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Abstract Sixty years of Operational Research

Abstract Sixty years of Operational Research
Abstract Sixty years of Operational Research

Sixty years of Operational Research

Ken Bowen

*

Royal Holloway,University of London,Egham Hill,Surrey TW200EX,UK

Received 10December 2001;accepted 30January 2003

Abstract

This paper describes the author ?s experience of 60years of Operational Research and presents some thoughts on the nature of the work of an Operational Researcher.ó2003Elsevier B.V.All rights reserved.

Keywords:History of OR;Practice of OR

1.Introduction

This is an account of the way in which my own work in Operational Research (OR)developed,and what sort of mathematics has aided me.I also discuss,in general terms,how OR elsewhere was proceeding,how the various strands stand today,and what,perhaps,the future may hold.

2.1941–1946

In January 1941,I became a naval analyst in technical radio intelligence 1managing an opera-tional department passing intelligence to Bletchley Park and other authorities.Additionally,I was

also responsible for developing ways by which the quality and quantity of information obtained could be enhanced,by improvements to equip-ment and to data-handling.I did not,at the time,see this as OR:indeed,it was not until much later that I ?rst heard the term and what it implied.

Improving the operational performance of the groups that I controlled,internally and externally,was,I now perceive,a successful OR task.How-ever,there were limitations on the value we could o?er to the users of our output,since we were never allowed to discuss the speci?c nature of how they used this intelligence,let alone the reasons why they needed it.Consequently,we could rarely go beyond a certain routine process:feed-back was very limited and face-to-face discussion was a rare event.

The mathematics I needed was largely that re-lated to radio-propagation and the working of transmitters,receivers and aerial systems.Fourier series also came in useful.Measurement was very much biased towards classi?cation:had I been of

*

Tel.:+44-1-784443082;fax:+44-1-784430766.

1

With keyed morse communications,our task was to match transmitters (Radio-Fingerprinting)and the operators (TINA):with other signals interest was mainly directed to their function and purpose.

0377-2217/$-see front matter ó2003Elsevier B.V.All rights reserved.

doi:10.1016/S0377-2217(03)00267-4

European Journal of Operational Research 153(2004)

618–623

https://www.doczj.com/doc/0a5883437.html,/locate/dsw

the calibre of my former tutor,Henry(JHC) Whitehead2,I might well have discovered fuzzy sets,which I recognised immediately when I met them25years later.Occasionally,I worked on equipment problems,primarily concerned with devices that improved the data I required.One exception was a study of how to run a long loop of recording wire over a drum made of threaded rods without tension building up and the wire snapping: an analogous problem was recently discussed on a TV programme,trying to reinvent the water rais-ing equipment that may have been used for the Hanging Gardens of Babylon!

3.1946–1954

The war ended with my having a great interest in radio equipment,and a generally diminished recall of my university mathematics.I could have gone back to do pure mathematical research,and I also had the possibility of a transfer to the(new) GCHQ at Cheltenham.However,a more attrac-tive option was to run a small statistical group to be concerned with the analysis of data from radio equipment under development,primarily naviga-tional aids,direction?nders and communication systems(radar was worked on elsewhere).My work could be described as data driven since I had no prior knowledge of statistics as a subject area.

Mathematically,it was interesting,mainly be-cause the distributions I dealt with were seldom standard,but I needed little more than basic cal-culus and algebra.From an OR standpoint,it would have been more what was called assessment, had it not been for the closeness with which I was able to work with the users and to incorporate both operational and technical factors.I was able to spend a lot of time at sea,partly on trials and partly just getting experience of equipment in use: this incidentally also gave me useful knowledge of radar which I was able to use later.

Apart from statistical work,I also carried out purely mathematical studies.The most interesting of these was an attempt to select from a number of useable frequencies(which could be modelled as the?rst n integers),a set in which no three were in arithmetic progression(AP).Operationally,two frequencies in use would cause interference on a third should the three be in AP,due to non-linear resonators inherent in a ship?s structure.The so-lution was required for very large values of n(up to several hundred)and the set selected was to be reasonably evenly spread over the whole range. You will recognise this as a now-solved problem in number theory.I did not solve it,but by a process of successive approximations starting from1,2,4, 5,10,11,13,14,28,29,31,32,37,38,40,41,...,I obtained a good enough set.There were no com-puters,and it is worth mention that,as with complicated statistical calculations,I was depen-dent on standard calculators,punched cards and a lot of arithmetic.

It may also be worthy of note that in many areas of work the geometry of conics proved to be an important aspect of the models I needed to develop.

4.Operational Research––?rst comment

I?rst became aware of OR in1949from a talk by E.C.(Bill)Williams,then Director of Opera-tional Research,Admiralty.Like Moli e re?s Bour-geois Gentilhomme,who found that he had been speaking prose all his life,I recognised what I had been doing,albeit not yet in full context,for the past10years.Helped by wise seniors,I planned my route towards involvement in tactical and strategic inquiry,so as to extend the equipment-oriented OR that had been my main endeavour.

I also looked at what was happening in indus-try,and it was very di?erent to what was going on in Naval Operational Research.The latter con-centrated on tactical problems,under considerable di?culty since there was no real(i.e.?ghting)en-vironment:games and exercises at sea were the vehicles for getting data to add to the limited amount of relevant wartime data(and later that from the Korean and Suez wars)to establish greater accuracy of estimation of Operational performance.Industry was moving primarily on

2Henry was in OR at the Admiralty with PMS Blackett for a

while,but he found it not to his mathematical taste and went to

Bletchley Park to work in cryptographic analysis.

K.Bowen/European Journal of Operational Research153(2004)618–623619

the‘‘housekeeping’’side:inventory control,stock control and other models tended to be mechanistic and in comparison to naval battle models,very sophisticated.Queuing theory and reliability the-ory were also becoming subjects in their own right. None of this seemed relevant to the current naval problems.Both were doing OR,but never did the twain meet.

5.1954–1961

For me,a key period was the Sta?Course at Greenwich in1954,followed by a course at the Naval Tactical School.Not only did this give me the status of a quali?ed Naval Sta?O?cer,but it introduced me to a range of tactical and strategic issues including ones of collaboration with the other two services.Following this,I might have gone on to the Department of OR,Admiralty but I chose to stay in my R&D Establishment with the opportunity of looking at some equipment as-sessments in a wider context.

An important one concerned a projected peri-scope detection radar,the potential of which I examined taking into account what sonar and other underwater systems(seaborne and airborne) could play in submarine detection.The study showed the radar to add little to the operational outcome of antisubmarine warfare and it was not proceeded with.

Another looked at the need for a UHF DF equipment,operating on the new UHF voice communications,helping to get aircraft safely back to the carrier.Again there were many alter-native aids,many of them radar,and it seemed again that only a small operational gain would be bought at a high price.I had however forgotten that the old VHF DF,albeit not very accurate, was user-friendly and the pilots loved it.In the words of one of my Naval advisers‘‘I agree with Bowen?s analysis,but not with his conclusions’’! The equipment was developed and I added human factors to my list of subject areas for essential study.

In1956,I went to sea(a period of18months)as Scienti?c Adviser to CinC Home Fleet/CINC-EASTLANT.I was responsible for all naval exercise analyses and,in one case,a major air defence exercise,I was also a member of the ex-ercise planning team,enabling me to set all re-quirements for data collection.My main NATO post was Records O?cer at the Maritime Head-quarters at Northwood:I redesigned the data collection and analysis process and the enhanced ?ow of useful intelligence to SACLANT was ac-knowledged:at least one other NATO headquar-ters adopted a similar reorganisation.The various analyses carried out,both for national and NATO working,had direct impact on tactical doctrine.

From1958to1961,I served as Scienti?c Ad-viser to the Director of Naval Plans,Admiralty and,in a part-time capacity,to the Chief of Am-phibious Warfare(CAW).My concerns were now at the strategic level;in many cases,the issues analysed were of3-service concern.My task was essentially to prepare reports and briefs for con-sideration at Chiefs of Sta?level,and I depended heavily on analyses carried out by both opera-tional research and equipment assessment scien-tists.

Mathematically,there was nothing that posed di?culties.The essential features of the work were to know what was going on in‘‘the corridors of power’’,to know those who were the authorities or experts in the many areas in which information might be required,and to provide timely and logically supported advice.Being‘‘right’’was im-portant:the work done had a major bearing on the Navy?s‘‘voice’’in debates with the other services and on the establishing of Naval policy.

Perhaps my most important contribution re-lated to the nuclear deterrent which was now passing from the RAF?s V-bomber force to the Navy?s planned POLARIS submarines.The de-terrent level was quoted as‘‘at least50%damage to each and every one of a stated number of Soviet Union cities’’.The rationale for this I found to be non-existent:it merely stated what the RAF could do!By changing the statement to‘‘an average level of50%’’,I showed that there could be,on that basis,a massive saving,and such a change was accepted in principle.This also triggered a much-needed debate on what might be considered to deter an attack on the UK and,further,whether the concept of an independent nuclear deterrent

620K.Bowen/European Journal of Operational Research153(2004)618–623

had military relevance or was purely a political/ diplomatic concept related to relations(particu-larly information exchange)with the US.Eventu-ally,the independent UK deterrent,became the smallest operationally viable force of POLARIS submarines that could be deployed!

Of other tasks that a?ected the future,it is in-teresting to note that tactical planning that I was involved in for CAW had an eventual pay-o?in the e?cient way in which the amphibious forces of the Royal Marines were deployed in the Falklands war.I was then retired from Defence,but I was able to predict quite accurately the operations that would be carried out(fortunately later work had helped to ensure that the relevant forces would survive!).

6.1961–1967

This period was my most intense phase of de-fence OR activity.Initially,in the Department of OR,Admiralty,I was concentrating on simple mathematical models in the?elds of anti-subma-rine warfare and air defence,using variants of Lanchester models of combat(di?erential equa-tions of battle),and also examining vulnerability of ships to torpedo and missile attack.My re-sponsibility was the development of operational models related to operations in support of friendly nations overseas.Indonesia and Kuwait were countries I examined in detail,the?rst as a po-tential enemy,the second as an ally threatened by Iraq.My most studied texts were the multivo-lumed Times atlases:such geographical aspects as water depths and beaches,what nations owned the many islands and who might threaten them,were among my many concerns.

Informally,I set up a group,including analysts from the other services and developed conceptual models of the diverse activities of an intervention in which the naval r^o le was to move,supply and defend military units;the Royal Marines with their helicopters and landing craft were special ele-ments.

Everything came together,when I moved in 1965to the new central Defence Operational Analysis Establishment at West By?eet,where ail that I had ever done and learnt seemed to serve my responsibilities for maritime warfare advice to the MOD.

My team slowly built up to include o?cers of ail three services,a few scientists with long expe-rience in naval warfare,and some with specialist knowledge of earlier OR studies of air and army problems.We expanded existing models,eschew-ing computer simulation models because of the then di?culty of getting large enough samples,and developed useful‘‘games’’to examine submarine attack processes and airborne movement of army units.

In1966–1967,we carried out major studies for the Secretary of State for Defence,a movement study to examine the intervention potential of existing forces and what would be needed in10 years time,and a more general appreciation of UK capabilities in antisubmarine warfare and the defence of major units.Both were successful studies.Importantly,the Royal Marine compo-nents of our defence forces were shown to be essential.

7.Operational Research––second comment

In general,application of OR in industry and commerce had expanded into many areas but it had become increasingly mathematical,concen-trating still on‘‘shop-?oor’’activities.There was certainly little of a strategic nature.There were however notable exceptions in some Government departments,at the National Coal Board,in the British Steel Corporation,and at Rolls Royce, and,in general,there were more than enough ideas to feed on to make membership of the OR Society a necessity.What I gained mainly bore fruit in strengthening my bias towards simple models for ‘‘casting light’’and against solution-oriented op-timisations.

Linear programming was the one modelling area that was well and truly adopted(it formed the central modelling approach for the second stage of the intervention movement studies referred to above).Otherwise,ideas for modelling were de-pendent of a large number of sources,few of them from conventional OR areas.

K.Bowen/European Journal of Operational Research153(2004)618–623621

8.1967–1979

My last12years in MOD were spent as an in-dependent researcher.My main topic was con?ict; initially,this was a concern with understanding how we might avert wars rather then how we might win them.I had sta?to support me,both in-house and in universities;these worked on further extensions of Lanchester Theory,on fuzzy logic and on research games.

The con?ict work gradually moved into studies of the operational research process itself:the logic that drove this was the interdependence of con?ict and problems.Increasingly,attention got focused on questions such as‘‘how do we work to ensure that we are studying the right problem?’’;‘‘how do we determine what models will best serve our purpose?’’;‘‘what limitations are there on possible ways ahead,unless organisations also are chan-ged?’’,and so on.Mathematics was not the key; subject areas such as psychology and the social sciences had relevant things to say,as had lin-guistics,particularly related to confusions caused by the way language was used.

None of this was new,since re?ection on my own practice,and my discussions with other practitioners,showed that we had often in e?ect dealt with these questions.But our processes were implicit not explicit,and were not fully understood nor adequately developed.

It is not possible to cover the wide range of inquiry that?lled the years up to my formal re-tirement in1979.Su?ce it to say that I ended with an association with many like-minded researchers in many countries,a good working knowledge of con?ict resolution processes and of decision theo-ries,and a certainty that except for problems that could be fully and simply de?ned,mathematics had a much more limited role to play in opera-tional research than many believed.

9.Operational Research––third comment

The1970s were not a good period for OR.As needs for help with decision problems shifted to-wards the strategic end of the spectrum,opera-tional research tools and processes were lacking.In defence,this was increasingly felt and the estab-lishment.I served came under increasing criticism. Some moves towards better links between foreign policy and defence analysts were attempted,but a change in the emphases of OR foundered on a general desire to hold fast to the familiar.This was the decade when Russell Acko?spoke out in two papers,published and debated by the OR Society,‘‘The future of OR is past’’and‘‘Resurrecting the future of OR’’[1,2].Across the board,industrial and civil government OR included,the future did not seem bright.

10.1979to date

Throughout the1980s,at Royal Holloway,I developed my own ideas on improving OR process, particularly in problem formulation and sharpened these through the work of a Research Assistant and two doctoral students on contracts and other consultancy work.I worked closely with individual researchers elsewhere who were developing practi-cal applications of meta and hypergames,cognitive mapping,Strategic Choice,systems thinking and other processes that provided structure for dealing with the largely unquanti?able aspects of prob-lems.We were all,in e?ect,seeking theories of decision aiding rather than theories of decision.We were not trying to replace mathematical OR ap-proaches but to understand better when various standard modelling techniques were appropriate and when they were not.

This sort of work has continued apace and much is now operationally available.Similar ex-tensions of the scope of OR have also taken place in many European countries.A Working Group, of which I am a member,ensures that communi-cation of ideas is widespread.I am less optimistic about the direction in which US operational re-search is moving.

11.Operational Research––fourth and?nal com-ment

Where does OR stand today?The number of analysts who understand the non-mathematical

622K.Bowen/European Journal of Operational Research153(2004)618–623

structuring processes are increasing in number and industry in particular is taking good advantage of this,either through their own sta?but also by using the growing number of strong consultancy groups.In government OR,similar tendencies are seen.In the case of defence,there are still big problems mainly because of the rapid move to-wards concepts of interposition and humanitarian aid.The balance needed between the so-called soft and hard techniques is under urgent examination.

The greatest di?culty for OR workers today is that,although improved methodology is available, any process used can only carve out an m-dimen-sional slice of an n-dimensional problem(m is likely to be very much less than n).Di?erent pro-cesses are chosen by di?erent people and although there may always be good help given,the end re-sults will not be the same.As yet,we have only vague understanding of the impact of the di?er-ences,although though there is nothing that seems to be inherently inconsistent between the processes available;techniques developed within individual processes certainly seem to be transferable.The logical problem is that,ultimately,the process is an individual?s way of working and even if we try to follow suit,we end up with our way of working not someone else?s.We seem to need something like a choreographer?s notation,to describe,step by step,what we are doing.

I have elsewhere made a plea for help from pure mathematics(see[3]).We already have in various places bits of graph theory and set theory,and ideas from topology,algebra,fuzzy logic and much more.The structures that de?ne the ways of working are very complicated with feedback and recursion everywhere.The catch-22situation is that operational researchers are not pure mathe-maticians(although some,like me,may have been such long ago)and pure mathematicians are not attracted by the messy,ill-de?ned worlds that operational researchers live in.If this can be overcome,maybe decision making can be helped by OR to come to take place in a more rational, cooperative and non-confrontational manner,with con?ict working to create desirable change with-out destroying continuity and stability.There is no harm in having a dream.

References

[1]R.L.Acko?,The future of operational research is past,

Journal of the Operational Research Society30(1979)93–104.

[2]R.L.Acko?,Resurrecting the future of operational re-

search,Journal of the Operational Research Society30 (1979)189–199.

[3]K.Bowen,A challenge:Can mathematics aid development

of the process of operational research?IMA Journal of Mathematics Applied in Business and Industry,2,73–77.

K.Bowen/European Journal of Operational Research153(2004)618–623623

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1简介2 2.4.3中文数字转换 (7) 2.5高级设置 (8) 2.5.1章节标题设置 (9) 2.5.2部分修改标题格式 (12) 2.5.3附录标题设置 (12) 2.5.4其他标题设置 (13) 2.5.5其他设置 (13) 2.6配置文件 (14) 3版本更新15 4开发人员17 1简介 这个宏包的部分原始代码来自于由王磊编写cjkbook.cls文档类,还有一小部分原始代码来自于吴凌云编写的GB.cap文件。原来的这些工作都是零零碎碎编写的,没有认真、系统的设计,也没有用户文档,非常不利于维护和改进。2003年,吴凌云用doc和docstrip工具重新编写了整个文档,并增加了许多新的功能。2007年,oseen和王越在ctex宏包基础上增加了对UTF-8编码的支持,开发出了ctexutf8宏包。2009年5月,我们在Google Code建立了ctex-kit项目1,对ctex宏包及相关宏包和脚本进行了整合,并加入了对XeT E X的支持。该项目由https://www.doczj.com/doc/0a5883437.html,社区的开发者共同维护,新版本号为v0.9。在开发新版本时,考虑到合作开发和调试的方便,我们不再使用doc和docstrip工具,改为直接编写宏包文件。 最初Knuth设计开发T E X的时候没有考虑到支持多国语言,特别是多字节的中日韩语言。这使得T E X以至后来的L A T E X对中文的支持一直不是很好。即使在CJK解决了中文字符处理的问题以后,中文用户使用L A T E X仍然要面对许多困难。最常见的就是中文化的标题。由于中文习惯和西方语言的不同,使得很难直接使用原有的标题结构来表示中文标题。因此需要对标准L A T E X宏包做较大的修改。此外,还有诸如中文字号的对应关系等等。ctex宏包正是尝试着解决这些问题。中间很多地方用到了在https://www.doczj.com/doc/0a5883437.html,论坛上的讨论结果,在此对参与讨论的朋友们表示感谢。 ctex宏包由五个主要文件构成:ctexart.cls、ctexrep.cls、ctexbook.cls和ctex.sty、ctexcap.sty。ctex.sty主要是提供整合的中文环境,可以配合大多数文档类使用。而ctexcap.sty则是在ctex.sty的基础上对L A T E X的三个标准文档类的格式进行修改以符合中文习惯,该宏包只能配合这三个标准文档类使用。ctexart.cls、ctexrep.cls、ctexbook.cls则是ctex.sty、ctexcap.sty分别和三个标准文档类结合产生的新文档类,除了包含ctex.sty、ctexcap.sty的所有功能,还加入了一些修改文档类缺省设置的内容(如使用五号字体为缺省字体)。 1https://www.doczj.com/doc/0a5883437.html,/p/ctex-kit/

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公文写作毕业论文写作要求和格式规范

(公文写作)毕业论文写作要求和格式规范

中国农业大学继续教育学院 毕业论文写作要求和格式规范 壹、写作要求 (壹)文体 毕业论文文体类型壹般分为:试验论文、专题论文、调查方案、文献综述、个案评述、计算设计等。学生根据自己的实际情况,能够选择适合的文体写作。 (二)文风 符合科研论文写作的基本要求:科学性、创造性、逻辑性、实用性、可读性、规范性等。写作态度要严肃认真,论证主题应有壹定理论或应用价值;立论应科学正确,论据应充实可靠,结构层次应清晰合理,推理论证应逻辑严密。行文应简练,文笔应通顺,文字应朴实,撰写应规范,要求使用科研论文特有的科学语言。 (三)论文结构和排列顺序 毕业论文,壹般由封面、独创性声明及版权授权书、摘要、目录、正文、后记、参考文献、附录等部分组成且按前后顺序排列。 1.封面:毕业论文(设计)封面(见文件5)具体要求如下: (1)论文题目应能概括论文的主要内容,切题、简洁,不超过30字,可分俩行排列; (2)层次:高起本,专升本,高起专; (3)专业名称:现开设园林、农林经济管理、会计学、工商管理等专业,应按照标准表述填写; (4)密级:涉密论文注明相应保密年限; (5)日期:毕业论文完成时间。 2.独创性声明和关于论文使用授权的说明:(略)。

3.摘要:论文摘要的字数壹般为300字左右。摘要是对论文的内容不加注释和评论的简短陈述,是文章内容的高度概括。主要内容包括:该项研究工作的内容、目的及其重要性;所使用的实验方法;总结研究成果,突出作者的新见解;研究结论及其意义。摘要中不列举例证,不描述研究过程,不做自我评价。 论文摘要后另起壹行注明本文的关键词,关键词是供检索用的主题词条,应采用能够覆盖论文内容的通用专业术语,符合学科分类,壹般为3~5个,按照词条的外延层次从大到小排列。 4.目录(目录示例见附件3):独立成页,包括论文中的壹级、二级标题、后记、参考文献、和附录以及各项所于的页码。 5.正文:包括前言、论文主体和结论 前言:为正文第壹部分内容,简单介绍本项研究的背景和国内外研究成果、研究现状,明确研究目的、意义以及要解决的问题。 论文主体:是全文的核心部分,于正文中应将调查、研究中所得的材料和数据加工整理和分析研究,提出论点,突出创新。内容可根据学科特点和研究内容的性质而不同。壹般包括:理论分析、计算方法、实验装置和测试方法、对实验结果或调研结果的分析和讨论,本研究方法和已有研究方法的比较等方面。内容要求论点正确,推理严谨,数据可靠,文字精炼,条理分明,重点突出。 结论:为正文最后壹部分,是对主要成果的归纳和总结,要突出创新点,且以简练的文字对所做的主要工作进行评价。 6.后记:对整个毕业论文工作进行简单的回顾总结,对给予毕业论文工作提供帮助的组织或个人表示感谢。内容应尽量简单明了,壹般为200字左右。 7.参考文献:是论文不可或缺的组成部分。它既可反映毕业论文工作中取材广博程度,又可反映文稿的科学依据和作者尊重他人研究成果的严肃态度,仍能够向读者提供有关

开信用证步骤及样本教学提纲

开信用证步骤及样本

填制进口开证申请书的步骤为: 1、DATE(申请开证日期)。在申请书右上角填写实际申请日期。 2、TO(致)。银行印制的申请书上事先都会印就开证银行的名称、地址,银行的SWIFT CODE、TELEX NO等也可同时显示。 3、PLEASE ISSUE ON OUR BEHALF AND/OR FOR OUR ACCOUNT THE FOLLOWING IRREVOABLE LETTER OF CREDIT(请开列以下不可撤销信用证)。如果信用证是保兑或可转让的,应在此加注有关字样。开证方式多为电开(BY TELEX),也可以是信开、快递或简电开立。 4、L/C NUMBER(信用证号码)。此栏由银行填写。 5、APPLICANT(申请人)。填写申请人的全称及详细地址,有的要求注明联系电话、传真号码等。 6、BENEFICIARY(受益人)。填写受益人的全称及详细地址。 7、ADVISING BANK(通知行)。由开证行填写。 8、AMOUNT(信用证金额)。分别用数字和文字两种形式表示,并且表明币制。如果允许有一定比率的上下浮动,要在信用证中明确表示出来。 9、EXPIRY DATE AND PLACE(到期日期和地点),填写信用证的有效期及到期地点。

10、PARTIAL SHIPMENT(分批装运)、TRANSHIPMENT(转运)。根据合同的实际规定打“×”进行选择。 11、LOADING IN CHARGE、FOR TRANSPORT TO、LATEST DATE OF SHIPMENT(装运地/港、目的地/港的名称,最迟装运日期)。按实际填写,如允许有转运地/港,也应清楚标明。 12、CREDIT AVAILABLE WITH/BY(付款方式)。在所提供的即期、承兑、议付和延期付款四种信用证有效兑付方式中选择与合同要求一致的类型。 13、BENEFICIARY'S DRAFT(汇票要求)。金额应根据合同规定填写为:发票金额的一定百分比;发票金额的100%(全部货款都用信用证支付);如部分信用证,部分托收时按信用证下的金额比例填写。付款期限可根据实际填写即期或远期,如属后者必须填写具体的天数。信用证条件下的付款人通常是开证行,也可能是开证行指定的另外一家银行。 信用证样本 Issue of a Documentary Credit (开证行,一般为出口商的往来银行,须示开证行的信用程度决定是否需要其他银行保兑confirmation 见49)

配合前面的ntheorem宏包产生各种定理结构

%=== 配合前面的ntheorem宏包产生各种定理结构,重定义一些正文相关标题===% \theoremstyle{plain} \theoremheaderfont{\normalfont\rmfamily\CJKfamily{hei}} \theorembodyfont{\normalfont\rm\CJKfamily{song}} \theoremindent0em \theoremseparator{\hspace{1em}} \theoremnumbering{arabic} %\theoremsymbol{} %定理结束时自动添加的标志 \newtheorem{definition}{\hspace{2em}定义}[chapter] %\newtheorem{definition}{\hei 定义}[section] %!!!注意当section为中国数字时,[sction]不可用! \newtheorem{proposition}{\hspace{2em}命题}[chapter] \newtheorem{property}{\hspace{2em}性质}[chapter] \newtheorem{lemma}{\hspace{2em}引理}[chapter] %\newtheorem{lemma}[definition]{引理} \newtheorem{theorem}{\hspace{2em}定理}[chapter] \newtheorem{axiom}{\hspace{2em}公理}[chapter] \newtheorem{corollary}{\hspace{2em}推论}[chapter] \newtheorem{exercise}{\hspace{2em}习题}[chapter] \theoremsymbol{$\blacksquare$} \newtheorem{example}{\hspace{2em}例}[chapter] \theoremstyle{nonumberplain} \theoremheaderfont{\CJKfamily{hei}\rmfamily} \theorembodyfont{\normalfont \rm \CJKfamily{song}} \theoremindent0em \theoremseparator{\hspace{1em}} \theoremsymbol{$\blacksquare$} \newtheorem{proof}{\hspace{2em}证明} \usepackage{amsmath}%数学 \usepackage[amsmath,thmmarks,hyperref]{ntheorem} \theoremstyle{break} \newtheorem{example}{Example}[section]

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