carbon emissions exist in China's economy and processing trade have more and more significant effects on carbon emissions.Regardless of the emissions of imported emissions or exports, most industries showed a growth trend in 2007. Compared with 2002, emissions although the sectoral emissions have changed for the entire economy from 2002 to 2002, The impact, of which the largest percentage of imported major department or China's export emissions remain unchanged. The largest import emissions (all or actual imports) come from the industries of electrical machinery and communications electronics, chemicals, smelting and rolling plus metals. Electrical machinery and communications electronics equipment, chemicals, textiles and other sectors are the largest emitters of exports, net exports of which are also the largest. Technological progress may be the most favorable and acceptable way for China and other developing countries toreduce their carbon emissions. Considering that the world’s largest carbon emissions and the recent increase in emissions are in developing countries, the historical responsibility for the current responsibilities, developed countries should also take more efforts to help developing countries reduce their carbon emissions. Economic growth through technical assistance And financial support. In the car's list of future emissions reductions, which include the total economic output, the carbon emissions reflected in international trade will be fair and reasonable.中文译文国际贸易对中国碳排放的影响: 一份具有经验性的分析作者：B Wei ，X Fang ，Y Wang摘要国际贸易是一个国家碳排放量重要的影响因素,自2002年加入世贸组织,中国对外贸易的快速发展对碳排放的影响越来越显著。
外文资料翻译
毕业设计外文资料翻译系别：管理系专业：班级：姓名：学号：外文出处：<<ENGINEERING MANAGEMENT PROFESSION>>工程管理专业附件：1、外文原文；2、外文资料翻译译文。
指导教师评语：签字：年月日1、外文原文；Scheduling systems and their selectionScheduling systemsNow we are ready to discuss the various methods for scheduling capital construction projects that are available. The two basic methods that will be discussed are bar charts and logic-diagram-based schedules. Both methods are used extensively, and sometimes interchangeably, in project and construction work. Each method has its advantages and disadvantages. Knowing when to select the correct method is half the battle in successfully making and controlling your project schedule.Bat chartsThe forerunner to the bar chart was developed by two industrial engineers, Frederick W. Taylor and Henry L. Gantt, for scheduling production operations during World War I. the name “Gantt chart” is still in use today to designate certain types of bar charts. It was sometime after World War I that bar-charting was adapted to the scheduling of construction projects.Bar charts are the simplest from of scheduling and have been in use the longest of any of the systems we have available. They offer the advantage of being cheap and simple to prepare; they are easy to read and update, and they are readily understood by anyone with a basic knowledge of the capital projects business. They are still in wide use today, even as a final product of the computerized CPM scheduling system. The main disadvantage of the bar chart is its inability to show enough detail to cover all the activities on larger, complex projects. On large projects, the number of pages required to bar- chart the project becomes cumbersome, and interrelation of work activities becomes difficult to follow from page to page.As the size and complexity of projects grew in the late fifties and sixties in the 20th century, finishing projects late became the rule rather than the exception. Late finishes, along with their associated cost overruns, caused increased pressure on owners and contractors to develop improved scheduling techniques. Now when we try to schedule a larger project in that sort of detail with bar charts, we quickly lose most of the advantages that we listed earlier. The schedule becomes unwieldy and difficult to interpret, and we run the risk of losing control of the project time plan.Logic- based schedulesFortunately, on the same time, the network schedule and the computer came on thecapital projects scene. We now had a tool available to make the many repetitive calculations for the earl and late start dates, and a place to store and sort the data needed to control a large number of work activities.In the late 1950s the U.S. Navy and the Du Pont Company concurrently developed two different logic-diagram-based scheduling systems at about the same time. The Naty’s system was called PERT, for Program Evaluation and Review Technique. Its first successful application was on the Polaris Missile Program. At about the same time, Du Pont first successfully used their critical path method (CPM) of logic diagram scheduling on several new petrochemical plants.Other owners and contractors lost no time in adapting the new scheduling methods to their projects in order to improve their timely completion performance. The CPM system was somewhat simpler than the PERT method, so it soon became the system favored for use on commercial and industrial capital projects. The KISS principle triumphed again! The basic logic-diagraming principles developed in the 1960s are still and graphical output. In the 1980s, the development of the relatively low-cost PC made the use of the CPM system possible for even the smallest companies.Shortly after the introduction of the PERT/CPM systems in the early sixties, the pendulum swung from simple bar charting to the side of overly detailed, computerized schedules. That didn’t work out as well as the early success with the systems had seemed to indicate it would. If a little bit of CPM was good, more had to be better! Everyone promptly defied the kiss principle and started to schedule in too much detail on each activity. The result was reams and reams of computer output that virtually inundated many untrained people.Most of the construction managers and field schedulers of that period were entrepreneurial craft people who had worked themselves up through the ranks. In many cases they were literally untrainable in the new technology of computerized CPM scheduling. Fortunately, some of the users of the newly developed techniques remembered the KISS principle and developed some easy-to-use systems. Several good mainframe programs came onto the market, including McDonnell Automation’s MSCS system, Metier’s Artemis system, and IBM’s PCS system. As computer capacity and new software bloomed , the programs developed and improved rapidly over the next 20 years.The rapid development of low-cost PC hardware and software has now virtually taken over the CPM capital projects scheduling market. Mainframe computers are now required only on the very largest and most complex projects, those whose logistics demands are too great for memory capabilities of the PC.Comparison and selection of scheduling systemsEvaluating the advantages and disadvantages of bar charts versus CPM allows us to select the most effective system for a given project. It also leads us to some simple rules that are applicable to the selection.Advantages of CPMA. Handling complex projectsThe number-one advantage of the CPM system is its ability to handle many work activities on complex projects with ease. Let me introduce a word of caution on that point: don’t fall into the trap of using more activities than necessary, just because it is easy to do so. You risk getting your schedule bogged down in too much detail, which Makes it harder to use and costs more money to operate. Remember , that's the same trap that almost killed the CPM system in its early days ! One way to avoid the problem is to break out some of the less complicated scheduling areas and use bar charts for them .They could be offsite areas such as small office buildings ,warehouses ,tank farms, and roads . A blend of the two systems often results in a simpler and more effective overall project schedule.B .Dry Run of the projectsAnother outstanding advantage of CPM is the intangible benefit of forcing the project team to dissect the project into all of its working parts. This forces the early analysis of each work activity. The CPM schedule an in checking the resulting logic diagram.The actual scheduling phase, such as calculating the early an late start dates and the associated float, is best left to the scheduling technicians and the computer. It is usually necessary to run the fist pas of the schedule several times, to test and debug the logic diagram before the final version is ready for review and approval.C. Beneficial Output SortsThe large menu of output sorts is another big advantage of a computerized CPM schedule. It allows the various interest members of the construction team to order the output sort best suited to their work. Most CPM programs will yield a sort menu as follows:(1)Total float per activity(2)Limited look-ahead sorts(3)Critical-path sort(4)Critical-equipment sort(5)Project-milestone sort(6)Bar-chat printout(7)Human resource levelingMost CMs, for example, will find the sorts by total float and by milestone most valuable for their needs. The total -float sort starts with the low-float(most critical)work activities listed first for immediate attention. The less critical high-float items show up later on the list. By using the period look- ahead sorts, one can also home in on specific time period, A 30-,60-,90-day look ahead sort will list only those critical items that will occur in the next 30,60,90 days. Material control people find the critical-item sort more convenient in tracking their required delivery dates and actual progress are fed in to the computer,, revised printouts quickly reflect the delivery changes and their effect on the field schedule. Field people usually find that the key-milestone-date sort better suits their needs.Most CPM scheduling software even delivers a bar-chart printout, which is most convenient for upper management and reporting purposes in reviewing project progress. Simplified bar charts are usually included in the progress reports to give a graphic view of actual progress against the schedule.The human resource leveling can level peak personnel requirements, which occur during the project's design and construction phases. By taking advantage of the available during the project's design and construction phases. By taking advantage of the available flat and rescheduling the start of noncritical activities, it's possible to shave personnel peaks. Leveling the personnel requirements leads to more effective use of the project's human resources. This option is invaluable for smoothing out craft manpower peaks in key areas of the work. Judicious use of the early and late start dates can also keep subcontractors from getting in each other's way.D. Convenient Schedule ControllingOn smaller projects, a simple time -scaled bar chart might be used in the progress report. The rapid turnaround of data by the computer also allows the project team to perform what-if exercises with the logic diagram. When scheduling problems arise, the project team can try alternative solutions by reworking elapsed times for problem activities. This generates new early and late start dates that can be shifted to improve the critical path. The computer calculates a new critical path in a matter of seconds, with immediate access to the new output data right there on the computer screen.A CPM/computer system also simplifies recycling the schedule. Recycling becomes necessary whenever schedule deviations grow to a point at which some of the intermediate goals are in jeopardy. Recycling involves revising any target dates that may have slipped beyond repair, perhaps because a significant change in scope has occurred. Exercising some what-if options should allow you to obtain the scheduling-revision option best suited to keeping the project on schedule.Disadvantages of CPMThere are only a few disadvantages to using the CPM method for project scheduling, and even these can be avoided with proper attention from the CM. However, overlooking any of the disadvantages can scuttle your effects to control the project schedule!It's extremely important that your key field people be trained in CPM techniques. That includes all levels from the design group to procurement, and through the construction management team. Remember the story about construction managers trashing the CPM/computer printouts in earlier days!I don't recommend controlling a large project with only a newly trained crew, or usinga new software system without running your old scheduling system in parallel, at least until the new system has been prove to work. If the new system breaks down for any reason, you will be without any means of controlling the end date on the project.The cost of running a CPM schedule is likely to be higher than that of using bar charts, particularly on smaller projects. That was especially true of running the CPM schedule on a mainframe computer. In recent years the relatively modest cost of PC hardware, software, and training has enabled us to expense off that cost for computerized CPM scheduling on a medium-to-large project. It might take several small-sized projects to cover the cost of a PC scheduling system.The cost of the training could be the sleeper in the scheduling cost budget, depending on the experience and computer literacy of your project people. But regardless of the cost, training is the linchpin of the whole system, so don’t ignore it.The real savings in using a PC-computerized schedule is that it will generate a good deal more data than is possible with bar charts. That means the unit cost of the data is low. However if the data is not being used (or worse, is being improperly used!), you will not be getting your money’s worth. It is up to the CM to see that the computerized schedule output is used in a cost-effective manner.The cost effectiveness of using CPMIt is difficult to accurately quantify the cost effectiveness of using CPM scheduling systems on capital projects. First, there is no absolute measure of the time saved by using CPM versus bar charts. Second, the value of the time saved must be balanced against the value to the owner of having earlier access to the facility. Any comparisons of that nature have proved to be highly speculative and difficult to verify.Most owners and contractors accept any additional cost of using CPM scheduling systems as a way to improve the odds of completing their projects on time. Those who do not believe that CPM saves money and ensures a project’s earlier completion date cancontinue to use manual bar-charting with reasonable hope of success.O’Brien’s book, CPM in Construction Management, contains a chapter on costs and some expected saving from using CPM. On average , the cost of applying a CPM system to a project is about 0.5 percent of the total facility cost. The major cost areas for using the system are schedules’ time , software cost ,and computer time.CMs must be aware of the type of scheduling system that is being proposed for their projects, so they can budget funds to cover the cost. Small projects can be done with a part-time scheduler; medium-size projects need at least one person full-time; and larger project require two or more schedulers to handle the workload. Include all computer costs (including necessary training)in the project budget. Be especially carefully if a mainframe computer is used.Advantages of bar-chart schedulesAs I said earlier, bar charts are inexpensive to produce and are easily understood by people with a minimum of scheduling training. I heartily recommend them for small, less complex projects, as being suitable and cost-effective. The more comprehensive CPM system is often too complicated, and represents unnecessary overkill when used on small projects. There are some good PC-based CPM programs available for scheduling a series of small projects, which draw from the same resource pool.The only thing that threatens the economic advantages of using bar charts on small projects has been the advent of PCs, Along with less complicated scheduling software. It is easy to temped into the use of a PC, with the construction manager or engineer acting as the project scheduler. That can be all right if the designated scheduler does the scheduling work in his or her free time. IF ,however, the project leader gets so involved in running the CPM schedule that he or she lets he rest of the rest of the project direction go its own way, the project is doomed to failure.Disadvantages of bar-chart schedulesBar charts have only a limited ability to show many detailed work activities and their associated interactions, They become bulky and unwieldy on larger project with as few as 100 activities.Bar charts cannot show clearly the interaction between early start and late finish dates of activities and the resulting float of noncritical activities. There is no clear identification of the critical path through the project that appears with the CPM system. Also, it’s impossible to develop the wealth of scheduling detail with a bar chart like that developed and manipulated with the CPM system. With bar charts there are no concise information sorts as with the CPM.Computer versus manual scheduling methodsThe major factors in selecting computer over manual scheduling methods are project size and complexity. Small projects are best done manually, since good time control is possible at low cost. However ,a complex plant turnaround project, with a relatively low budget but working three shifts on a tight schedule, definitely warrants a computerized CP approach.On larger projects using CPM, computer operation is a must if the many repetitive critical path calculations are to be performed in short time. Manipulating and sorting the expanded database of project information is well worth the additional expense if the system is properly applied. The arrival of PCs and minicomputers, with their associated scheduling software, has brought the cost well within acceptable limits. The simpler operations of the PC-based systems have also reduced the cost of the necessary CPM training.Scheduling system selectionOur discussion of the advantages and disadvantages of the available scheduling systems should allow us to develop guidelines for selecting an effective scheduling system. The selection involves such factors as:1.Size and complexity of project2.Scope of services required3.Sophistication of user organizations(i.e., client, field organization, subcontractors,and so on )4.Available scheduling systems5.Scheduling budget6.Client preference7.Mixing schedule and costSize of projectWe have already discussed this point earlier. The rule of thumb is bar charts and manual systems for small projects, and computerized CPM for medium-size and lager projects. The level of sophistication of the system tends to become greater as the projects become larger.Complexity of projectEven small complex projects can make good use of computerized CPM schedules, if the fewer activities take place in a very short time span. An example is a plant turnaround worth﹩1 million or less, with only 10 days to do it. On the other hand, a﹩1 million project with a 12-month schedule might not warrant a computerized CPM schedule.Scope of servicesFull-scope design, procurement and construction projects lend themselves to more complex scheduling methods, because of the extra interfaces among the many design, procurement, and construction activities. A project involving just one of these macroactivities could effectively controlled with a less sophisticated and less costly system.Sophistication of user organizationsThe sophistication of user organizations is probably the most overlooked factor in selecting a scheduling system. Often, the need to produce a full-blown CPM schedule exists. However, one key project group may not be experienced enough in CPM to properly interpret their part in it. Assure yourself that the failure of that group to perform properly will not defeat the propose scheduling method.An example would be working with a client in a developing country. If the client’s people lacked system, they might not feel comfortable using it to track job progress. Also, they might not keep their contributions to the project on schedule/. Another example would be an inexperienced construction force not being able to sue the output of the CPM scheduling system, such as we discussed earlier.The worst possible case would occur if the CM were not versed in the selected scheduling system! That underscores the need for present-day CMs to stay current on the latest CPM scheduling methods available in their companies and the marketplace. I definitely recommend that you success-oriented CMs do further, more in- depth study of logic-based scheduling than I have presented here.If there is a shortage of CPM know-how in your organization, it is possible to hire a CPM consultant to handle your project scheduling. At least one member of your team, however, should have enough knowledge of the work. That is the best way to ensure that the resulting schedule will be effective for your project.Existing company systems availableThe availability of company systems is important, because we want to use a system that has been in use within the organization, and that has been thoroughly tested on prior similar projects. Introducing a new system on a project often causes more problems than it solves. As an owner’s project manager, you would do well to assure yourself that the contractor is proficient in the system before allowing its use on your project. It is also not a good idea to force the use of your corporate standard system on the contractor just because your organization is familiar with it. A much wiser curse is to train your people in the use of the contractor’s scheduling system.Scheduling budgetIf the field indirect cost budget dose not allow sophisticated scheduling method, you are going to come up short of money. Most computerized CPM scheduling costs have a tendency to grow and overrun their budgets. A common problem is job stretch-out, which increase the schedule cycles, which in return runs up the scheduling personnel hours and computer time. A factual estimate of the total cost of the proposed scheduling system is needed if an effective system for the project to be selected.Client preferenceOwners who want computerized CPM schedules, and who are willing to pay for them, are entitled to have them. If the owner does not specify a preference for a scheduling system, some common ground for developing a cost-effective system will have to be found.In recent years most federal government contracts have required adherence to a strict contractual standard, calling for use of CPM schedule-control and reporting,. Careful attention must be given to investigating the latest scheduling requirements for any federal work on which you may be proposing.2、外文资料翻译译文。
外文翻译原文
DOI10.1007/s10711-012-9699-zORIGINAL PAPERParking garages with optimal dynamicsMeital Cohen·Barak WeissReceived:19January2011/Accepted:22January2012©Springer Science+Business Media B.V.2012Abstract We construct generalized polygons(‘parking garages’)in which the billiard flow satisfies the Veech dichotomy,although the associated translation surface obtained from the Zemlyakov–Katok unfolding is not a lattice surface.We also explain the difficulties in constructing a genuine polygon with these properties.Keywords Active vitamin D·Parathyroid hormone-related peptide·Translation surfaces·Parking garages·Veech dichotomy·BilliardsMathematics Subject Classification(2000)37E351Introduction and statement of resultsA parking garage is an immersion h:N→R2,where N is a two dimensional compact connected manifold with boundary,and h(∂N)is afinite union of linear segments.A parking garage is called rational if the group generated by the linear parts of the reflections in the boundary segments isfinite.If h is actually an embedding,the parking garage is a polygon; thus polygons form a subset of parking garages,and rationals polygons(i.e.polygons all of whose angles are rational multiples ofπ)form a subset of rational parking garages.The dynamics of the billiardflow in a rational polygon has been intensively studied for over a century;see[7]for an early example,and[5,10,13,16]for recent surveys.The defi-nition of the billiardflow on a polygon readily extends to a parking garage:on the interior of N the billiardflow is the geodesicflow on the unit tangent bundle of N(with respect to the pullback of the Euclidean metric)and at the boundary,theflow is defined by elastic reflection (angle of incidence equals the angle of return).Theflow is undefined at thefinitely many M.Cohen·B.Weiss(B)Ben Gurion University,84105Be’er Sheva,Israele-mail:barakw@math.bgu.ac.ilM.Cohene-mail:comei@bgu.ac.ilpoints of N which map to‘corners’,i.e.endpoints of boundary segments,and hence at thecountable union of codimension1submanifolds corresponding to points in the unit tangentbundle for which the corresponding geodesics eventually arrive at corners in positive or neg-ative time.Since the direction of motion of a trajectory changes at a boundary segment viaa reflection in its side,for rational parking garages,onlyfinitely many directions of motionare assumed.In other words,the phase space of the billiardflow decomposes into invarianttwo-dimensional subsets corresponding tofixing the directions of motion.Veech[12]discovered that the billiardflow in some special polygons exhibits a strikingly he found polygons for which,in any initial direction,theflow is eithercompletely periodic(all orbits are periodic),or uniquely ergodic(all orbits are equidistrib-uted).Following McMullen we will say that a polygon with these properties has optimaldynamics.We briefly summarize Veech’s strategy of proof.A standard unfolding construc-tion usually attributed to Zemlyakov and Katok[15]1,associates to any rational polygon Pa translation surface M P,such that the billiardflow on P is essentially equivalent to thestraightlineflow on M P.Associated with any translation surface M is a Fuchsian group M,now known as the Veech group of M,which is typically trivial.Veech found M and P forwhich this group is a non-arithmetic lattice in SL2(R).We will call these lattice surfaces and lattice polygons respectively.Veech investigated the SL2(R)-action on the moduli space of translation surfaces,and building on earlier work of Masur,showed that lattice surfaces haveoptimal dynamics.From this it follows that lattice polygons have optimal dynamics.This chain of reasoning remains valid if one starts with a parking garage instead of apolygon;namely,the unfolding construction associates a translation surface to a parkinggarage,and one may define a lattice parking garage in an analogous way.The arguments ofVeech then show that the billiardflow in a lattice parking garage has optimal dynamics.Thisgeneralization is not vacuous:lattice parking garages,which are not polygons,were recentlydiscovered by Bouw and Möller[2].The term‘parking garage’was coined by Möller.A natural question is whether Veech’s result admits a converse,i.e.whether non-latticepolygons or parking garages may also have optimal dynamics.In[11],Smillie and the sec-ond-named author showed that there are non-lattice translation surfaces which have optimaldynamics.However translation surfaces arising from billiards form a set of measure zero inthe moduli space of translation surfaces,and it was not clear whether the examples of[11]arise from polygons or parking garages.In this paper we show:Theorem1.1There are non-lattice parking garages with optimal dynamics.An example of such a parking garage is shown in Fig.1.Veech’s work shows that for lattice polygons,the directions in which all orbits are periodicare precisely those containing a saddle connection,i.e.a billiard path connecting corners ofthe polygon which unfold to singularities of the corresponding surface.Following Cheunget al.[3],if a polygon P has optimal dynamics,and the periodic directions coincide with thedirections of saddle connections,we will say that P satisfies strict ergodicity and topologicaldichotomy.It is not clear to us whether our example satisfies this stronger property.As weexplain in Remark3.2below,this would follow if it were known that the center of the regularn-gon is a‘connection point’in the sense of Gutkin,Hubert and Schmidt[8]for some nwhich is an odd multiple of3.Veech also showed that for a lattice polygon P,the number N P(T)of periodic strips on P of length at most T satisfies a quadratic growth estimate of the form N P(T)∼cT2for a positive constant c.As we explain in Remark3.3,our examples also satisfy such a quadratic growth estimate.1But dating back at least to Fox and Kershner[7].Fig.1A non-lattice parkinggarage with optimal dynamics.(Here 2/n represents angle 2π/n )It remains an open question whether there is a genuine polygon which has optimal dynam-ics and is not a lattice polygon.Although our results make it seem likely that such a polygon exists,in her M.Sc.thesis [4],the first-named author obtained severe restrictions on such a polygon.In particular she showed that there are no such polygons which may be constructed from any of the currently known lattice examples via the covering construction as in [11,13].We explain these results and prove a representative special case in §4.2PreliminariesIn this section we cite some results which we will need,and deduce simple consequences.For the sake of brevity we will refer the reader to [10,11,16]for definitions of translation surfaces.Suppose S 1,S 2are compact orientable surfaces and π:S 2→S 1is a branched cover.That is,πis continuous and surjective,and there is a finite 1⊂S 1,called the set of branch points ,such that for 2=π−1( 1),the restriction of πto S 2 2is a covering map of finite degree d ,and for any p ∈ 1,#π−1(p )<d .A ramification point is a point q ∈ 2for which there is a neighborhood U such that {q }=U ∩π−1(π(q ))and for all u ∈U {q },# U ∩π−1(π(u )) ≥2.If M 1,M 2are translation surfaces,a translation map is a surjective map M 2→M 1which is a translation in charts.It is a branched cover.In contrast to other authors (cf.[8,13]),we do not require that the set of branch points be distinct from the singularities of M 1,or that they be marked.It is clear that the ramification points of the cover are singularities on M 2.If M is a lattice surface,a point p ∈M is called periodic if its orbit under the group of affine automorphisms of M is finite.A point p ∈M is called a connection point if any seg-ment joining a singularity with p is contained in a saddle connection (i.e.a segment joining singularities)on M .The following proposition summarizes results discussed in [7,9–11]:Proposition 2.1(a)A non-minimal direction on a translation surface contains a saddle connection.(b)If M 1is a lattice surface,M 2→M 1is translation map with a unique branch point,then any minimal direction on M 2is uniquely ergodic.(c)If M2→M1is a translation map such that M1is a lattice surface,then all branchpoints are periodic if and only if M2is a lattice surface.(d)If M2→M1is a translation map with a unique branch point,such that M1is a latticesurface and the branch point is a connection point,then any saddle connection direction on M2is periodic.Corollary2.2Let M2→M1be a translation map such that M1is a lattice surface with a unique branch point p.Then:(1)M2has optimal dynamics.(2)If p is a connection point then M2satisfies topological dichotomy and strict ergodicity.(3)If p is not a periodic point then M2is not a lattice surface.Proof To prove(1),by(b),the minimal directions are uniquely ergodic,and we need to prove that the remaining directions are either completely periodic or uniquely ergodic. By(a),in any non-minimal direction on M2there is a saddle connectionδ,and there are three possibilities:(i)δprojects to a saddle connection on M1.(ii)δprojects to a geodesic segment connecting the branch point p to itself.(iii)δprojects to a geodesic segment connecting p to a singularity.In case(i)and(ii)since M1is a lattice surface,the direction is periodic on M1,hence on M2as well.In case(iii),there are two subcases:ifδprojects to a part of a saddle connec-tion on M1,then it is also a periodic direction.Otherwise,in light of Proposition2.1(a),the direction must be minimal in M1,and hence,by Proposition2.1(b),uniquely ergodic in M2. This proves(1).Note also that if p is a connection point then the last subcase does not arise, so all directions which are non-minimal on M2are periodic.This proves(2).Statement(3) follows from(c).We now describe the unfolding construction[7,15],extended to parking garages.Let P=(h:N→R2).An edge of P is a connected subset L of∂N such that h(L)is a straight segment and L is maximal with these properties(with respect to inclusion).A vertex of P is any point which is an endpoint of an edge.The angle at a vertex is the total interior angle, measured via the pullback of the Euclidean metric,at the vertex.By convention we always choose the positive angles.Note that for polygons,angles are less than2π,but for parking garages there is no apriori upper bound on the angle at a vertex.Since our parking garages are rational,all angles are rational multiples ofπ,and we always write them as p/q,omitting πfrom the notation.Let G P be the dihedral group generated by the linear parts of reflections in h(L),for all edges L.For the sake of brevity,if there is a reflection with linear part gfixing a line parallel to L,we will say that gfixes L.Let S be the topological space obtained from N×G P by identifying(x,g1)with(x,g2)whenever g−11g2fixes an edge containing h(x).Topologically S is a compact orientable surface,and the immersions g◦h on each N×{g}induce an atlas of charts to R2which endows S with a translation surface structure.We denote this translation surface by M P,and writeπP for the map N×G P→M P.We will be interested in a‘partial unfolding’which is a variant of this construction,in which we reflect a parking garage repeatedly around several of its edges to form a larger parking garage.Formally,suppose P=(h:N→R2)and Q=(h :N →R2)are parking garages.For ≥1,we say that P tiles Q by reflections,and that is the number of tiles,if the following holds.There are maps h 1,...h :N→N and g1,...,g ∈G P(not necessarily distinct)satisfying:(A)The h i are homeomorphisms onto their images,and N = h i (N ).(B)For each i ,the linear part of h ◦h i ◦h −1is everywhere equal to g i .(C)For each 1≤i <j ≤ ,let L i j =h i (N )∩h j (N )and L =(h i )−1(L i j ).Then (h j )−1◦h i is the identity on L ,and L is either empty,or a vertex,or an edge of P .If L is an edge then h i (N )∪h j (N )is a neighborhood of L i j.If L i j is a vertex then there is a finite set of i =i 1,i 2,...,i k =j such that h i s (N )contains a neighborhood of L i j ,and each consecutive pair h i t (N ),h i t +1(N )intersect along an edge containing L i j .V orobets [13]realized that a tiling of parking garages gives rise to a branched cover.More precisely:Proposition 2.3Suppose P tiles Q by reflections with tiles,M P ,M Q are the correspond-ing translation surfaces obtained via the unfolding construction,and G P ,G Q are the cor-responding reflection groups.Then there is a translation map M Q →M P ,such that the following hold:(1)G Q ⊂G P .(2)The branch points are contained in the G P -orbit of the vertices of P .(3)The degree of the cover is [G P :G Q ].(4)Let z ∈M P be a point which is represented (as an element of N ×{1,...,r })by(x ,k )with x a vertex in P with angle m n (where gcd (m ,n )=1).Let (y i )⊂M Q be the pre-images of z,with angles k i m n in Q .Then z is a branch point of the cover if and only if k i n for some i.Proof Assertion (1)follows from the fact that Q is tiled by P .Since this will be impor-tant in the sequel,we will describe the covering map M Q →M P in detail.We will map (x ,g )∈N ×G Q to πP (x ,gg i )∈M P ,where x =h i (x ).We now check that this map is independent of the choice of x ,i ,and descends to a well-defined map M Q →M P ,which is a translation in charts.If x =h i (x 1)=h j (x 2)then x 1=x 2since (h i )−1◦h j is the identity.If x is in the relative interior of an edge L i j thenπP (x ,gg i )=πP (x ,gg j )(1)since (gg i )−1gg j =g −1i g j fixes an edge containing h (x 1).If x 1is a vertex of P then one proves (1)by an induction on k ,where k is as in (C).This shows that the map is well-defined.We now show that it descends to a map M Q →M P .Suppose (x ,g ),(x ,g )are two points in N ×G Q which are identified in M Q ,i.e.x ∈∂N is in the relative interior of an edge fixed by g −1g .By (C)there is a unique i such that x is in the image of h i .Thus (x ,g )maps to (x ,gg i )and (x ,g )maps to (x ,g g i ),and g −1i g −1g g i fixes the edge through x =g −1i (x ).It remains to show that the map we have defined is a translation in charts.This follows immediately from the chain rule and (B).Assertion (2)is simple and left to the reader.For assertion (3)we note that M P (resp.M Q )is made of |G P |(resp. |G Q |)copies of P .The point z will be a branch point if and only if the total angle around z ∈M P differs from the total angle around one of the pre-images y i ∈M Q .The total angle at a singularity corresponding to a vertex with angle r /s (where gcd (r ,s )=1)is 2r π,thus the total angle at z is 2m πand the total angle at y i is 2k i m πgcd (k i ,n ).Assertion (4)follows.3Non-lattice dynamically optimal parking garagesIn this section we prove the following result,which immediately implies Theorem1.1: Theorem3.1Let n≥9be an odd number divisible by3,and let P be an isosceles triangle with equal angles1/n.Let Q be the parking garage made of four copies of P glued as in Fig.1, so that Q has vertices(in cyclic order)with angles1/n,2/n,3/n,(n−2)/n,2/n,3(n−2)/n. Then M P is a lattice surface and M Q→M P is a translation map with one aperiodic branchpoint.In particular Q is a non-lattice parking garage with optimal dynamics.Proof The translation surface M P is the double n-gon,one of Veech’s original examples of lattice surfaces[12].The groups G P and G Q are both equal to the dihedral group D n.Thus by Proposition2.3,the degree of the cover M Q→M P is four.Again by Proposition2.3, since n is odd and divisible by3,the only vertices which correspond to branch points are the two vertices z1,z2with angle2/n(they correspond to the case k i=2while the other vertices correspond to1or3).In the surface M P there are two points which correspond to vertices of equal angle in P(the centers of the two n-gons),and these points are known to be aperiodic [9].We need to check that z1and z2both map to the same point in M P.This follows from the fact that both are opposite the vertex z3with angle3/n,which also corresponds to the center of an n-gon,so in M P project to a point which is distinct from z3. Remark3.2As of this writing,it is not known whether the center of the regular n-gon is a connection point on the double n-gon surface.If this turns out to be the case for some n which is an odd multiple of3,then by Corollary2.2(2),our construction satisfies strict ergodicity and topological dichotomy.See[1]for some recent related results.Remark3.3Since our examples are obtained by taking branched covers over lattice surfaces, a theorem of Eskin et al.[6,Thm.8.12]shows that our examples also satisfy a quadratic growth estimate of the form N P(T)∼cT2;moreover§9of[6]explains how one may explicitly compute the constant c.4Non-lattice optimal polygons are hard tofindIn this section we present results indicating that the above considerations will not easily yield a non-lattice polygon with optimal dynamics.Isolating the properties necessary for our proof of Theorem3.1,we say that a pair of polygons(P,Q)is suitable if the following hold:•P is a lattice polygon.•P tiles Q by reflections.•The corresponding cover M Q→M P as in Proposition2.3has a unique branch point which is aperiodic.In her M.Sc.thesis at Ben Gurion University,thefirst-named author conducted an exten-sive search for a suitable pair of polygons.By Corollary2.2,such a pair will have yielded a non-lattice polygon with optimal dynamics.The search begins with a list of candidates for P,i.e.a list of currently known lattice polygons.At present,due to work of many authors, there is a fairly large list of known lattice polygons but there is no classification of all lattice polygons.In[4],the full list of lattice polygons known as of this writing is given,and the following is proved:Theorem4.1(M.Cohen)Among the list of lattice surfaces given in[4],there is no P for which there is Q such that(P,Q)is a suitable pair.The proof of Theorem4.1contains a detailed case-by-case analysis for each of the differ-ent possible P.These cases involve some common arguments which we will illustrate in this section,by proving the special case in which P is any of the obtuse triangles investigated byWard[14]:Theorem4.2For n≥4,let P=P n be the(lattice)triangle with angles1n,12n,2n−32n.Then there is no polygon Q for which(P,Q)is a suitable pair.Our proof relies on some auxiliary statements which are of independent interest.In all of them,M Q→M P is the branched cover with unique branch point corresponding to a suitable pair(P,Q).These statements are also valid in the more general case in which P,Q are parking garages.Recall that an affine automorphism of a translation surface is a homeomorphism which is linear in charts.We denote by Aff(M)the group of affine automorphisms of M and by D:Aff(M)→GL2(R)the homomorphism mapping an affine automorphism to its linear part.Note that we allow orientation-reversing affine automorphisms,i.e.detϕmay be1 or−1.We now explain how G P acts on M P by translation equivalence.LetπP:N×G P→M P and S be as in the discussion preceding Proposition2.3,and let g∈G P.Since the left action of g on G is a permutation and preserves the gluing ruleπP,the map N×G P→N×G P sending(x,g )to(x,g−1g )induces a homeomorphismϕ:S→S and g◦h◦ϕis a translation in charts.Thus g∈G P gives a translation isomorphism of M P,and similarly g∈G P gives a translation isomorphism of M Q.Lemma4.3The branch point of the cover p:M Q→M P isfixed by G Q.Proof Since G Q⊂G P,any g∈G Q induces translation isomorphisms of both M P and M Q.We denote both by g.The definition of p given in thefirst paragraph of the proof of Proposition2.3shows that p◦g=g◦p;namely both maps are induced by sending (x ,g )∈N ×G Q toπP(x,gg g i),where x =h i(x).Since the cover p has a unique branch point,any g∈G Q mustfix it. Lemma4.4If an affine automorphismϕof a translation surface has infinitely manyfixed points then Dϕfixes a nonzero vector,in its linear action on R2.Proof Suppose by contradiction that the linear action of Dϕon the plane has zero as a uniquefixed point,and let Fϕbe the set offixed points forϕ.For any x∈Fϕwhich is not a singularity,there is a chart from a neighborhood U x of x to R2with x→0,and a smaller neighborhood V x⊂U x,such thatϕ(V x)⊂U x and when expressed in this chart,ϕ|V x is given by the linear action of Dϕon the plane.In particular x is the onlyfixed point in V x. Similarly,if x∈Fϕis a singularity,then there is a neighborhood U x of x which maps to R2 via afinite branched cover ramified at x→0,such that the action ofϕin V x⊂U x covers the linear action of Dϕ.Again we see that x is the onlyfixed point in V x.By compactness wefind that Fϕisfinite,contrary to hypothesis. Lemma4.5Suppose M is a lattice surface andϕ∈Aff(M)has Dϕ=−Id.Then afixed point forϕis periodic.Proof LetF1={σ∈Aff(M):Dσ=−Id}.Thenϕ∈F1and F1isfinite,since it is a coset for the group ker D which is known to be finite.Let A⊂M be the set of points which arefixed by someσ∈F1.By Lemma4.4this is afinite set,which contains thefixed points forϕ.Thus in order to prove the Lemma,it suffices to show that A is Aff(M)-invariant.Letψ∈Aff(M),and let x∈A,so that x=σ(x)with Dσ=−Id.Since-Id is central in GL2(R),D(σψ)=D(ψσ),so there is f∈ker D such thatψσ=fσψ.Thereforeψ(x)=ψσ(x)=fσψ(x),and fσ∈F1.This proves thatψ(x)∈A.Remark4.6This improves Theorem10of[8],where a similar conclusion is obtained under the additional assumptions that M is hyperelliptic and Aff(M)is generated by elliptic ele-ments.The following are immediate consequences:Corollary4.7Suppose(P,Q)is a suitable pair.Then•−Id/∈D(G Q).•None of the angles between two edges of Q are of the form p/q with gcd(p,q)=1and q even.Proof of Theorem4.2We will suppose that Q is such that(P,Q)are a suitable pair and reach a contradiction.If n is even,then Aff(M P)contains a rotation byπwhichfixes the points in M P coming from vertices of P.Thus by Lemma4.5all vertices of P give rise to periodic points,contradicting Proposition2.1(c).So n must be odd.Let x1,x2,x3be the vertices of P with corresponding angles1/n,1/2n,(2n−3)/2n. Then x3gives rise to a singularity,hence a periodic point.Also using Lemma4.5and the rotation byπ,one sees that x2also gives rise to a periodic point.So the unique branch point must correspond to the vertex x1.The images of the vertex x1in P give rise to two regular points in M P,marked c1,c2in Fig.2.Any element of G P acts on{c1,c2}by a permutation, so by Lemma4.3,G Q must be contained in the subgroup of index twofixing both of the c i. Let e1be the edge of P opposite x1.Since the reflection in e1,or any edge which is an image of e1under G P,swaps the c i,we have:e1is not a boundary edge of Q.(2) We now claim that in Q,any vertex which corresponds to the vertex x3from P is alwaysdoubled,i.e.consists of an angle of(2n−3)/n.Indeed,for any polygon P0,the group G P0 is the dihedral group D N where N is the least common multiple of the denominators of theangles at vertices of P0.In particular it contains-Id when N is even.Writing(2n−3)/2n in reduced form we have an even denominator,and since,by Corollary4.7,−Id/∈G Q,in Q the angle at vertex x3must be multiplied by an even integer2k.Since2k(2n−3)/2n is bigger than2if k>1,and since the total angle at a vertex of a polygon is less than2π,we must have k=1,i.e.any vertex in Q corresponding to the vertex x3is always doubled.This establishes the claim.It is here that we have used the assumption that Q is a polygon and not a parking garage.Fig.2Ward’s surface,n=5Fig.3Two options to start the construction ofQThere are two possible configurations in which a vertex x3is doubled,as shown in Fig.3. The bold lines indicate lines which are external,i.e.boundary edges of Q.By(2),the con-figuration on the right cannot occur.Let us denote the polygon on the left hand side of Fig.3by Q0.It cannot be equal to Q,since it is a lattice polygon.We now enlarge Q0by adding copies of P step by step,as described in Fig.4.Without loss of generality wefirst add triangle number1.By(2),the broken line indicates a side which must be internal in Q.Therefore,we add triangle number 2.We denote the resulting polygon by Q1.One can check by computing angles,using thefact that n is odd,and using Proposition2.3(4)that the cover M Q1→M P will branch overthe points a corresponding to vertex x2.Since the allowed branching is only over the points corresponding to x1,we must have Q1 Q,so we continue the construction.Without loss of generality we add triangle number3.Again,by(2),the broken line indicates a side which must be internal in Q.Therefore,we add triangle number4,obtaining Q2.Now,using Prop-osition2.3(4)again,in the cover M Q2→M P we have branching over two vertices u andv which are both of type x1and correspond to distinct points c1and c2in M P.This implies Q2 Q.Fig.4Steps of the construction of QSince both vertices u and v are delimited by2external sides,we cannot change the angle to prevent the branching over one of these points.This means that no matter how we continue to construct Q,the branching in the cover M Q→M P will occur over at least two points—a contradiction.Acknowledgments We are grateful to Yitwah Cheung and Patrick Hooper for helpful discussions,and to the referee for a careful reading and helpful remarks which improved the presentation.This research was supported by the Israel Science Foundation and the Binational Science Foundation.References1.Arnoux,P.,Schmidt,T.:Veech surfaces with non-periodic directions in the tracefield.J.Mod.Dyn.3(4),611–629(2009)2.Bouw,I.,Möller,M.:Teichmüller curves,triangle groups,and Lyapunov exponents.Ann.Math.172,139–185(2010)3.Cheung,Y.,Hubert,P.,Masur,H.:Topological dichotomy and strict ergodicity for translation surfaces.Ergod.Theory Dyn.Syst.28,1729–1748(2008)4.Cohen,M.:Looking for a Billiard Table which is not a Lattice Polygon but satisfies the Veech dichotomy,M.Sc.thesis,Ben-Gurion University(2010)/pdf/1011.32175.DeMarco,L.:The conformal geometry of billiards.Bull.AMS48(1),33–52(2011)6.Eskin,A.,Marklof,J.,Morris,D.:Unipotentflows on the space of branched covers of Veech surfaces.Ergod.Theorm Dyn.Syst.26(1),129–162(2006)7.Fox,R.H.,Kershner,R.B.:Concerning the transitive properties of geodesics on a rational polyhe-dron.Duke Math.J.2(1),147–150(1936)8.Gutkin,E.,Hubert,P.,Schmidt,T.:Affine diffeomorphisms of translation surfaces:Periodic points,Fuchsian groups,and arithmeticity.Ann.Sci.École Norm.Sup.(4)36,847–866(2003)9.Hubert,P.,Schmidt,T.:Infinitely generated Veech groups.Duke Math.J.123(1),49–69(2004)10.Masur,H.,Tabachnikov,S.:Rational billiards andflat structures.In:Handbook of dynamical systems,vol.1A,pp.1015–1089.North-Holland,Amsterdam(2002)11.Smillie,J.,Weiss,B.:Veech dichotomy and the lattice property.Ergod.Theorm.Dyn.Syst.28,1959–1972(2008)Geom Dedicata12.Veech,W.A.:Teichmüller curves in moduli space,Eisenstein series and an application to triangularbilliards.Invent.Math.97,553–583(1989)13.V orobets,Y.:Planar structures and billiards in rational polygons:the Veech alternative.(Russian);trans-lation in Russian Math.Surveys51(5),779–817(1996)14.Ward,C.C.:Calculation of Fuchsian groups associated to billiards in a rational triangle.Ergod.TheoryDyn.Syst.18,1019–1042(1998)15.Zemlyakov,A.,Katok,A.:Topological transitivity of billiards in polygons,Math.Notes USSR Acad.Sci:18:2291–300(1975).(English translation in Math.Notes18:2760–764)16.Zorich,A.:Flat surfaces.In:Cartier,P.,Julia,B.,Moussa,P.,Vanhove,P.(eds.)Frontiers in numbertheory,physics and geometry,Springer,Berlin(2006)123。
土木工程外文翻译-原文
外文原文Response of a reinforced concrete infilled—frame structure to removal of twoadjacent columnsMehrdad Sasani_Northeastern University, 400 Snell Engineering Center，Boston，MA 02115, UnitedStatesReceived 27 June 2007；received in revised form 26 December 2007；accepted 24January 2008Available online 19 March 2008AbstractThe response of Hotel San Diego，a six—story reinforced concrete infilled-frame structure，is evaluated following the simultaneous removal of two adjacent exterior columns. Analytical models of the structure using the Finite Element Method as well as the Applied Element Method are used to calculate global and local deformations. The analytical results show good agreement with experimental data. The structure resisted progressive collapse with a measured maximum vertical displacement of only one quarter of an inch （6.4 mm）。
工程管理外文翻译(原文+译文)
Concrete Construction matterT. Pauly, M. J. N. PriestleyAbstractViewed in terms of accepted practices, concrete construction operations leave much to be desired with respect to the quality, serviceability, and safety of completed structures. The shortcomings of these operations became abundantly clear when a magnitude 7.6 earthquake struck northern Paki-stan on October 8, 2005, destroying thousands of buildings, damaging bridges, and killing an esti-mated 79,000 people. The unusually low quality of construction operations prevalent was a major cause of the immense devastation.Keywords: Concrete Placing Curing Construction TechnologyPlacing ConcreteIf concrete is placed in the surface, the sur-face should be filled with water sufficiently to prevent it from absorbing the concrete of its water. If fresh concrete is to be placed on or nearby to concrete that has solidified, the surface of the placed concrete should be cleaned absolutely, preferably with a high-pressure air or water jet or steel-wire brushes. The surface should be wet, but there should be no much water. A little quantity of cement grout should be brushed over the whole area, and then followed immediately with the application of a 1/2-in Layer of mortar. The fresh concrete should be placed on or against the mortar.In order to decrease the disintegration re-sulting from carriage after it is placed. The con-crete should be placed as nearly as probably in itsfinal point. It should be placed in layers to permit uniform compaction. The time interval between the placing of layers should be limited to assure perfect bond between the fresh and previously placed concrete.In placing concrete in deeper patters, a ves-sel should be used to limit the free fall to not over 3 or 4 ft, in order to prevent concrete disintegra-tion. The vessel is a pipe made of lightweight metal, having adjustable lengths and attached to the bottom of a hopper into which the concrete is deposited. As the patters are filled, sections of the pipe may be removed.Immediately after the concrete is placed, it should be compacted by hand pudding or a me-chanical vibrator to eliminate voids. The vibrator should be left in one position only long enough to reduce the concrete around it to a plastic mass; then the vibrator should be moved, or disintegra-tion of the aggregate will occur. In general, the vibrator should not be permitted to penetrate concrete in the prior lift.The mainly advantage of vibrating is that it permits the use of a drier concrete, which has a higher strength because of the reduced water content. Among the advantages of vibrating con-crete are the following:1.The decreased water permits a reduction in the cement and fine aggregate because less cement paste is needed.2.The lower water content decreases shrinkage and voids.3.The drier concrete decreases the cost of finishing the surface.4.Mechanical vibration may replace three to eight hand puddles.5.The lower water content increases the strength of the concrete.6.The drier mixture permits theremoval of some patters more quickly, which may reduce the cost of patters.Curing ConcreteIf concrete is to gain its maximum strength and other desirable properties, it should be cured with adequate moisture and at a favorable tem-perature. Failure to provide these conditions may result in an inferior concrete.The initial moisture in concrete is adequate to hydrate all the cement, provided it is not should replace the moisture that does evaporate. This may be accomplished by many methods, such as leaving the patters in place, keeping the surface wet, or covering the surface with a liquid curing compound, which comes being to a water-tight membrane that prevents the escape of the initial water. Curing compounds may be applied by brushes or pressure sprayers. A gallon will cover 200 to 300 sq ft.Concrete should be placed at a temperature not less than 40 or more than 80°F.A lower tem-perature will decrease the rate of setting, while ahigher temperature will decrease the ultimate strength.Placing Concrete in Cold WeatherWhen the concrete is placed during cold weather, it is usually necessary to preheat the water, the aggregate, or both in order that the ini-tial temperature will assure an initial set and gain in strength .Preheating the water is the most ef-fective method of providing the necessary tem-perature. For this purpose a water reservoir should be equipped with pipe coils through which steam can be passed, or steam may bedischarged directly into the water, several outlets being used to given better distribution of the heat.When the temperatures of the mixtures are known, some specific charts may be used to cal-culate the temperature of concrete. A straight line pass all three scales, passing through every two known temperatures, will assure the determina-tion of the third temperature. If the surface of sand isdry, the fact lines of the scales giving the temperature of concrete should be used. However, if the sand contains about 3 percent moisture, the dotted lines should be used.Specifications usually demand that freshly placed concrete shall be kept at a temperature of not less than 70°F for 3 days or 50°F for 5 days after it is placed. Some proper method must be provided to keep the demanded temperature when the cold weather is estimated.Reinforcing steels for concreteCompared with concrete, steel is a high strength material. The useful strength of ordinary reinforcing steels in tension as well as compres-sion, i.e., the yield strength, is about 15 times the compressive strength of common structural con-crete, and well over 100 times its tensile strength. On the other hand, steel is a high-cost material compared with concrete. It follow that the two materials are the best used in combination if theconcrete is made to resist the compressive stresses and the compressive force, longitudinal steel reinforcing bars are located close to the ten-sion face to resist the tension force., and usually additional steel bars are so disposed that they re-sist the inclined tension stresses that are caused by the shear force in the beams. However, rein-forcement is also used for resisting compressive forces primarily where it is desired to reduce the cross-sectional dimensions of compression members, as in the lower-floor columns of multi-story buildings. Even if no such necessity exits , a minimum amount of reinforce- ment is placed in all compression members to safeguard them against the effects of small accidental bending moments that might crack and even fail an unre-inforced member.For most effective reinforcing action, it is essential that steel and concrete deform together, i. e., that there be a sufficiently strong bond be-tween the two materials to ensure that no relative movements of the steel bars and the surrounding concrete occur. This bond is provided by the rela-tively large chemical adhesion which develops at the steel-concrete interface, by the natural roughness of the mill scale of hot-rolled rein-forcing bars , and by the closely spaced rib-shap-ed surface deformations with which reinforcing bars are furnished in order to provide a high de-gree of interlocking of the two materials.Steel is used in two different ways in con-crete structures: as reinforcing steel and as prestressing steel .reinforcing steel is placed in the forms prior to casting of the concrete. Stresses in the steel, as in the hardened concrete, are caused only by the loads on the structure, except for possible parasitic stresses from shrinkage or similar causes. In contrast, in priestesses concrete structures large tension forces are applied to the reinforcement prior to letting it act jointly with the concrete in resistingexternal.The most common type of reinforcing steel is in the form of round bars, sometimes called rebars, available in a large range of diameters,from 10 to 35 mm for ordinary applications and in two heavy bar sizes off 44 and 57 mm these bars are furnished with surface deformations for the purpose of increasing resistance to slip be-tween steel and concrete minimum requirements for these deformations have been developed in experimental research. Different bar producers use different patterns, all of which satisfy these requirements.Welding of rebars in making splices, or for convenience in fabricating reinforcing cages for placement in the forms, may result in metal-lurgical changes that reduce both strength and ductility, and special restrictions must be placed both strength and ductility, and special restric-tions must be placed both on the type of steel used and the welding procedures the provisions of ASTM A706 relatespecifically to welding.In reinforced concrete a long-time trend is evident toward the use of higher strength materi-als, both steel and concrete.Reinforcing bars with 40ksi yield stress , almost standard 20 years ago , have largely been replaced by bars with 60ksi yield stress , both because they are more economical and because their use tends to reduce congestion of steel in the forms .The ACI Code permits reinforcing steels up to Fy=80ksi. Such high strength steels usually yield gradually but have no yield plateau in this situation the ACI Code requires that at the speci-fied minimum yield strength the total strain shall not exceed 0.0035 this is necessary to make cur-rent design methods, which were developed for sharp-yielding steels with a yield plateau, appli-cable to such higher strength steels. there is no ASTM specification for deformed bars may be used , according to the ACI Code , providing they meet the requirements stated under special circumstances steel in this higher strength range has its place, e.g., in lower-story columns of high-rise buildings.In order to minimize corrosion of rein-forcement and consequent spelling of concrete under sever exposure conditions such as in bridge decks subjected to deicing chemicals , galvanized or epoxy-coated rebars may be specified.Repair of Concrete StructuresReinforced concrete is generally a very du-rable structural material and very little repair work is usually needed. However, its durability can be affected by a variety of causes, including those of design and construction faults, use of inferior materials and exposure to aggressive en-vironment. The need for a repair is primarily dic-tated by the severity of the deterioration as de-termined from the diagnosis. Good workmanship is essential if any thing more than just a cosmetic treatment to the creation is required.1. performance requirements of repair systemHaving established the causes of the defect by carefully diagnosing the distress, the next step should be to consider the requirements of the re-pair method that will offer an effective solution to the problem (see fig.).①DurabilityIt is important to select repair materials that provide adequate durability. Materials used for the repair job should be at least as durable as the substrate concrete to which it is applied.②Protection of steelThe mechanism of protection provided to the reinforcing depends on the type of repair ma-terials used. For example, cementations materials can protect the steel from further corrosion by their inhibitive effect of increasing the alkalinity of the concrete, whereas epoxy resin mortars can give protection against the ingress of oxygen,moisture and other harmful agents.③Bond with substrateThe bond with the substrate must produce an integral repair to prevent entry of moisture and atmospheric gases at the interface. With most re-pair materials, the bond is greatly enhanced with the use of a suitable bonding aid such as an un-filled epoxy resin systems and slurry of Portland cement, plus any latex additives for a Portland cement-based repair system. Precautions should also be takento remove all loose and friable ma-terials from the surfaces to be bonded.④Dimensional StabilityShrinkage of materials during curing should be kept to a minimum. Subsequent dimensional change should be very close in the substrate in order to prevent failure⑤Initial Resistance to Environmentally In-duced DamageSome initial exposure conditions may lead to premature damage lo repairs. For example, partially cured Portland cement repairs can dete-riorate from hot weather preventing full hydration of the cement. To prevent this from happening extra protection during curing time may be nec-essary.⑥Ease of ApplicationMaterials should be easily mixed and ap-plied so that they can be worked readily into small crevices and voids. Ideally, the material should not stick to tools, and should not shear while being trowel led nor slump after placement.⑦AppearanceThe degree to which the repair material should match the existing concrete will depend on the use of the structure and the client' s re-quirements. A surface coating may be required when appearance is important or when cover to reinforcement is small.2. Selection of Repair MethodsA suitable repair counteracts all the defi-ciencies which are relevant to the use of the structure.The selection of tile correct method and material for a particular, application requires careful consideration, whether to meet special requirements for placing strength, durability or other short-or long-term properties. These con-siderations include:1. Nature of the DistressIf alive crack is filled with a rigid material, then either the repair material will eventually fail or some new cracking will occur adjacent to the original crack. Repairs to live cracks must either use flexible materials to accommodate move-ments or else steps must be taken prior to the re-pair to eliminate the movement.2. Position of the CrackTechniques which rely on gravity to intro-duce the material into the crack are more suc-cessfully carried out on horizontal surfaces but are rarely effective on vertical ones.3. EnvironmentIf moisture, water or contaminants are found in the crack, then it is necessary to rectify the leaks Repair to slop leaks may be further com-plicated by the need to make the repairs while the structure is in service and the environment is damp.4. WorkmanshipThe skill the operatives available to carry put the repairs is another relevant factors. Some-times this can mean the difference between a permanent repair and premature failure of the re-pair material.5. CostThe cost of repair materials is usually small compared with the costs of providing access, preparation and actual labor.6. AppearanceThe repair surface may be unsightly, par-ticularly when it appears on a prominent part of the building. In this case, the repair system will include some form of treatment over the entire surface.Reference[1]Philip Jodidio, Contemporary European Architecture, Taschen, Koln, pp.148-153[2]Ann Breen & Dick Rigby, Waterfronts, McGraw-Hill, Inc. New York, 1994, pp.297-300[3]Ann Breen & Dick Rigby, The New Waterfront, Thames and Hudson, London, 1996, pp.118-120[4]Ann Breen & Dick Rigby, The New Waterfront, Thames and Hudson, London, 1996, pp.52-55[5]Robert Holden, International Landscape Design, Laurence King Publishing, London, 1996, pp.10-27[6] A new concept in refrigerant control for heat pumps ,J.R.Harnish,IIR Conference Pa-per,Cleveland,Ohio.May,1996[7]Carrier Corporation-Catalog 523 848,1997[8]Waste Heat Management Handbook, Na-tional Bureau of Standardc Handbook 121, Pub-lica-tion PB 264959, February,1997Ten design principles for air to air heat pumps,Allen Trask,ASHRAE Journal,July,1997重庆科技学院学生毕业设计（论文）外文译文学院建建筑工程学院专业班级工管103学生姓名李学号201044241附件1：外文资料翻译译文混凝土施工事项T.Pauly, M.J.N.Priestley摘要：根据一般承认的惯例看,巴基斯坦的混凝土结构建筑物在结构上的质量，效用和安全需要上都留下了很多值得关注的问题。
外文翻译原文.
e c o l o g i c a l e n g i n e e r i n g 28(2006124–130a v a i l ab l e a t w w w.sc i e n c ed i re c t.c omj o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /e c o l e n gPlant-biofilm oxidation ditch for in situ treatm ent of polluted watersQi-Tang Wu a ,∗,Ting Gao a ,Shucai Zeng a ,Hong Chua ba College of Natural Resources and Environment,South China Agricultural University,Guangzhou 510642,ChinabDepartment of Civil and Structural Engineering,Hong Kong Polytechnic University,Hung Hom,Kowloon,Hong Kong SAR,Chinaa r t i c l ei n f o Article history:Received 17December 2005Received in revised form 16May 2006Accepted 18May 2006Keywords:Plant-biofilm oxidation ditch (PBFODIn situWastewater treatmenta b s t r a c tEutrophication of surface water bodies is a problem of increasing environmental and ecolog-ical concern worldwide and is particularly serious in China.In the present study,oxidation ditches were connected to a lake receiving municipal sewage sludges.T wo 24m 2(width 2m,length 12mparallel plastic oxidation ditches material were installed on a lake near the inlet of the municipal sewage.Zizania caduciflora and Canna generalis were grown in the ditches with plastic floating supporters for the removal of N and P from the sewage.The experiment was conducted firstly with municipal sewage in autumn–winter seasons for about 150daysunder the following conditions:2m 3/h influent flow,0.75kW jet-flow aerator(air/water of 5,18h HRT (hydrological retention timeand a return ratio of 10.Then it was run with the polluted lake water in summer–autumn for about 160days with an aerator of 1.25kW and an influent of 6m 3/h (air/water 3.3,HRT 6h.The performance was quite stable during the experimental period for the municipal sewage treatment.The average removal rates of COD (chemical oxygen demand,SS (suspended solids,TP (total phosphorus,NH 4+-N and inorganic-N were 70.6,75.8,72.6,52.1and50.3%,respectively.For the polluted lake water treatment,the average concentrations of COD,NH 4+-N and TP were 42.7,13.1and 1.09mg/L,respectively,in the influent and were 25.1,6.4and 0.38mg/L,respectively,in the effluent.The capacity of the plants to remove N and P by direct uptake was limited,but the indi-rect mechanisms also occurred.The proposed process,transforming the natural lake into a wastewater treatment plant,could evidently reduce the costs of the sewage collection,the land space requirement and the construction compared with conventional sewage treat-ment plants,and is especially suited to conditions in south China and south-east Asia.©2006Elsevier B.V .All rights reserved.1.IntroductionMany water bodies are subject to eutrophication due to eco-nomic constraints in reducing point sources of nutrients and/or to a high proportion of diffuse sources,and the prob-lem is particularly common in China because the proportion of treated municipal sewage is still low due to the relatively high capital investmentrequired.Accordingly,43.5%of 130investi-gated major lakes in China were found to be highly eutrophied∗Corresponding author .Tel.:+862085280296;fax:+862085288326.E-mail address:qitangwu@ (Q.-T.Wu.and 45%were of intermediate status (Li et al.,2000.These pol-luted lakes were mainly located in economically developed regions and especially around cities where large amounts of municipal sewage are discharged without appropriate treat-ment.Increasingly,natural or constructed wetlands,including buffer zones(Correll,2005,are being used for removal of pol-lutants from wastewater or for treatment of stormwater runoff from agricultural land and other non-point sources (Mitsch ete c o l o g i c a l e n g i n e e r i n g28(2006124–130125Table1–COD and BOD5of the study lake sampled at three points for5days inMay2003COD(mg/LBOD5(mg/LBOD5/COD13May89.5135.700.4083.3334.500.4189.5136.600.4114May55.5624.800.4589.5135.200.3949.3820.900.4227May105.1141.300.3981.0832.300.40111.1141.000.3728May60.0026.830.4563.3327.700.4463.3327.000.4329May90.0035.700.4093.3337.000.40117.9949.400.42al.,2000;Coveney et al.,2002;Belmont et al.,2004.However, this method requires a large land area in addition to the lake in question.For in situ treatment of hypereutrophic water bodies where the transparency of the water does not allow regrowth of submerged macrophytes,phosphorus precipitation in eutrophic lakes by iron application(Deppe and Benndorf, 2002or by additions of lime(Walpersdorf et al.,2004has been reported.Aeration of river water has been employed to remediate polluted rivers since the1970s(Wang et al.,1999. Increasing oxygen transfer inflow by stones placed in rivers was studied by Cokgor and Kucukali(2004.Growingfloating aquatic macrophytes(Sooknah and Wilkie,2004or terrestrial green plants usingfloating supports(Li and Wu,1997,physical ecological engineering(PEEN(Pu et al.,1998,and biotic addi-tives have also been applied(Chen,2003.However,these sim-ple designs do not constitute a real water treatment system and the efficiencies of these treatments are unsatisfactory.Activated sludge systems have been proved efficient treat-ing municipal sewage since the1960s(Ray,1995.However, this type of system has not been used for in situ remediation of polluted lakes or rivers.In the present study,the oxidation ditch technique was adopted on a lake receiving municipal sewage sludge.Floating green plants and the biofilms com-prisingfloating materials and plant roots were also added to enhance N and P removal.A pilot scale experiment was set up to test the feasibility and performance of the plant-enhanced oxidation ditch for in situ treatment ofboth the municipal sewage and the polluted lake water.2.Experimental2.1.Site descriptionThe study lake was situated at South China Agricultural Uni-versity,Guangzhou,China.The area of the lake was about 10000m2and the depth0.5–3m.This lake received the munic-ipal sewage from the residential area around the university.Fig.1–Surface arrangement of the plant-biofilm oxidation ditch and the waterflows.(1Wall of nylon tissue;(2nets of5mm;(3nets of0.25mm;(4oxidation ditch;(5jet-flow aerator;(6water pump;(7floating green plants;(8sewage entry.2.2.Establishment of the plant-biofilm oxidationditchesT wo24m2(width2m,length12mparallel oxidation ditches made of plastic materials were installed along the lake bank near the sewage inlet.The inner ditch was made of cement and the outer ditch was isolated with nylon tissues andfix-ing PVC(polyvinyl chloridetubes.Fig.1showsthe surface arrangement and the waterflow path.The coarse suspended solids in the influent werefiltered by two pl astic nets,one with a pore size of5mm and the other with a pore size of0.25mm,whereas the suspended solids in the effluent werefiltered by a plastic net with a pore size of 0.25mm.Zizania caduciflora and Canna generalis were grown in the ditch with theplast icfloating supporters which held the plants in position.Thefloating supporters were made of closed126e c o l o g i c a l e n g i n e e r i n g28(2006124–130PVC tubes and nylon nets and each was3.6m2.Zizania caduci-flora was grown on twofloating supporters an d Canna gener-alis on another two supporters.The plants were planted in four columns andfive lines.The twofloating supporters with Canna generalis were near the influent and the two with Zizania caduciflora were near the effluent.The entire disposal system is shown in Photo1.2.3.Conduct of the experimentsAn experiment was conductedfirstly on municipal sewage in autumn–winter seasons of2003–2004for about150days. The aeration of the oxidation ditch was achieved using a jet-flow aerator of0.75kW(Aqua Co.,Italy;air generation10m3/h, water jet rate22–28m3/h.The water sampling started on18 September2003and endedon12February2004.The influent was2m3/h created by a water pump of0.37kW.With the jet-flow aerator of0.75kW the theoretical air/water ratio was5, HRT was18h and the return ratio was10–13.The system was then run with the polluted lake water in summer and autumn2004for about160days with an aerator of1.25kW and with an influent of6m3/h(air/water3.3,HRT 6h.The influent was not created by water pump but by the driving fo rce of the jet-flow aerator.The water sampling for the second run started on15May2004and endedon15October 2004.2.4.Sampling and analysisThe influent and effluent were sampled every3–5days at 08:00–09:00a.m.andat17:00–18:00p.m.,each with three sam-pling re plicates for thefirst run.For the second run,the influ-ent and effluent were sampled1day a week.The water sam-pler took0–30cm surface water.The samples were analyzed for COD Cr,BOD5,SS,TP,NO3−-N,NH4+-N and pH according to standard methods(APHA,1995.The plant s were transplanted ontofloating supporters two weeks before water sampling and thefirst harvest was carried out60days later and at the termination of thefirst run for the municipal sewage.The plant biomass and N and P con-tents were measured according to the methods proposed by the Soil and Agro-Chemical Analysis Committee of China(Lu, 2000.The total uptakes of N and P were calculated and com-pared with the total removal of these elements calculated by the cumulative removal each day following measurement of a water sample.Total N removal=(average N in influent−average N in effluent×48×D iwhere48was the treated water volume per day in m3/day;D i was the number of days following the water sampling and before the next sampling.3.Results and discussionTable2shows the removal of COD Cr and SS by plant-biofilm oxidation ditch for the treatment of the municipal sewage in autumn–winter seasons of2003–2004.The removal of COD Cr varied from60to79%with an average of70%for the influent COD Cr ranging from100to200mg/L,a nd resulted in effluent COD Cr valuesfrom30to55mg/L(Table2,Fig.2.The average removal percentage was about75%for SS and variedfrom68to82%(Table2.The effluent SS was about 30mg/L which is the effluent limit value of the second grade for the sewage treatment plants in China(GB18918,2002 (Fig.3,for the influents varying from60to240mg/L.The average NH4+-N removal from influent was52%,which was lower in winter than in autumn(Table3.This may be due to lower bacterial activity in winter,but theinfluent NH4+-NTable2–Removal of COD and SS by the plant-biofilm oxidation ditch for the in situ treatment of municipal sewage each month in autumn–winter seasons of2003–2004Period Sampled days Water temperature(◦CInfluent(mg/LEffluent(mg/LRemoval(%COD Cr18–30September528.0118.54(3.01a34.34(7.8367.74 3–28October826.1123.91(4.0333.51(4.2672.661–7November326.0153.94(2.7337.60(3.8175.4918–28November423.1170.22(4.2835.45(5.3778.711–15December419.3180.36(8.2039.24(7.0677.6511–31January314.5128.46(3.6652.04(5.2359.504–12February216.8178.35(4.1662.86(5.8362.47Average150.54(4.3042.15(5.6370.60SS18–30September528.0160.4041.6074.18 3–28October826.1144.3826.2581.171–7November326.0116.0033.3370.7918–28November423.1111.7521.5080.981–15December419.390.5028.5068.4211–31January314.5104.0017.3382.384–12February216.8120.5033.0072.57Average121.0828.7975.78e c o l o g i c a l e n g i n e e r i n g28(2006124–130127Fig.2–COD in the influent and effluent of the plant-biofilm oxidation ditch for the in situ treatment of municipal sewage in autumn–winter seasons of2003–2004.was also higher in winter(Fig.4probably because of lower water consumption in the cold season.The total inorganic-N removal was similar to that for NH4+-N(Table3.NO3−-N concentrations were rather similar in the influent and the effluent.The total P removal varied from63to78%and was higher and more regular than N removal(Table3.The P concentra-tion in treated effluent was about1mg/L(Fig.5and conformed to the Chinese municipal sewage treatment standard which is set to3mg/L for second grade regions and1.5forfirst grade regions(GB18918,2002.Fig.6shows typical changes in the water quality param-eters for the sampling points from inlet to outlet.Thisindi-Fig.3–Suspended solids concentration in the influent and effluent of the p lant-biofilm oxidation ditch for the in situ treatment of municipal sewage in autumn–winter seasons of2003–2004.cates that COD and SS decreased gradually,but NH4+-N and TP dropped substantially following the mixing with the return water by the aerator and then decreased slowly,while NO3−-N and pH of the water remained virtually unchanged.The water DO increased dramatically following the aeration,decreased slowly thereafter and remained rather high even in the efflu-ent(about5.5mg/L.For the second run treating the polluted lake water on-site,the average influent COD Cr was42.7mg/L and the effluent 25.1mg/L for about160days during summer–autumn seasons (Fig.7.The removal of NH4+-N was about50%from about13.1 to6.4mg/L.Total-P in the effluents was rather stable,bei ngTable3–The removal of N and P by the plant-biofilm oxidation ditch for the in situ treatment of municipal sewage for each month in autumn–winter seasons of2003–2004Period Sampled days Water temperature(◦CInfluent(mg/LEffluent(mg/LRemoval(%NH4+-N18–30September528.020.60(0.30a7.16(0.2264.72 3–28October826.126.55(0.2310.15(0.2061.671–7November326.030.00(0.4113.67(0.2254.5118–28November423.135.15(0.7915.95(0.2653.991–15December419.335.89(0.3515.93(0.2755.1511–31January314.530.57(0.6918.59(0.2236.634–12February216.835.23(0.0521.61(0.0637.72Average30.57(0.4014.72(0.2152.06NH4+-N+NO3−-N18–30September528.023.06(0.159.24(0.1159.94 3–28October826.128.31(0.1212.01(0.1457.571–7November326.031.42(0.2114.58(0.1153.5918–28November423.136.32(0.4016.81(0.1353.721–15December419.337.41(0.1917.54(0.1453.1111–31January314.531.96(0.3720.07(0.1337.204–12February216.837.11(0.0323.35(0.0337.08Average32.23(0.2116.23(0.1150.32TP18–30September528.0 3.56(0.070.81(0.0475.56 3–28October826.1 4.01(0.140.87(0.0478.241–7November326.0 4.37(0.13 1.20(0.0472.5618–28November423.1 4.89(0.16 1.13(0.0776.661–15December319.5 4.86(0.80 1.38(0.2371.07 11–31January314.5 3.75(0.45 1.35(0.0363.32 4–12February216.8 4.75(0.10 1.51(0.0566.20 Average 4.31(0.16 1.16(0.0471.89128e c o l o g i c a l e n g i n e e r i n g 28(2006 124–130Fig.4–NH 4+-N concentration in the influent and effluent of the plant-biofilm oxidation ditch for the in situ treatment of municipal sewage in autumn–winter seasons of2003–2004.Fig.5–Total-P concentration in the influent and effluent of the plant-biofilm oxidation ditch for the in situ treatment of municipal sewage in autumn–winter seasons of2003–2004.Fig.6–T ypical changes in the pollutants in theplant-biofilm oxidation ditch during the in situ treatment ofFig.7–The influent and effluent concentrations of COD (up,NH 4+-N (medianand total-P (bottomin theplant-biofilm oxidation ditch treating polluted lake water.about 0.38mg/L from an average of 1.09mg/L in the influents.The removal of COD Cr ,NH 4+-N and Total-P was then quite sat-isfactory both for the municipal sewage and the polluted lake water.The removal of N and P was somewhat higher than con-ventional oxidation ditches,perhaps due to the existence of the plant-biofilm in the studiedsystem.However,the direct uptake rates of N and P by green plants were almost negligi-ble compared to the total removal of these elements by the whole system (Table4.However,the plants may have cre-ated localized anaerobic conditions by their root exudates and dead biomass and enhance the denitrification of N by micro-organisms as occurs in constructed wetlands (Hone,2000.Besides the green plants,the proposed system also con-tains biofilm coated to the plastic materials.The high velocity of return-fluent was different to the conventional oxidation ditch.Kugaprasatham et al.(1982showed that the increase of the fluent velocity could increase the density of the biofilm if the nutrient conditions were suitable for bacteria growth.Simultaneous nitrification/denitrification (SND(Van Mun ch etal.,1996may also occur in the system.Concerning the P removal of the system,biological phos-phate removal processes may occur but were not significant because there was no sludge removal and very little sludge precipitation after the run for treatment of municipal sewage.This may partly due to the existence of some ferric chains which were added to precipitate and fix the nylon tissue to the lake bottom,with formation of precipitates of ferric phos-e c o l o g i c a l e n g i n e e r i n g 2 8 ( 2 0 0 6 124–130 129 Table 4 – Proportions of N and P uptake by plants and total removal in the plant-biofilm oxidation ditch treating municipal sewage Date Days ZCa Harvested fresh biomass (g CG ZC 5 September–4 November 5 November–6 January Total or average a Plant uptake (g N CG 5.30 13.03 System removal (kg N CG P Percent of plant uptake N (% P (% P ZC 0.88 0.24 2.79 60 63 123 2200 625 9725 2750 4150 4.85 1.20 24.38 0.72 0.95 37.63 65.45 103.1 7.13 12.78 19.91 0.03 0.02 0.02 0.02 0.01 0.01 ZC: Zizania caduciflo ra; CG: Canna generalis. tained for at least 1 year. The actual mechanisms still remain to be identified. The oxidation ditch has been used for many years worldwide as an economical and efficient wastewater treatment technology that can remove COD, nitrogen and a fraction of the phosphorusefficiently. Anaerobic tanks (Liu et al., 2002 and phased isolation ditch systems with intra-channel clarifier (Hong et al., 2003 were added to the system to increase the TP removal efficiency. The proposed process takes an artificial process in combination with natural purification, transforming the natural lake into the wastewater treatment plant, and could evidently reduce the costs of sewage collection, the landspace requirement and the construction costs compared with the conventional sewage treatment plants. This process could be especially suitable to subtropical regions and to many water bodies in south China and southeast Asia where sewage treatment facilities are not well established. China. The authors are grateful to Dr. P. Christie, Department of Agricultural and Environmental Science, Queen’s University Belfast, UK, and Dr. Y. Ouyang, Department of Water Resources, St. Johns River Water Management District, Palatka, FL, USA, for their valuable suggestions and language corrections. references 4. Conclusions The present study adapted the oxidation ditch on the lake surface for in situ treatment of municipal sewage or polluted lake water in combination with plant biofilms for performing N and P removal, and running experiments at pilot scale for about 1.5 years resulted in the following observations: (1 The system was quite satisfactory and stable for treatment of municipal sewage and polluted lake water in removing COD, NH4 + -N and P. (2 The direct uptake of N and P by plants was negligible in comparison with the totalremoval by the system, but indirect mechanisms via plant root exudates and biofilms merit further studies. (3 The proposed process could dramatically reduce the costs of sewage collection, the land-space requirement and the construction costs compared with conventional sewage treatment plants; might be suitable for treatment of both municipal sewage and polluted lake water; and could lead to the promotion of wastewater treatment in many developing countries. Acknowledgements This study was funded by Department of Science and Technology of Guangdong Province (Grant no. 2004B33301007, American Public Health Association (APHA, 1995. Standards Methods for the Examination of Water and Wastewater, 19th ed. American Public Health Association, Washington, DC. Belmont, M.A., Cantellano, E., Thompson, S., Williamson, M.,S’anchez, A., Metcalfe, C.D., 2004. Treatment of domestic wastewater in a pilot-scale natural treatment system in central Mexico. Ecol. Eng. 23, 299–311. Chen, Y.C., 2003. Bioremediation Engineering of Polluted Environment. Chemical Industry Press, Beijing, p. 304 (in Chinese. 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A physico-ecological engineering experiment for water treatment in a hypertrophic lake in China. Ecol. Eng. 10, 179–190. Ray, B.T., 1995. Environmental Engineering. PWS Publishing Company, New York, pp. 299–341. Sooknah, R.D., Wilkie, A.C., 2004. Nutrient removal by floating aquatic macrophytes cultured in anaerobically digested flushed dairy manure wastewater. Ecol. Eng. 22, 27–42. Van Munch, E.P., Land, P., Keller, J., 1996. Simultaneous nitrification and denitrification in bench-scale sequencing batch reactors. Water Sci. Technol. 20,277–284. Wang, C.X., Lin, H., Shi, K.H., 1999. Restoration of polluted river by pure oxygen aeration. Shanghai Environ. Sci. 18, 411–413 (in Chinese. Walpersdorf, E., Neumann, T., Stuben, D., 2004. Efficiency of natural calcite precipitation compared to lake marl application used for water quality improvement in an eutrophic lake. Appl. Geochem. 19, 1687–1698.。
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毕业设计外文文献翻译院系：数学与计算机科学学院年级专业：12级数学与应用数学姓名：施钰桢学号：121301025有限维向量空间本文译自：Paul R.Halmos. Finite-Dimensional Vector Spaces. Library of Congress Cataloging in Publication Data, 1916.§2.向量空间现在我们来到了这本书的基本概念这里.有如下的定义，令F是一个数域; F中的元素叫做标量.定义：向量空间V满足以下公理.（A）对于任意的x和y，在V中有唯一确定的向量与它们对应，称为x与y的和，并记作x+ y，满足：（1）交换律，x+ y= y+x.（2）结合律，x+（y+z）=(x+y)+z.（3）在V中存在一个独特的向量0（称为原点），对于任意向量x使得+0.xx=（4）对于任意向量x，V中存在一个向量-x与之对应，使得x+（- x）= 0. （B）对于任意α和x，其中α是一个标量，x是V中的向量，在V中有唯一确定的向量与它们对应，称为α和x的积，记作αx，有如下公式：（1）乘法结合律，α（βx）=（αβ）x.（2）对每个向量x有，1x=x.（C）（1）向量乘法分配律，α（x+ y）=αx+αy.（2）标量乘法分配律，（α+β）x=αx+βx.这些公理在逻辑上不要求是独立的，它们只是其中的一个特性，为了方便我们研究.向量空间V和数域F之间的关系通常被描述为V是F上的向量空间.如果F是实数域R，V被称为实数向量空间;同样，如果F是Q或者是E，我们称V为有理向量空间或复数向量空间.§3.实例在讨论关于公理的影响前，我们举一些例子.在整个操作中我们将一遍又一遍参考这些例子，并利用现有的符号.（1）让1E （=E ）为复数的集合，如果我们令x +y 和αx 为普通的复数加 法和乘法，则1E 为复数域上的向量空间.（2）p 为所有多项式的集合，变量t 为复数系.我们解释到复数多项式的加法和乘法能写成向量加法和乘法，就称p 为复数向量空间；原点在多项式p 中恒等于零.这本书的典型例子即实例（1）太过简单实例（2）太复杂.我们再举一个例子，复数向量空间（我们将在后面看到）一般足够为我们所用.（3）设n E ,n =1,2,…, 是所有n 元复数的集合.如果x =（1ξ，...,n ξ）和 y =（1η，...,n η），根据定义,有x +y = (1ξ+1η,…, n ξ+n η),x α= (α1ξ,…, αn ξ),0 = (0,…,0),-x = (-1ξ,…,- n ξ).这些§2中的真理（A ），（B ）与（C ）都很容易满足，所以n E 是一个复数向量空间，被称为n 维复坐标空间.（4）对于每个正整数n ，设n P 为所有多项式的集合（复系数，如实例（2））当维≤n -1时，多项式恒等于零. （通常都是以维来讨论的，这多项式的维是没有定义，所以我们不能说维≤n -1）跟线性运算的解释一样（加法和标量乘法）如（2）n P 是一个复数向量空间.(5)与n E 相近的所有n 维实数为n R ，它跟n E 的加法和标量乘法的定义相同，但现在我们只考虑实数标量α，空间n R 是一个实数向量空间，它会被称为n 维实坐标空间.（6）前述所有实例可以进行推广.例如，（1）中的一个明显的概括，可以说每个所述的数域可以被视为其自身的向量空间.一个常见的推广（3）和（5）是由任意数域F和n维F元素构成集合nF;相同情况下线性运算的正式定义为F=E.（7）根据定义，数域至少具有两个元素;一个是向量空间.由于每个向量空间包含原点，实际上（即除符号）一个向量空间只具有一个向量，这个是最简单的向量空间将用 来表示.（8）如果在所有实数域R中，加法和有理实数乘法的定义跟之前是一样的，那么R为实数向量空间.（9）如果在所有复数的集合E中，加法和复实数乘法的定义跟之前是一样的，那么E为复数向量空间. （将此例与（1）对比，他们有很大的不同）§4.评论公理和符号的评论.数域和向量空间的公理存在惊人的相似之处（和同样惊人的差异）.在这两种情况下，公理（A）中描述了该系统的加法结构，公理（B）描述了其乘法结构，公理（C）说明两种结构的联系，（在§1和§2）中的公理（A）的交换律是代数中较为熟悉的术语; （§2）中公理（B）及（C）中承认了标量作为运算的符号.我们顺便提下，如果标量是元素（而不是数域），相应的向量空间的广义概念称为模.特殊实向量空间（如2R和3R）是熟悉的几何图形.似乎在这个阶段坚持R以外的数域显然是没有任何理由的，特别是复数域E.我们希望读者愿意去相信它，我们后面尽量使用复数性质（共轭，代数包闭），并且，我们的研究结果为希尔伯特空间的复数的推广在向量空间中的两个应用程序现代（量子力学）物理和数学中发挥重要的作用.它的一大缺点就是画图难度大.对普通图（阿根图）1E和2R 图是无法区别的，用图形表示似乎是超出人能达到的范围.因此我们不得不使用E和n R，例如将2E称为平面.一些图像语言来区分n最后，我们对符号评论.我们观察到的符号0具有两个含义：一个作为标量，一个作为向量.为了使情况变的不那么糟，我们将在后面引入线性泛函与线性变换来给它下定义.幸运的是，0 的各种解释由此可得知，紧记这句话，我们就不会混淆了.练习1.证明，如果x 和y 是向量，α是一个标量，则下面的关系成立.0),(00),(0),(=∙=-=+αc b xx a00),(=∙x d (观察到相同的符号被用在这个等式的两边;左侧它表示的是标量，右侧它表示的是向量.)(e) 如果αx =0，那么α=0或x =0（或α=0且x =0）(f) –x =(-1) x(g) y +(x -y )=x (这里x -y =x +（-y ）)2. 如果P 是素数，则nP Z 是向量空间（cf. §1，例3）;在这个向量空间里有多少个向量？3. 设V 是所有（命令）对数或实数的集合.如果),(21ξξ=x 和),(21ηη=y 为V 中的元素，有x +y = ），（2211ηξηξ++αx = ），（01αξ 0 =（0,0） -x = ），（21--ξξ在线性操作的这些定义中V 是一个向量空间吗？为什么？4. 有时一个向量空间中的一个子集,本身就是一个向量空间(线性操作已经给出).例如,向量空间3E 和3E 中子集V 组成的向量），，（321ξξξ，有（a ）1ξ是实数（b ）1ξ=0（c ）1ξ=0或2ξ=0（d ）1ξ+2ξ=0（e ）1ξ+2ξ=1在这种情况下V 是向量空间？5. 考虑到向量空间p 和p 中的子集V 组成的向量(多项式)x ,有（a ）x 有3维（b ）2x （0）=x （1）（c ）x （t ）≥0，（0 ≤ t ≤ 1）（d ）x （t ）=x （1-t ），t 取任意数在这种情况下V 是向量空间？§5.线性关系既然我们已经描述了向量空间,我们一定会对空间中的元素关系感到兴趣. 我们对求和符号描述几句.如果一组向量被赋于相应的一组指标i 即为i x ,如果没有必要或者不方便对指标进行详细说明,我们将简单地讲一组向量{i x }.(我们承认相同的向量可能有两个不同的指标与之相对应.因此,应该说,重要的不是向量出现在{i x }中,而是它们是如何出现的.) 如果考虑指标集是有限的,我们就把相应的向量之和记为i i x ∑（或者，可更加明确的记为∑=n1i i x ）.为了避免频繁和繁琐,承认i i x ∑作为一般理论的总结是一个好主意，即使之前没有指标i 作总结,或者更准确地说,即考虑指标集是空的.（当然,在这种情况下是没有向量和，或者更准确地说, {i x }也是空的）.这种“空的和”很显然定义为向量0.定义：如果存在一组相对应的标量{i a },且它们不全为0，使得0=∑ii i x a 则称有限向量组{i x }是线性相关.另一方面,如果使0=∑ii i x a 当且仅当i a =0(对于任意i ),则称{i x }是线性无关.这个定义的说法是指在空集情况下,虽然可能产生矛盾,但其它部分的理论还是相对吻合的.其结果表明，空集向量是线性无关的.实际上,如果没有指标i ,那么从向量中挑出一部分并分配给选定的非零标量使其之和消失是不可能的.问题不在于避免赋值为零,而在于分配指标.注意,这种观点表明,空集不是线性相关;线性无关的定义与直接否定线性相关的定义是等价的，这个说法还是需要一些直观理由.最简单的说法是“0=∑ii i x a 当且仅当i a =0(对于任意i )”.假使没有指标i ，则另有说法：“如果0=∑ii i x a 没有指标i ，则i a ≠0”,如果不存在指标i ，这个版本显然是如此.线性相关和无关是向量集的属性，它是司空见惯的,然而对于向量本身的形容词应用,我们有时会说“一组线性无关的向量”而不是“线性无关的一组向量”.它也可以简单的说向量x 的线性相关和无关，并不一定要是有限集.为了深入了解线性相关的意义，我们用已有的向量空间的例子来学习.(1) 如果x 和y 是1E 中的任意两个向量,则x 和y 是一组线性相关.如果x = y =0，这个并不重要;如果不是这样的,那么我们有y x +(-x )y =0的关系.很明显, 因为每组包含一个线性相关的子集本身就是线性相关,这表明在1E 的各个组中包含多个元素是一组线性相关.(2) 在空间P 情况下，向量y x ,和z 的定义，有,1)(),1()(,1)(2t t z t t t y t t x -=-=-=例如,当x +y -z =0则线性相关.然而对于无限的向量集,,,,210 x x x 的定义，有,,)(,)(,1)(2210 t t x t t x t x ===是一组线性无关的,如果存在形式01100=+++n n x a x a x a那么，我们就得到一个多项式的恒等式：010=+++n n t a t a a由此可得 010====n a a a(3) 正如我们前面提到的,空间n E 是我们要研究的原型,让我们来看看,当n = 3，对于那些熟悉的高维几何,线性相关的概念 (或者,更确切的说,与其类似的(3R ))在这个领域有一个具体的几何意义.我们只提及在几何语言中若两个向量是线性相关的，当且仅当它们是共线.（如果有人认为一个向量不是作为空间中的一个点,而是作为一个箭头指向即从原点指向某个给定的点,由于两次忽略了“原点”，所以前面的句子应该修改下）.我们目前介绍了向量空间中线性流形（或向量子空间）的概念，并在这方面，我们将偶尔使用这类几何语言.§6.线性组合我们说，只要ii i x a x ∑=，则x 是}{i x 一个线性组合;我们将没有任何进一步的解释，能使这个术语的所用语句更加简单.因此我们说,假如x 是}{i x 的线性组合,那么在{}i x 中x 是线性无关的；我们留给读者证明，如果{}i x 是线性无关的，它的充分必要条件是x 是}{i x 的一个线性组合.需要注意的是，按照空的和的定义，原点是空集的线性组合，而且这是此向量的唯一属性.下面的定理是关于线性相关的基本结果.定理：非零向量组)2(,,1n k x x k ≤≤ 是线性相关的，充分必要条件是向量组中至少有一个向量，可由其余个向量线性表示.证明.假设)2(,,1n k x x k ≤≤ 是线性相关的，则存在一组不为零的a ，使011=++k k x a x a成立，我们不妨设0≠k a ，我们就可得到1-1,,k x x 之间是线性相关.即111--++-=k kk k k x a a x a a x 因此k x 可由其余向量线性表示. 这证明了必要性条件;充分性是显而易见的,因为正如我们之前所说的,每组包含一个线性相关的子集其本身就是线性相关.§7.基定义：在向量空间V 中，存在一组线性无关的集合x ，使得V 中的每个元素都可以用x 线性表示，则称集合x 为向量空间V 中的一个基.如果向量空间V 含有一个有限的基,则称V 是有限维的.除了偶尔考虑这些例子以外,在这本书中,我们主要将注意力集中于有限维向量空间.例如基，我们再次转向向量空间P 和n E .在向量空间P 中，集合}{n x 其中 2,1,0,)(n ==n t t x n ，是它的一个基;通过定义，每一个多项式是n x 的一个有限维的线性组合.此外P 有无限维的基，对给定的任意有限多项式，我们可以发现有比他们的维数高的多项式;后者多项式显然不是前者的线性组合.关于基础一个例子，在n E 中向量n i x i ,,1, =,i x 的第j 个坐标定义成ij δ (在这里我们第一次使用克罗内克积δ;它是由当j i =，ij δ=1和当j i ≠，ij δ=0定义的).因此,我们认为,向量)1,0,0(),0,1,0(),0,0,1(321===x x x 是3E 中的一组基.不难看出,它们是线性无关的,公式332211321),,(x x x x ξξξξξξ++==证明了在3E 中每一个x 是它们的一个线性组合.一般在有限维向量空间V 中，,基},,{n 1x x 中的每个x 可以写成如下形式：ii i x x ∑=ξ 我们断言，x 是由ξ唯一确定.这一说法的依据是线性相关理论中所使用到的论证.如果我们有ii i x x ∑=η，那么可以通过减法，可得 0)=-∑i ii i x ηξ（ 由于i x 是线性无关的，这意味着0-i i =ηξ其中n i ,,1 =，换言之，η和ξ是一样的.参考文献[1] N.Bourbaki, Algebre; Chap.Ⅱ（Algebre lineaire ）, Paris, 1947,and Chap. Ⅲ(Algebre mullilineaire), Paris, 1948.[2] B.L. Van Der Waerden, Modern algebra, New York, 1953.[3] S.Banch, Theorie des operations lineaires, Warszawa, 1932.[4] F.Riesz and B. Sz.-Nagy, Functional analysis, New York, 1955.[5] P.R.Halmos, Introduction to Hilbert space, New York, 1951.[6] M.H.Stone,Linear transformations in Hilbert space, New York, 1932.[7] R.Courant and D.Hilbert, Methods of mathematical phsics,New York,1953.[8] J.V on Neumann,Mathematical foundations of quantum mechanics,Princeton,1955.Finite-Dimensional Vector Spaces§2. Vector spacesWe come now to the basic concept of this book. For the definition that follows we assume that we are given a particular field F ; the scalars to be used are to be elements of F .Definition. A vector space is a set V of elements called vectors satisfying the follo-wing axioms.（A）To every pair , x and y，of vectors in ʋthere corresponds a vector x + y, called the sum of x and y , in such a way that(1) addition is commutative , x + y = y + x(2) addition is associative, x+(y+z)= (x+y)+z(3) there exists in V a unique vector 0 (called the origin) such that x+ 0 =xfor every vector x, and(4) to every vector x in V there corresponds a unique vector -x such thatx+(-x)=0（B）To every pair , α and x，where α is a scalar and x is a vector in V, there corresponds a vector αx in V, called the product of α and x，in sucha way that(1) multiplication by scalars is associative, α(βx)=(αβ) x, and(2) 1x=x for every vector x.（C）(1) Multiplication by scalars is distributive with respect to vector addition,α(x+y)= αx+αy, and(2) multiplication by vectors is distributive with respect to scalar addition, (α+β)x=αx+βxThese axioms are not claimed to be logically independent ; they are merely a co-nvenient characterization of the objects we wish to study . the relation between a vector spaces V and the underlying field F is usually described by saying that V is a vector space over F . if F is the field R of real numbers , V is called a real vector space ; similarly if F is Q or if F is E, we speak of rational vector spaces or com-plexvector space.§3. ExamplesBefore discussing the implications of the axioms，we give some examples. We shall refer to these examples over and over again，and we shall use the notation established here throughout the rest of our work.(1)Let 1E（=E）be the set of all complex numbers；if we interpret x+y and ax as ordinary complex numerical addition and multiplication.1E becomesa complex vector space.(2) Let p be the set of all polynomials , with complex coefficients, in a variable t. To make p into a complex vector space , We interpret vector addition and scal ar multiplication as the ordinary addition of two polynomials and the multiplication ofa polynomial by a complex number; the origin in p is the polynomial identically zero.Example (1) is too simple and example (2) is too complicated to be typical of the main contents of this book .we give now another example of complex vector spaces which ( as we shall see later ) is general enough for all our purposes.(3)Let n E ，n =1,2,…, be the set of all n -tuples of complex numbers. ifx =(n ξξ，，1) and y =(n ηη，， 1) are elements of n E ,we write ,by definition, x +y = (1ξ+1η,…, n ξ+n η),x α= (α1ξ,…, αn ξ),0 = (0,…,0),-x = (-1ξ,…,- n ξ).It is easy to verity that all parts of our axioms (A),(b).and(c), §2,are satisfied, so that n E is a complex vector space; it will be called n-adimensional comple x coordinate space.(4) For each positive integer n , let n p be the set of all polynomials (with comple x coefficients , as in example (2)) of degree ≤n -1, together with the polynomial id entically zero . (in the usual discussion of degree ,the degree of this polynomial is no t defined , so that We cannot say that it has degree ≤n -1. ) With the same interpreta tion of the linear operations (addition and scalar multiplication ) as in ( 2 ) , n p i s a complex vector space.(5) A close relative of n E is the set n R of all n-tuples of real numbers. W ith the same formal definitions of addition and scalar multiplication as for n E , ex cept that now we consider only real scalar α, the space n R is A real vector spa-ce; it will be called n-dimensional real coordinate space.(6) All the preceding examples can be generalized. Thus, for instance, an obviou s generalization of (1) can be described by saying that every field may be regarded as a vector space over itself. A common generalization of ( 3 ) and ( 5 ) atarts with a n arbitrary field F and forms the set F of n-tuples of elements of F ; the formal d efinitions of the Linear operations are the same as for the case F =E .(7) A field , by definition , has at least two elements ; A vector space however, may have only one . Since every vector space contains an origin, there is essentially (i.e , except for notation ) only one vector space having only one vector . This most trivial vector space will be denoted by θ.(8) If , in the set R of all real numbers, addition is defined as usual and multipli cation of a real number by a rational number is difined as usual, then R becomes a r ational vector space.(9) If, in the set E of all complex numbers, addition is defined as usual and mu ltiplication of a complex number by a real number is defined as usual, then E beco mes a real vector space. ( Compare this example with (1); they are quite different.)§4. CommentsA few comments are in order on our axioms and notation .There are striking simila rities ( and equally striking differences ) between the axioms for a field and the axio ms for a vector space over a field. in both cases, the axioms ( A ) describe the additiv e structure of the system , the axioms (B) describe Its multiplicative structure , and the axioms ( C ) describe the connection between the two structures, Those familiar with algebraic terminology will have recognized the axioms ( A ) (in both 1 and 2 ) as the defining conditions of an abelian ( commutative ) group; the axioms (B ) and (C ) (in §2 ) express the fact that the group admits scalars as operators. We mention in passing that if the scalars are elements of a ring ( instead of A field) , the general ized concept corresponding to a vector space is called A module.Special real vector spaces ( such as 2R and 3R ) are familiar in geometry. There seems at this stage to be no excuse for Our apparently uninteresting insistence on fiel ds other than R , and, in particular , on the fielde E of complex numbers .We hope that the reader is wulling to take it on faith that we shall have to make use of deep properties of complex numbers later ( conjugation , algebraic closure ) , and that in bo th the applications of vector spaces to modern (quantum mechanical ) physics and th e mathematical generalization of our results to Hilbert space complex numbers play an important role. Their one great disadvantage is the difficulty of drawing pictur es ; the ordinary picture ( Argand diagram ) of 1E is indistinguishable from that of 2R , and a graphic representation of 2E seems to be out of human reach. On the occ asions when we have to use pictoral language we shall therefore use the terminology of n R in n E , and speak of 2E, for example as a plane.Finally we comment on notation . We observe that the symbol 0 has been used in two meanings : Once as a scalar and once as a vector. To make the situation worse, we shall later, when we Introduce linear functionals and Linear transformations , give it still other meanings. Fortunately the relations among the various interpretatio ns of 0 are such that , after this word of waning , no confusion should arise fromthis practice.Exercises1.Prove that if x and y are vectors and if is a scalar，then the following relations hold.0),(00),(0),(=∙=-=+αc b xx a00),(=∙x d （observe that the same symbol is used on both sides of this equation ；on the left it denotes a scalar, on the right it denotes a vector.）(e) if αx =0，then either α=0 or x =0（or both ）(f) –x =(-1) x(g) y +(x -y )=x (Here x -y =x +（-y ）)2. if P is a prime, then n P Z is a vector space over P Z (cf. §1,ex.3); howmany vectors are there in this vector space?3. let V be the set of all (ordered) pairs or real numbers. If ),(21ξξ=x a ),(21ηη=y are elements of V , writex +y = ），（2211ηξηξ++αx = ），（01αξ 0 =（0,0）-x = ），（21--ξξ Is V a vector space with respect to these definitions of the linear operations?why?4. Sometimes a subset of a vector apace is itself a vector space (with respe ct to the linear operations already given). Consider, for example, the vector space 3E and the subsets V of 3E consisting of those vectors (321,,ξξξ) for which（a ）1ξ is real,（b ）1ξ=0,（c ）either 1ξ=0 or 2ξ=0,（d ）1ξ+2ξ=0（e ）1ξ+2ξ=1In which of these cases is V a vector space?5. Consider the vector space p and the subsets V of p consisting of those vectors (polynomials) x for which（a ）x has degree 3,（b ）2x （0）=x （1）,（c ）x （t ）≥0 whenever 0 ≤ t ≤ 1,（d ）x （t ）=x （1-t ）for all t .In which of these cases is V a vector space?§5. Linear dependenceNow that we have described the spaces we shall work with, we must specify the relations among the element of those spaces that will be of interest to us.We begin with a few words about the summation notation . if corresponding to each of a set of indices i there is gaven a vector i x , and if it is not necessary or n ot convenient to specify the set of indices exactly, we shall simply speak of a set {}i x of vectors . (we admit the possibility that the same vector corresponds to two di stinct Indices. in all honesty, therefore, it should be stated that what is important is not which vectors appear in {}i x , but how they appear. ) If the index-set under cons ideration is finite , we shall denote the sum of the corresponding vector by ∑i i x (or,when desirable , by a more explicit symbol such as ∑=n i i x 1) . In order to avoid freque nt and fussy case distinctions, it is a good Idea to admit Into the general theory sums s uch as ∑i i x even when there are no indices i to be summed over , Or , more precis ely , even when the index – setunder consideration is empty . ( in that case of cours e, there are no vectors to sum , or , more precisely , the set {}i x is also empty. ) The value of such an " empty sum " is defined , naturally enough, to be the vector 0.Definition. A finite set {}i x of vectors is linearly dependent if there exists a c orresponding set {}i a of scalars, not all zero,such that0=∑i i ix aIf, on the other hand, 0=∑i i i x a implies that i a = 0 for each i , the {}i x is l inearly independent.The wording of this definition is intended to cover the case of the empty set; th e result in that case , though passibly paradoxical, dovetails very satisfactorily with the rest of the theory. The result is that the empty set of vectors is linearly ind ependent . indeed, if there are no indices i , then it is not possible to pick out some of them and to assign to the selected ones a non-zero scalar so as to make a certain sum vanish. The trouble is not in avoiding the assignment of zero ; it is infinding an index to which something can be as assigned. Note that this argument shows that th e empty set is not linearly dependent ; for the reader not acquainted with arguig by“vacuous implication,” the equivalence of the definition of linear independence wit h the straightforward negation of the definition of linear dependence needs a little additional intuitive justification. The easiest way to feel comfortable about the assertion “0=∑ii i x a implies That i a =0 for each i ,” in case there are no ind ices i , is to rephrase it this Way:”if 0=∑i i i x a , then there is no index i forwhich i a ≠0.” This version is obviously true if there is no index i at allLinear dependence and Independence are properties of sets of vectors; it is custo mary, however , to apply the adjectives to vectors themselves, and thus we shall som etimes say " a set of linearly independent vectors” instead of “a linearly independe nt set of vectors.” it will be convenient also to speak of the linear dependence and i ndependence of a not necessarily finite set , x , of vectors. We shall say that x is line arly independent if every finite subset of x is such; otherwise x is linearly depende nt.To gain insight into the meaning of linear dependence , let us study the examples o f vector spaces that we already have.(1) If x and y are any two vectors in 1E , then x and y form a linearly dependent set. If x =y =0, this is trivial; if not, then we have, for example, th e relation y x +(-x )y =0. Since it is clear that every set containing a linearly dependent subset is itself linearly dependent, this shows that in 1E erery set c ontaining more than one element is a linearly dependent set.(2) More interesting is the situation in the space P the vectors y x ,, and z defined by,1)(),1()(,1)(2t t z t t t y t t x -=-=-=are, for example,linearly deendent, since x +y -z =0. However, the infinite set o f vectors ,,,,210 x x x ,defined by,,)(,)(,1)(2210 t t x t t x t x ===is a linearly independent set, for if we hadany relation of the form01100=+++n n x a x a x athen we should have a polynomial identity010=+++n n t a t a aWhence 010=+==n a a a(3) As we mentioned before , the spaces n E are the prototype of what we want to study ; let us examine, for example , the case n =3. To those familiar with higher -dimensional geometry , the notion of linear dependence in this space ( or , more properly speaking , in its real analogue 3R ) has a concrete geometric meaning, which w e shall only mention, In geometrical language, two vectors are linearly dependent i f and only if they are on collinear with the origin .(If one thinks of a vector not as a point in a space but as an arrow pointing from the origin to some given poi nt, the preceding sentence should be modified by crossing out the phrase “With the or igin " both times that it occurs. ) We shall presently Introduce the notion of linear manifolds (or vector subspaces) in a vector space, and, in that connection , we s hall occasionally use the language suggested by such geometrical considerations.§6.Linear combinationsWe shall say, whenever ii i x a x ∑=, that x is a linear combination of {}i x ;we shall use without any further explanation all the simple grammatical implic ations of this terminology. Thus we shall say, in case x is a linear combinatio n of {}i x , that x is linearly independent on {}i x ; we shall leave to the reade r the proof that if {}i x is linearly independent, then a necessary and sufficient condition that x be a linear combination of {}i x is that the enlarged set, obta ined by adjoining x to {}i x , be linearly dependent. Note that, in accordance with the definition of an empty sum, the origin is a linear combination of the emptyset of vectors; it is, mareover, the only vector with this property.The following theorem is the fundamental result concerning linear dependenc e.Theorem. The set of non-zero vectors n x x ,,1 is linearly dependent if an d only if some n k x k ≤≤2,, is a linear combination of the preceding ones. Proof. Let us suppose that the vectors n x x ,,1 are linearly dependent, an d let k be the first integer between 2 and n for which k x x ,,1 are linea rly dependent. (If worse comes to worst, our assumption assures us that n k =will do.) Then011=++k k x a x afor a suitable set of a’s (not all zero); moreover, whatever the a’s, we cannot have 0=k a , for then we should have a linear dependence relation among 11,,-k x x contrary to the definition of k . Hence111--++-=k kk k k x a a x a a x as was to be proved. This proves the necessity of our condition; sufficiency is clear since, as we remarked before, every set containing a linearly dependent s et is itself such.§7. BasesDefinition. A (linear) basis (or a coordinate system) in a vector space V is a set x of linearly independent vectors such that every vector in V is a linear combination of elements of x . a vector space V is finitedimensional if it has a finite basis.Except for the occasional consideration of examples we shall restrict our atte ntion, throughout this book, to finite-dimensional vector spaces.For example of bases we turn again to the spaces P and n E . in P , the se t }{n x , Where 2,1,0,)(n ==n t t x n , is a basis; every polynomial is, by definit ion, a linear combination of a finite number of n x . Moreover P has no finite basis, for, given any finite set of polynomials, we can find a polynomial of h igher degree than any of them; this latter polynomial is obviously not a linear combination of the former ones.An example of a basis in n E is the set of vectors n i x i ,,1, =, defined by the condition that the j -th coordinate of i x is ij δ. (Here we use for the first time the popular kronecker δ; it is defined by ij δ=1 if j i = and ij δ=0 if j i ≠.) Thus we assert that in 3E the vectors )0,1,0(),0,0,1(21==x x and )1,0,0(3=x form a basis. It is easy to see that they are linearly independent; t he formula332211321),,(x x x x ξξξξξξ++==proves that every x in 3E is a linear combination of them.In a general finite-dimendional vector space V , with basis },,{n 1x x , we know thatevery x can be written in the formii i x x ∑=ξ we assert that the s 'ξ are uniquely determined by x . The proof of this asserti on is an argument often used in the theory of linear dependence. If we had ii i x x ∑=η, then we should have, by subtraction, 0)=-∑i i i i x ηξ（Since the i x are linearly independent, this implies that 0-i i =ηξ for n i ,,1 =; in other words, the s 'ξ are the same as the s 'η.RECOMMENDED READING[1] N.Bourbaki, Algebre; Chap.Ⅱ（Algebre lineaire ）, Paris, 1947,and Chap. Ⅲ(Algebre mullilineaire), Paris, 1948.[2] B.L. Van Der Waerden, Modern algebra, New York, 1953.[3] S.Banch, Theorie des operations lineaires, Warszawa, 1932.[4] F.Riesz and B. Sz.-Nagy, Functional analysis, New York, 1955.[5] P.R.Halmos, Introduction to Hilbert space, New York, 1951.[6] M.H.Stone,Linear transformations in Hilbert space, New York, 1932.[7] R.Courant and D.Hilbert, Methods of mathematical phsics,New York,1953.[8] J.V on Neumann,Mathematical foundations of quantum mechanics,Princeton,1955.。