黑箱法今日数学及其应用

2020年11月30日发(作者：阎正衡)
out city created, and care masses life, focus work, in-depth investigation, more out boutique masterpiece, makes we of research results more to into led of decision vision, more to in national some has effect of newspaper Shang published, for advance work, and publicity changde play due of role. Third, information submitted to be pragmatic. Quick and timely. The ancients said: for the time system; statement back for the time being, nothing. Therefore, the submission of information to do ng, send and read faster approval and feedback to implement quickly. To be true and accurate. True mainly reflect the full picture of events, one is one, two, this is the life of the information. Accuracy is primarily qualitative and quantitative questions, quantitative objective of publicQualitative logic. To be reliable and useful. We submit information to have access to decision-making, to guide and promote the work and solve practical problems. Mixed cum.
On the negative information and emergency information, rapid escalation in strict accordance with the procedures, firm, newspaper, newspapers, never late, fail to report, false claim and skimming. Investee 2. supervision and insist on, around and protecting their interests to touch the truth, seek practical results. Adhere to people-oriented, the most important thing is to realize, safeguard and develop the fundamental interests of the overwhelming majority of the people. We carry out inspection, so must go deep among the masses, go deep into the realities, always pay attention to the people's livelihood, to grasp the public sentiment, and earnestly safeguard the benefit, addressing the masses are most concerned about and reflecting the strongest issues, efforts to solve the problem of decisions implemented and not implemented. One is to stick to principles. Right of inspection is one of the most important powers of the Office, should not only dare to use, but also with caution. So-called
dared to use, is to hold a number of important issues, bold supervision over supervision, track inspection, problems are not solved do not pass, the blame does not hold did not miss, dissatisfaction of the masses did not miss, the real right of supervision authority, with the benefits. Call with caution, is supervising departments should strengthen the consciousness of authorized strictly according to procedure, preventing the supervision and excessive to prevent adding burden to grass-roots. To this end, the supervision Department of the Party Committee of supervision must be under city and County party Committee Secretary-General (Office). Second, we should focus on. Is the Governor, those related to the globalEvent, Governor the protracted difficult, strong Governor during emergency urgent. Not having special departments in charge of the General Governor, under the normal procedure can do good things not Governor, not authorized by County leaders, not the Governor. Third is to solve
the problem. The purpose of supervision, to resolve the problem. To adhere to and further improve the
今日数学及其应用
2009-01-13 10:20:57
王梓坤：数学家，中国科学院院士。1929年4月30日生于湖南零陵，195 2年毕业于武汉大学，
1958年获苏联莫斯科大学副博士学位，1988年获澳大利亚麦克里大学名誉 科学博士学位。先后
任南开大学和北京师范大学教授（1984年至1989年任该校校长），同时任汕 头大学（1993年
起任该校数学研究所所长）教授。1991年当选为中国科学院院士（学部委员）。 专长概率论，
并在随机过程等方面的研究与教学中取得多项系统的重要成果。

一、数学科学、高新科技与国家富强

1．对数学的新认识之一 “国家的繁荣富强 ，关键在于高新的科技和高效率的经济管理。”这是当
代有识之士的一个共同见解，也已为各发达国家的 历史所证实。在我国，邓小平同志把科技对生
产建设的重要性提到前所未有的高度；在美国，科学院院士 J．G．Glimm也曾幽默地说过：40
年前，中国有句话说“枪杆子里面出政权”，而从90年代起 ，在全球应是“科学技术里面出政权”。
他的话反映了国外许多人士对科技重要性的新认识。从最近海湾 战争可以看出，高技术是保持国
家竞争力的关键因素。 “高新技术的基础是应用科学，而应用科学的基 础是数学”。这句话把数
学对高新技术的作用，从而对国富民强的作用，清楚地表达出来。当代科技的一 个突出特点是定
量化。人们在许多现代化的设计和控制中，从一个大工程的战略计划、新产品的制作、成 本的结
算、施工、验收、直到贮存、运输、销售和维修等等都必须十分精确地规定大小、方位、时间、< br>速度、成本等数字指标。精确定量思维是对当代科技人员共同的要求。所谓定量思维是指人们从
实 际中提炼数学问题，抽象化为数学模型，用数学计算求出此模型的解或近似解，然后回到现实
中进行检验 ，必要时修改模型使之更切合实际，最后编制解题的软件包，以便得到更广泛的方便
的应用。

2．新认识之二 数学科学对经济发展和竞争十分重要。好的经济工作者决不止是定性思维者，
他不能只满足于粗线条的大致估计，而必须同时是一位定量思维者。数学科学不仅帮助人们在经
营中获利 ，而且给予人们以能力，包括直观思维、逻辑推理、精确计算以及结论的明确无误。这
些都是精明的经济 工作者和科技人员所应具备的工作素质；大而言之，也是每个公民的科学文化
素质。所以数学科学对提高 一个民族的科学和文化素质起着非常重要的作用。

3．新认识之三 “高技术本质上是一种 数学技术”。这种观点已为越来越多的人所接受。许多西方
公司意识到：利用计算技术去解决复杂的方程 和最优化问题，已改变了工业过程的组织和新产品
的设计。数学大大地增强了他们在经济竞争中的力量。 无怪乎美国科学院院士J．G．Glimm不
仅称数学为非常重要的科学，而且说它是授予人以能力的技 术。他说：“数学对经济竞争力至为
重要，数学是一种关键的普遍适用的，并授予人以能力的技术。”时 至今日，数学已兼有科学与
技术两种品质，这是其它学科所少有的，不可不知。

由 于对数学重要性的重新认识，在欧洲建立了“欧洲工业数学联合会”，以加强数学与工业的联系，
同时培 养工业数学家去满足工业对数学的要求。在一篇有关的报告中，列举了欧洲工业中提出的
20个数学问题 ，其中包括：齿轮设计、冷轧钢板的焊接、海堤安全高度的计算、密码问题、自
动生产线的设计、化工厂 中定常态的决定、连续铸造的控制、霜冻起伏的预测、发动机中汽轮机
构件的排列、电化学绘图等等。

4．数学与诺贝尔经济奖 数学对经济学的发展起了很大的作用。今天，一位不懂数学的经济学
eelings survey, by looking up public sentiments to find problems. Problems will increase its special supervision, set up accounts, hold on to it. We should conscientiously implement the leading contracting matters, secured, had an answer to everything, then settles rate of 100%. Have an impact on some of the outstanding issues, supervision departments and information components together, play the supervisory role of the news media to promote problem solving. Investee 3. insist on a daily run, around the practice of truth catching efficiency, focus specification. To give full play to the party Office around connecting, coordinating internal and external features, contact, rally at all levels, to motivate every aspect, adhere to the truth, strengthening standardized management to achieve coherent, efficient and effective functioning of the daily work of the Party Committee. Is processing messages should strive to streamline, standardize and quality. Streamlining is to control the number of
messages, compress messages, reducing procedures, improve message handling efficiency. Specifications, is to strictly enforce the ban issued by the Communist party authorities in document handling regulations and provincial and municipal regulations, conscientiously strengthen and improve communications management to ensure that party documents orderly. High quality, is to improve the quality of message processing, it is necessary to accurately implementing the intention of the Party Committee, clearance, good communications, policy program closed, ensuring that there is no error. Second meeting scheduled to ensure thorough, safe and efficient. Any arrangements for the meetings and events, carefully arranged, item-by-item interface implemented, sure. o vigorously streamline meetings, activities, number of pressure reduction, scale to ensure that leadership emerged from the General Conference and entertainment services, focus on big things, matters. Third, reception services
should lay stress on humane, personal, cultural and human. Reception and work directly with people, reception services directly affecting the Office of party Committee The image of the region. At the same time strengthening the construction of library, improve the reception conditions, more human-oriented, personal, cultural work into the reception, a little more human needs, a little more human care more humane atmosphere, and constantly improve the service, improve the quality of service. Meanwhile, to further pay special attention to the daily work of the other Office System. Confidential work responsibility system for leading cadres to implement security as a leader, to improve the confidentiality of classified personnel, especially leading cadres, strengthening party and Government focus on vital sectors of security management, to advance privacy management standardization, modernization of security techniques as a means of administration according to law and security
enforcement, ensure the safety of the party and State secrets. Confidential work to meet the demands of new technology development
out city created, and care masses life, focus work, in-depth investigation, more out boutique masterpiece, makes we of research results more to into led of decision vision, more to in national some has effect of newspaper Shang published, for advance work, and publicity changde play due of role. Third, information submitted to be pragmatic. Quick and timely. The ancients said: for the time system; statement back for the time being, nothing. Therefore, the submission of information to do ng, send and read faster approval and feedback to implement quickly. To be true and accurate. True mainly reflect the full picture of events, one is one, two, this is the life of the information. Accuracy is primarily qualitative and quantitative questions, quantitative objective of publicQualitative logic. To be reliable and useful. We submit information to have access to decision-making, to guide and promote the work and solve practical problems. Mixed cum.
On the negative information and emergency information, rapid escalation in strict accordance with the procedures, firm, newspaper, newspapers, never late, fail to report, false claim and skimming. Investee 2. supervision and insist on, around and protecting their interests to touch the truth, see practical results. Adhere to people-oriented, the most important thing is to realize, safeguard and develop the fundamental interests of the overwhelming majority of the people. We carry out inspection, so must go deep among the masses, go deep into the realities, always pay attention to the people's livelihood, to grasp the public sentiment, and earnestly safeguard the benefit, addressing the masses are most concerned about and reflecting the strongest issues, efforts to solve the problem of decisions implemented and not implemented. One is to stick to principles. Right of inspection is one of the most important powers of the Office, should not only dare to use, but also with caution. So-called
dared to use, is to hold a number of important issues, bold supervision over supervision, track inspection, problems are not solved do not pass, the blame does not hold did not miss, dissatisfaction of the masses did not miss, the real right of supervision authority, with the benefits. Call with caution, is supervising departments should strengthen the consciousness of authorized strictly according to procedure, preventing the supervision and excessive to prevent adding burden to grass-roots. To this end, the supervision Department of the Party Committee of supervision must be under city and County party Committee Secretary-General (Office). Second, we should focus on. Is the Governor, those related to the globalEvent, Governor the protracted difficult, strong Governor during emergency urgent. Not having special departments in charge of the General Governor, under the normal procedure can do good things not Governor, not authorized by County leaders, not the Governor. Third is to solve
the problem. The purpose of supervision, to resolve the problem. To adhere to and further improve the
家 决不会成为杰出的经济学家。1969年至1981年间颁发的13个诺贝尔经济学奖中，有7个获
奖工 作是相当数学化的。其中有Kantorovich“由于对物资最优调拨理论的贡献”而获1975年奖，Klein“设计预测经济变动的计算机模式”（获1980奖年），Tobin“投资决策的数学模型”（ 获1981
年奖）等等。在经济学中，用到的数学非常广泛，有的还很精深。其中包括线性规划、几何规 划、
非线性规划、不动点定理、变分法、控制理论、动态规划、凸集理论、概率论、数理统计、随机过程、有限结构（图论、格论）、矩阵论、微分方程、对策论、多值函数、集值测度，以及Arrow
的合理意图次序理论等等，它们应用于经济学的许多部门，特别是数理经济学和计量经济学。

5．爱因斯坦的见解 在数学与其他科学的关系方面，培根曾说数学是“通向科学大门的钥匙”；伽利略说“自然界的伟大的书是用数学语言写成的”。物理定律，以及科学的许多最基本的原理，全
是 用数学公式表示的。引力的思想早已有之，但只有当牛顿用精确的数学公式表达时，才成为科
学中最重要 、最著名的万有引力定律。另一位物理大师爱因斯坦认为，“理论物理学家越来越不
得不服从于纯数学的 形式的支配”；他还认定理论物理的“创造性原则寓于数学之中”。他自己的工
作证实了这一思想，正是 黎曼几何为广义相对论提供了数学框架。科学大师们的工作和思想，引
导到如下的信念：“我们生活在受 精确的数学定律制约的宇宙之中”，正是这种制约使得世界成为
可认识的。世界可知是唯物认识论中的最 重要的原理。

6．数学是什么？ 恩格斯说：数学是研究现实中数量关系和空间形式的科学 。虽然时间已过去
一百多年，这一答案大体上还是恰当的，不过应该把“数量”和“空间”作广义的理解 。数量不仅是
实数，而且是向量、张量，甚至是有代数结构的抽象集合中的元；而空间也不是仅指三维空 间，
还有n维、无穷维以及具有某种结构的抽象空间。这样，恩格斯的答案已基本上包含了数学的
主要内容，尽管还有一些重要的篇章如数理逻辑等包不进去。

7．数学的特点 数学的特 点是：内容的抽象性、应用的广泛性、推理的严谨性和结论的明确性。
数学虽不研究事物的质，但任一事 物必有量和形，所以数学是无处不在、无时不用的。两种事物，
如果有相同的量或形，便可用相同的数学 方法，因而数学必然、也必须是抽象的。同一个拉普拉
斯（Laplace）方程，既可用来表示热平衡 态、溶质动态平衡、弹性膜的平衡位置，也可表示静
态电磁场、真空中的引力势等等。数学中严谨的推理 和一丝不苟的计算，使得每一数学结论不可
动摇。这种思想方法不仅培养了数学家，也有助于提高全国人 民的科学文化素质。它是人类巨大
的精神财富。爱因斯坦关于欧氏几何曾说：“世界第一次目睹了一个逻 辑体系的奇迹，这个逻辑
体系如此精密地一步一步推进，以致它每一个命题都是绝对不容置疑的——我这 里说的是欧几里
得几何。推理的这种可赞叹的胜利，使人类的理智获得了为取得以后成就所必需的信心。 ”

8．数学的成份 数学大体上可分为三大部分：基础数学、应用数学和计算数学。基础数 学是数
学中的核心，也是最纯粹最抽象的部分。它大致由三个分支组成：分析、代数和几何。这三者又< br>相互交叉和渗透，从而产生解析几何、解析数论、代数几何等学科。此外研究随机现象的概率论、
研究形式推理的数理逻辑等，也属于基础数学。

应用数学研究现实中具体的数学问题，它既 采用基础数学的成果，同时又反过来从实际中提炼问
题、探讨新思想和新方法以丰富基础数学。数学应用 的领域虽无边际，但大致也可分为三方面：
经济建设（工、农、商等）；科学与技术（特别是高科技）； 军事与国防，详述见后。运筹学、
控制论与数理统计等学科中，大部分内容属于应用数学；而经济数学、 生物数学等，则是比较标
准的应用数学学科。

eelings survey, by looking up public sentiments to find problems. Problems will increase its special supervision, set up accounts, hold on to it. We should conscientiously implement the leading contracting matters, secured, had an answer to everything, then settles rate of 100%. Have an impact on some of the outstanding issues, supervision departments and information components together, play the supervisory role of the news media to promote problem solving. Investee 3. insist on a daily run, around the practice of truth catching efficiency, focus specification. To give full play to the party Office around connecting, coordinating internal and external features, contact, rally at all levels, to motivate every aspect, adhere to the truth, strengthening standardized management to achieve coherent, efficient and effective functioning of the daily work of the Party Committee. Is processing messages should strive to streamline, standardize and quality. Streamlining is to control the number of
messages, compress messages, reducing procedures, improve message handling efficiency. Specifications, is to strictly enforce the ban issued by the Communist party authorities in document handling regulations and provincial and municipal regulations, conscientiously strengthen and improve communications management to ensure that party documents orderly. High quality, is to improve the quality of message processing, it is necessary to accurately implementing the intention of the Party Committee, clearance, good communications, policy program closed, ensuring that there is no error. Second meeting scheduled to ensure thorough, safe and efficient. Any arrangements for the meetings and events, carefully arranged, item-by-item interface implemented, sure. o vigorously streamline meetings, activities, number of pressure reduction, scale to ensure that leadership emerged from the General Conference and entertainment services, focus on big things, matters. Third, reception services
should lay stress on humane, personal, cultural and human. Reception and work directly with people, reception services directly affecting the Office of party Committee The image of the region. At the same time strengthening the construction of library, improve the reception conditions, more human-oriented, personal, cultural work into the reception, a little more human needs, a little more human care more humane atmosphere, and constantly improve the service, improve the quality of service. Meanwhile, to further pay special attention to the daily work of the other Office System. Confidential work responsibility system for leading cadres to implement security as a leader, to improve the confidentiality of classified personnel, especially leading cadres, strengthening party and Government focus on vital sectors of security management, to advance privacy management standardization, modernization of security techniques as a means of administration according to law and security
enforcement, ensure the safety of the party and State secrets. Confidential work to meet the demands of new technology development
out city created, and care masses life, focus work, in-depth investigation, more out boutique masterpiece, makes we of research results more to into led of decision vision, more to in national some has effect of newspaper Shang published, for advance work, and publicity changde play due of role. Third, information submitted to be pragmatic. Quick and timely. The ancients said: for the time system; statement back for the time being, nothing. Therefore, the submission of information to do ourng, send and read faster approval and feedback to implement quickly. To be true and accurate. True mainly reflect the full picture of events, one is one, two, this is the life of the information. Accuracy is primarily qualitative and quantitative questions, quantitative objective of publicQualitative logic. To be reliable and useful. We submit information to have access to decision-making, to guide and promote the work and solve practical problems. Mixed cum.
On the negative information and emergency information, rapid escalation in strict accordance with the procedures, firm, newspaper, newspapers, never late, fail to report, false claim and skimming. Investee 2. supervision and insist on, around and protecting their interests to touch the truth, seek practical results. Adhere to people-oriented, the most important thing is to realize, safeguard and develop the fundamental interests of the overwhelming majority of the people. We carry out inspection, so must go deep among the masses, go deep into the realities, always pay attention to the people's livelihood, to grasp the public sentiment, and earnestly safeguard the benefit, addressing the masses are most concerned about and reflecting the strongest issues, efforts to solve the problem of decisions implemented and not implemented. One is to stick to principles. Right of inspection is one of the most important powers of the Office, should not only dare to use, but also with caution. So-called
dared to use, is to hold a number of important issues, bold supervision over supervision, track inspection, problems are not solved do not pass, the blame does not hold did not miss, dissatisfaction of the masses did not miss, the real right of supervision authority, with the benefits. Call with caution, is supervising departments should strengthen the consciousness of authorized strictly according to procedure, preventing the supervision and excessive to prevent adding burden to grass-roots. To this end, the supervision Department of the Party Committee of supervision must be under city and County party Committee Secretary-General (Office). Second, we should focus on. Is the Governor, those related to the globalEvent, Governor the protracted difficult, strong Governor during emergency urgent. Not having special departments in charge of the General Governor, under the normal procedure can do good things not Governor, not authorized by County leaders, not the Governor. Third is to solve
the problem. The purpose of supervision, to resolve the problem. To adhere to and further improve the
计 算数学偏重于计算，早期它致力于求出各种方程（代数方程、（偏）微分方程、微积分方程等）
的数值解 。近40年来，计算数学有了极其迅速的发展，这主要是由于电子计算机的出现。计算
机的高速计算使得 许多过去无法求解的问题成为可解，从而大大扩展了数学的应用范围。例如，
短期天气预报、高速运行器 的控制，离开计算数学和计算机是不可能的。近期，由于计算机模拟、
计算辅助证明（如四色问题的证实 ）在人工智能中的应用，以及计算力学、计算物理、计算化学、
计算几何、计算概率等新学科的诞生等等 ，使得计算数学雄风大振。今天，人们已把计算作为与
理论、实验鼎足而立的第三种科学方法而引入科学 界。

基础数学、应用数学与计算数学既有各自的特点又紧密相互联系。一个重大的数学问题 ，特别是
从实际中提出的数学问题，都需要上述三种数学的内容和方法。建立数学模型，寻求解题方法，
需要基础数学和应用数学，而使解题方法得以实现，则离不开计算数学。这三种数学互相补充，
互相渗透，大大地促进了整个数学科学的发展。

9．现代数学的新特点 数学内部各分支间 的相互渗透、数学与其他科学（如控制论）的相互渗
透、电子计算机的出现，正是当代数学三个新的特点 。由于相互渗透而导致许多新问题和古老难
题的解决，其成绩往往出乎意外而使人惊异。例如，对素数的 研究以往认为很少有实用价值，却
不料它在密码学中受到重用。密码学认为，千位以上的整数的素因子分 解，几十年内在计算上不
可能实现。但荷兰数学家得到了一个当前最好的因子分解算法，这严重地冲击了 上述想法和密码
的安全性。又如泛函分析中的无穷维Von Neumann代数解决了拓扑学三维空间 中打结理论中一
些难题。描写孤立波的KdV方程用于代数中，解决了Riemann提出的一个重要问 题。描写随机
现象的Malliavin演算给出了著名的Atiyah-Singer指数定理的新证 明，并推广了这一定理。更使
人感叹的是物理中的杨振宁——米尔斯规范场与陈省身研究的纤维丛间的紧 密联系，二者间的主
要术语竟可一一对应。例如，规范形式——主纤维丛、规范势——主纤维丛上的连络 、相因子——
平行移动、电磁作用——U（1）丛上的连络等等。无怪乎杨振宁说：“我非常惊奇地发现 ，规范
场说是纤维丛的连络，而数学家们在提出纤维丛上的连络时，并未涉及到物理世界”。

学科间的相互渗透是当今各门科学技术高速发展的必然后果，也是重要原因；只有置身于众多高
新科技急剧发展的大背景中，数学内、外部的相互渗透才是可能的，也是容易理解的。

10．数学发展的趋势 今后数学的发展必然比最近数十年更迅速，成绩更巨大。科学技术越积累，人类认识、利用和改造自然的能力越增长，科学技术便越快发展，形成一良性循环。作为其中的
一部 分，数学也必然如此。总体上，高速发展是完全可以预言的；但至于哪些分支发展得更快些，
更好些，则 既依赖于该学科本身的活力又依赖于科技大背景的波动和社会的需要，难以肯定回答。
不过从目前的情况 看，非线性数学是一重要发展方向。线性方程的特征是叠加原理成立：如φ1、
φ2是方程的两个解，则 a1φ1＋a2φ2也是解，其中a1、a2是常数。例如薛定谔方程或拉普拉
斯方程都是线性的。线性 数学比较成熟。但还有许多问题是非线性的，如牛顿引力论中的基本定
律是平方反比关系，粮食产量对肥 料未必成正比等。引人注目的冲击波、孤立子、混沌现象、n
体问题等都是非线性的。非线性问题，不仅 涉及面广，而且难度也大，这反而更能引发人们研究
的兴趣。

除去非线性数学外， 离散数学（涉及数论、抽象代数、数理逻辑、组合论、图论、博奕论、规划
论等），概率论与数理统计、 计算数学以及数学对生物学、经济学、语言学、管理学、控制论、
复杂性等的渗透和应用，都会有更大的 发展。其它数学也同样会有迅速的进展；甚至会爆出新的、
出人意料的大冷门；晴空一鹤排云上，更引诗 情到碧霄，这也是非常可能的。
eelings survey, by looking up public sentiments to find problems. Problems will increase its special supervision, set up accounts, hold on to it. We should conscientiously implement the leading contracting matters, secured, had an answer to everything, then settles rate of 100%. Have an impact on some of the outstanding issues, supervision departments and information components together, play the supervisory role of the news media to promote problem solving. Investee 3. insist on a daily run, around the practice of truth catching efficiency, focus specification. To give full play to the party Office around connecting, coordinating internal and external features, contact, rally at all levels, to motivate every aspect, adhere to the truth, strengthening standardized management to achieve coherent, efficient and effective functioning of the daily work of the Party Committee. Is processing messages should strive to streamline, standardize and quality. Streamlining is to control the number of
messages, compress messages, reducing procedures, improve message handling efficiency. Specifications, is to strictly enforce the ban issued by the Communist party authorities in document handling regulations and provincial and municipal regulations, conscientiously strengthen and improve communications management to ensure that party documents orderly. High quality, is to improve the quality of message processing, it is necessary to accurately implementing the intention of the Party Committee, clearance, good communications, policy program closed, ensuring that there is no error. Second meeting scheduled to ensure thorough, safe and efficient. Any arrangements for the meetings and events, carefully arranged, item-by-item interface implemented, sure. o vigorously streamline meetings, activities, number of pressure reduction, scale to ensure that leadership emerged from the General Conference and entertainment services, focus on big things, matters. Third, reception services
should lay stress on humane, personal, cultural and human. Reception and work directly with people, reception services directly affecting the Office of party Committee The image of the region. At the same time strengthening the construction of library, improve the reception conditions, more human- oriented, personal, cultural work into the reception, a little more human needs, a little more human care more humane atmosphere, and constantly improve the service, improve the quality of service. Meanwhile, to further pay special attention to the daily work of the other Office System. Confidential work responsibility system for leading cadres to implement security as a leader, to improve the confidentiality of classified personnel, especially leading cadres, strengthening party and Government focus on vital sectors of security management, to advance privacy management standardization, modernization of security techniques as a means of administration according to law and security
enforcement, ensure the safety of the party and State secrets. Confidential work to meet the demands of new technology development
out city created, and care masses life, focus work, in-depth investigation, more out boutique masterpiece, makes we of research results more to into led of decision vision, more to in national some has effect of newspaper Shang published, for advance work, and publicity changde play due of role. Third, information submitted to be pragmatic. Quick and timely. The ancients said: for the time system; statement back for the time being, nothing. Therefore, the submission of information to do ng, send and read faster approval and feedback to implement quickly. To be true and accurate. True mainly reflect the full picture of events, one is one, two, this is the life of the information. Accuracy is primarily qualitative and quantitative questions, quantitative objective of publicQualitative logic. To be reliable and useful. We submit information to have access to decision-making, to guide and promote the work and solve practical problems. Mixed cum.
On the negative information and emergency information, rapid escalation in strict accordance with the procedures, firm, newspaper, newspapers, never late, fail to report, false claim and skimming. Investee 2. supervision and insist on, around and protecting their interests to touch the truth, see practical results. Adhere to people-oriented, the most important thing is to realize, safeguard and develop the fundamental interests of the overwhelming majority of the people. We carry out inspection, so must go deep among the masses, go deep into the realities, always pay attention to the people's livelihood, to grasp the public sentiment, and earnestly safeguard the benefit, addressing the masses are most concerned about and reflecting the strongest issues, efforts to solve the problem of decisions implemented and not implemented. One is to stick to principles. Right of inspection is one of the most important powers of the Office, should not only dare to use, but also with caution. So-called
dared to use, is to hold a number of important issues, bold supervision over supervision, track inspection, problems are not solved do not pass, the blame does not hold did not miss, dissatisfaction of the masses did not miss, the real right of supervision authority, with the benefits. Call with caution, is supervising departments should strengthen the consciousness of authorized strictly according to procedure, preventing the supervision and excessive to prevent adding burden to grass-roots. To this end, the supervision Department of the Party Committee of supervision must be under city and County party Committee Secretary-General (Office). Second, we should focus on. Is the Governor, those related to the globalEvent, Governor the protracted difficult, strong Governor during emergency urgent. Not having special departments in charge of the General Governor, under the normal procedure can do good things not Governor, not authorized by County leaders, not the Governor. Third is to solve
the problem. The purpose of supervision, to resolve the problem. To adhere to and further improve the

二、大哉数学之为用

1959年5月，华罗庚教授在《人民日报》上发表了《大哉 数学之为用》，精彩地叙述了数学的
各种应用：宇宙之大、粒子之微、火箭之速、化工之巧、地球之变、 生物之谜、日用之繁等各个
方面，无处不有数学的重要贡献。很难比这篇文章写得更全面了。下面只举些 60年代以后数学
的若干重大应用，以见一斑。我们会看到，有些重要问题的解决，数学方法是唯一的， 也就是说，
除数学外，用任何其他方法、仪器、手段都会一筹莫展。

1．沙漠风暴与数学战 1990年伊拉克点燃了科威特的数百口油井，浓烟遮天蔽日。美国及其盟军在沙漠风暴以前，曾严肃地考虑点燃所有油井的后果。据美国《超级计算评论》杂志披露，五
角大 楼要求太平洋-赛拉研究公司研究此问题。该公司利用Navier-Stokes方程和有热损失能量
方程作为计算模型，在进行一系列模拟计算后得出结论：大火的烟雾可能招致一场重大的污染事
件，它将 波及到波斯湾、伊朗南部、巴基斯坦和印度北部，但不会失去控制，不会造成全球性的
气候变化，不会对 地球的生态和经济系统造成不可挽回的损失。这样才促成美国下定决心。所以
人们说第一次世界大战是化 学战（火药），第二次是物理战（原子弹），海湾战争是数学战。

数学在军事方面的应用不 可忽视。再举三个例子，海湾战争中，美国将大批人员和物资调运到位，
只用了短短一个月时间。这是由 于他们运用了运筹学和优化技术。另一例是：采用可靠性方法，
美国研制MZ导弹的发射试验从原来的3 6次减少为25次，可靠性却从72％提高到93％。再者，
我国研制原子弹，试验次数仅为西方的1／ 10，从原子弹到氢弹只用了2年8个月，重要原因
之一是有许多优秀数学家参加了工作。

2．太阳系是稳定的吗？ 地球的前途如何？是一个虽然遥远却非常有趣而重要的问题。将来太
阳系是否会保持现状？是否有某行星脱离太阳系？行星间是否会碰撞？数学证明，太阳系在相当
长时间内 是稳定的，至少10亿年内如此。科学家还用计算模拟以研究恒星消亡过程。太阳最后
变成一颗白矮星； 但一颗质量约为8-10倍于太阳的恒星则会发生超新星爆炸：由于热源枯竭而
收缩到一个小城市大小， 密度达到原来的100万亿倍。这些物质产生巨大的刚性反弹而爆炸，
恒星外壳被炸掉而剩下的残余成为 中子星。天文学是数学的重要用武场所，1846年勒维耶通过
计算在笔尖上发现海王星，在科学史上传 为佳话。在多体问题的研究中，由于初始条件不同，多
体系统的运动或表现为规则的，或表现为混沌的。 行星沿椭圆运动是规则运动的例子，而小行星
在Kirkwook窗口的运动是混沌运动的例子：与木星 的共振相互作用导致偏心率随机的变化，有
时朝这一方向，有时朝另一方向；无规则变化的偏心率可能变 得很大，这时小行星便可能陨落，
例如落到火星上。

3．石油勘探 这是数学取得 重大经济效益的应用场所之一。石油深藏地下，人们通过人工地震
记下反向回来的地震波，波形随着地层 地质的不同而变化。用计算机处理所得的波形数据可以提
供地下岩层、岩性以及有关石油、天然气等的知 识。1991年5月，美国壳牌石油公司应用计算
技术于新奥尔良以南39公里的河流之下930公里处 ，探明了一个储量超过10亿桶的大油田。
我国在这方面也做了许多工作（见后）。在数据处理中，Wi ener滤波起到重要作用。

4．DNA与CT 如果说二次大战以前，数学主要用于天文 、物理，那么，现在数学已深入到化学、
生物和经济、管理等社会科学中。例如，DNA是分子生物学的 重要研究对象，是遗传信息的携
带者，它具有一种特别的立体结构——双螺旋结构，后者在细胞核中呈扭 曲、绞拧、打结和圈套
eelings survey, by looking up public sentiments to find problems. Problems will increase its special supervision, set up accounts, hold on to it. We should conscientiously implement the leading contracting matters, secured, had an answer to everything, then settles rate of 100%. Have an impact on some of the outstanding issues, supervision departments and information components together, play the supervisory role of the news media to promote problem solving. Investee 3. insist on a daily run, around the practice of truth catching efficiency, focus specification. To give full play to the party Office around connecting, coordinating internal and external features, contact, rally at all levels, to motivate every aspect, adhere to the truth, strengthening standardized management to achieve coherent, efficient and effective functioning of the daily work of the Party Committee. Is processing messages should strive to streamline, standardize and quality. Streamlining is to control the number of
messages, compress messages, reducing procedures, improve message handling efficiency. Specifications, is to strictly enforce the ban issued by the Communist party authorities in document handling regulations and provincial and municipal regulations, conscientiously strengthen and improve communications management to ensure that party documents orderly. High quality, is to improve the quality of message processing, it is necessary to accurately implementing the intention of the Party Committee, clearance, good communications, policy program closed, ensuring that there is no error. Second meeting scheduled to ensure thorough, safe and efficient. Any arrangements for the meetings and events, carefully arranged, item-by-item interface implemented, sure. o vigorously streamline meetings, activities, number of pressure reduction, scale to ensure that leadership emerged from the General Conference and entertainment services, focus on big things, matters. Third, reception services
should lay stress on humane, personal, cultural and human. Reception and work directly with people, reception services directly affecting the Office of party Committee The image of the region. At the same time strengthening the construction of library, improve the reception conditions, more human- oriented, personal, cultural work into the reception, a little more human needs, a little more human care more humane atmosphere, and constantly improve the service, improve the quality of service. Meanwhile, to further pay special attention to the daily work of the other Office System. Confidential work responsibility system for leading cadres to implement security as a leader, to improve the confidentiality of classified personnel, especially leading cadres, strengthening party and Government focus on vital sectors of security management, to advance privacy management standardization, modernization of security techniques as a means of administration according to law and security
enforcement, ensure the safety of the party and State secrets. Confidential work to meet the demands of new technology development
out city created, and care masses life, focus work, in-depth investigation, more out boutique masterpiece, makes we of research results more to into led of decision vision, more to in national some has effect of newspaper Shang published, for advance work, and publicity changde play due of role. Third, information submitted to be pragmatic. Quick and timely. The ancients said: for the time system; statement back for the time being, nothing. Therefore, the submission of information to do ourng, send and read faster approval and feedback to implement quickly. To be true and accurate. True mainly reflect the full picture of events, one is one, two, this is the life of the information. Accuracy is primarily qualitative and quantitative questions, quantitative objective of publicQualitative logic. To be reliable and useful. We submit information to have access to decision-making, to guide and promote the work and solve practical problems. Mixed cum.
On the negative information and emergency information, rapid escalation in strict accordance with the procedures, firm, newspaper, newspapers, never late, fail to report, false claim and skimming. Investee 2. supervision and insist on, around and protecting their interests to touch the truth, seek practical results. Adhere to people-oriented, the most important thing is to realize, safeguard and develop the fundamental interests of the overwhelming majority of the people. We carry out inspection, so must go deep among the masses, go deep into the realities, always pay attention to the people's livelihood, to grasp the public sentiment, and earnestly safeguard the benefit, addressing the masses are most concerned about and reflecting the strongest issues, efforts to solve the problem of decisions implemented and not implemented. One is to stick to principles. Right of inspection is one of the most important powers of the Office, should not only dare to use, but also with caution. So-called
dared to use, is to hold a number of important issues, bold supervision over supervision, track inspection, problems are not solved do not pass, the blame does not hold did not miss, dissatisfaction of the masses did not miss, the real right of supervision authority, with the benefits. Call with caution, is supervising departments should strengthen the consciousness of authorized strictly according to procedure, preventing the supervision and excessive to prevent adding burden to grass-roots. To this end, the supervision Department of the Party Committee of supervision must be under city and County party Committee Secretary-General (Office). Second, we should focus on. Is the Governor, those related to the globalEvent, Governor the protracted difficult, strong Governor during emergency urgent. Not having special departments in charge of the General Governor, under the normal procedure can do good things not Governor, not authorized by County leaders, not the Governor. Third is to solve
the problem. The purpose of supervision, to resolve the problem. To adhere to and further improve the
等 形状，这正好是数学中的扭结理论研究的对象，北京大学姜伯驹教授对此深有研究。下面两项
有关生物、 医学和化学的高技术中，数学起着关键性作用。X射线计算机层析摄影仪（简称CT）
的问世是本世纪医 学中的奇迹，其原理是基于不同的物质有不同的X射线衰减系数。如果能够
确定人体的衰减系数的分布， 就能重建其断层或三维图像。但通过X射线透射时，只能测量到
人体的直线上的X射线衰减系数的平均值 （是一积分）。当直线变化时，此平均值（依赖于某
参数）也随之变化。能否通过此平均值以求出整个衰 减系统的分布呢？人们利用数学中的Radon
变换解决了此问题，Radon变换已成为CT理论的核 心。首创CT理论的A．M．Cormark（美）
及第一台CT制作者C．N．Hounsfield （英）因而荣获1979年诺贝尔医学和生理学奖。另一项
高技术是H．Hauptman与J．Kar le合作，发明了测定分子结构的新方法，利用它可以直接显
示被X射线透射的分子的立体结构。人们应 用此方法，并结合利用计算机，已测出包括维生素、
激素等数万种分子结构，推动了有机化学、药物学和 生物学等的发展；二发明人分享了1985年
的诺贝尔化学奖。由此可见在此二项技术中数学的关键作用 。

5．飞机制造 制造业中广泛地用到数学，今以飞机为例，设计师必须考虑结构强度与稳 定性，
这是用有限元来分析的，而机翼的振动情况则需解特征值问题；为了使飞机省油与提高速度必需< br>找到一种最佳机翼和整个机体的形状；如何为飞行员选择最优控制参数，也是必须考虑的问题。
飞 机设计在极大程度上以计算为基础，人们研究描绘机翼和整个机体附近气流的方程。工程设计
和制造工艺 主要靠计算机辅助设计（CAD）和计算机辅助制造（CAM）两大工具，而这两者又
都以数学为理论基 础。计算流体力学可以帮助人们设计新的飞行器。数学模型已代替了许多的实
验，如风洞实验，既便宜、 省时，又有适用性、安全性。以前利用风洞设计飞机某一部件，若要
改变某一部位，必须在机械车间建一 模型；而今天设计一数学模型，只要通过键盘打进新的参数
即可。自动导航与自动着陆系统是根据卡尔曼 滤波的方法设计的，而后者主要又是数学。在涡轮
机、压缩机、内燃机、发电机、数据存储磁盘、大规模 集成电路、汽车车身、船体等的设计中，
也都用到了类似的先进数学设计方法。

6．Hardy的故事 G．H．Hardy（1877—1947）是英国著名的数学家，他推崇数学 的“纯粹”和“美”，
认为数学是一种永久性的艺术品。他从不谈（甚至轻视）数学的应用，他写道：“ 我从不干任何
有用的事情，我的任何一项发现都没有，或者说不可能给这个世界的安逸带来最细微的变化 ……
他们（指某些数学家）的工作，也和我的同样无用”。但他万万没有想到，1908年他发表的一篇
短文却在群体遗传学中得到重要应用。那篇文章可直观地解释如下：人的某种遗传学病（如色盲），在一群体中是否会由于一代一代地遗传而患者越来越多？20世纪初有些生物学家认为确会如
此，如 果这样，那么势必后代每个人都会成为患者。Hardy利用简单的概率运算，指出这种说法
是错误的。 他证明了：患者的分布是平稳的，不随时间而改变。差不多同时，德国的一位医师
Weinberg也得 到同样的结论。这一发现被称为Hardy－Weinberg定律。

7．高超的数学工具——在宏观经济中的应用 宏观经济学研究经济综合指标的控制，例如研究
失业、价格水平以及收支平衡的控制等。而微观经济学则针对买方和卖方，讨论消费与生产中的
选择问题 。1972年以来，承担调整美国经济的政府机构联邦储备局，以最优控制方法，特别是
线性二次方法为 背景，提出了包括失业与通货膨胀平衡的政策建议。1973年，《商业周刊》登
了一篇文章，概述了最 优控制在经济学中的潜在作用，文章说：“你如何努力地及时地刹住过于
繁荣的经济，而又不至于滑入灾 难性衰退的危险之中？……美国的决策者们恰好面临这种情形，
而从经济学家那里极少得到明确的建议… …对这种两难的情况，可从最优控制理论得到方法上的
帮助”。利用控制理论和梯度法，人们求解了南朝 鲜经济的最优计划模型（参考Economet－rica，
Vol.33，May，1970，ck等 的文章）。美国、加拿大、智利等也有类似的经济模型。
eelings survey, by looking up public sentiments to find problems. Problems will increase its special supervision, set up accounts, hold on to it. We should conscientiously implement the leading contracting matters, secured, had an answer to everything, then settles rate of 100%. Have an impact on some of the outstanding issues, supervision departments and information components together, play the supervisory role of the news media to promote problem solving. Investee 3. insist on a daily run, around the practice of truth catching efficiency, focus specification. To give full play to the party Office around connecting, coordinating internal and external features, contact, rally at all levels, to motivate every aspect, adhere to the truth, strengthening standardized management to achieve coherent, efficient and effective functioning of the daily work of the Party Committee. Is processing messages should strive to streamline, standardize and quality. Streamlining is to control the number of
messages, compress messages, reducing procedures, improve message handling efficiency. Specifications, is to strictly enforce the ban issued by the Communist party authorities in document handling regulations and provincial and municipal regulations, conscientiously strengthen and improve communications management to ensure that party documents orderly. High quality, is to improve the quality of message processing, it is necessary to accurately implementing the intention of the Party Committee, clearance, good communications, policy program closed, ensuring that there is no error. Second meeting scheduled to ensure thorough, safe and efficient. Any arrangements for the meetings and events, carefully arranged, item-by-item interface implemented, sure. o vigorously streamline meetings, activities, number of pressure reduction, scale to ensure that leadership emerged from the General Conference and entertainment services, focus on big things, matters. Third, reception services
should lay stress on humane, personal, cultural and human. Reception and work directly with people, reception services directly affecting the Office of party Committee The image of the region. At the same time strengthening the construction of library, improve the reception conditions, more human-oriented, personal, cultural work into the reception, a little more human needs, a little more human care more humane atmosphere, and constantly improve the service, improve the quality of service. Meanwhile, to further pay special attention to the daily work of the other Office System. Confidential work responsibility system for leading cadres to implement security as a leader, to improve the confidentiality of classified personnel, especially leading cadres, strengthening party and Government focus on vital sectors of security management, to advance privacy management standardization, modernization of security techniques as a means of administration according to law and security
enforcement, ensure the safety of the party and State secrets. Confidential work to meet the demands of new technology development
out city created, and care masses life, focus work, in-depth investigation, more out boutique masterpiece, makes we of research results more to into led of decision vision, more to in national some has effect of newspaper Shang published, for advance work, and publicity changde play due of role. Third, information submitted to be pragmatic. Quick and timely. The ancients said: for the time system; statement back for the time being, nothing. Therefore, the submission of information to do ng, send and read faster approval and feedback to implement quickly. To be true and accurate. True mainly reflect the full picture of events, one is one, two, this is the life of the information. Accuracy is primarily qualitative and quantitative questions, quantitative objective of publicQualitative logic. To be reliable and useful. We submit information to have access to decision-making, to guide and promote the work and solve practical problems. Mixed cum.
On the negative information and emergency information, rapid escalation in strict accordance with the procedures, firm, newspaper, newspapers, never late, fail to report, false claim and skimming. Investee 2. supervision and insist on, around and protecting their interests to touch the truth, see practical results. Adhere to people-oriented, the most important thing is to realize, safeguard and develop the fundamental interests of the overwhelming majority of the people. We carry out inspection, so must go deep among the masses, go deep into the realities, always pay attention to the people's livelihood, to grasp the public sentiment, and earnestly safeguard the benefit, addressing the masses are most concerned about and reflecting the strongest issues, efforts to solve the problem of decisions implemented and not implemented. One is to stick to principles. Right of inspection is one of the most important powers of the Office, should not only dare to use, but also with caution. So-called
dared to use, is to hold a number of important issues, bold supervision over supervision, track inspection, problems are not solved do not pass, the blame does not hold did not miss, dissatisfaction of the masses did not miss, the real right of supervision authority, with the benefits. Call with caution, is supervising departments should strengthen the consciousness of authorized strictly according to procedure, preventing the supervision and excessive to prevent adding burden to grass-roots. To this end, the supervision Department of the Party Committee of supervision must be under city and County party Committee Secretary-General (Office). Second, we should focus on. Is the Governor, those related to the globalEvent, Governor the protracted difficult, strong Governor during emergency urgent. Not having special departments in charge of the General Governor, under the normal procedure can do good things not Governor, not authorized by County leaders, not the Governor. Third is to solve
the problem. The purpose of supervision, to resolve the problem. To adhere to and further improve the

8．提高产品质量——数字在微观经济学中之应用 数理统计学的应用极为广泛，它的优势是从
有限次的观察或实验中提取重要的信息。数理统计中的篇章“实验设计”、“质量控制（QC）”、“多
元分析”等对提高产品的质量往往能起到重要的作用。一家美国电视机制造公司被日本人买下，
这家公司 的废品率非常高。通过运用QC后，废品率下降到2％。下面的例子说明美国电话电报
公司如何使用QC 以提高质量。问题是关于自动化装配线，这一装配线由几个机件组成，其生产
率出奇的低，而人们又找不 出原因。QC方法首先是收集数据以确定失败模式，很快找出问题的
症结是生产线上所用的塑料成分的尺 度变化太大；这些塑料部件过分弯曲；金属元件间的焊接点
过厚，使机件运行阻塞。经过一年的改进，生 产率增加121％，工作时间减少61％，产品成功
率从90％增到98%。

一般 地，某产品的质量依赖于若干个因素（原料、工艺时间等等），每一因素又有若干种可能的
选择，如何挑 出最优的选择搭配以求获得最佳的产品，是统计实验设计（SED）的主要研究问
题。SED有一段发展 史，20年代，R．A．Fisher在农业中运用SED，取得前所未有的成功。
20年代中叶蒂皮特 运用SED于棉纺工业，随后又用于化学和制药工业。50年代，美国戴明把
SED介绍到日本，对日本 制造业产生很大影响，日本工程师田口用此法以减小产品性能异性从
而提高产品质量。日本工业广泛运用 统计质量控制，后又发展成全面质量管理，这项措施大大提
高了日本产品的质量，在国际上最有竞争力， 引起了巨大的反响。80年代，许多美国工业公司
通过田口把统计方法用到设计和制造中，产品质量不断 地得以提高。

三、近年来数学在我国的应用

1992年9月，中国工 业与应用数学学会召开了第二次大会，会上李大潜教授宣读了《努力发展
中国的工业与应用数学》的报告 ，其中叙述了我国应用数学的新进展。本节便以这篇报告为基础，
补充若干新材料。后者是由一些研究所 和大学所提供的，自然是挂一漏万。如前所述，数学应用
可分成在经济建设（1—8段）、在科学技术（ 9—14，16）、在军事与安全（15）三者中的应
用。

1．优化、控制与统筹 人们希望在一定条件下，在多种策略中选取其一以获得最大利益；数学
上，这要求目标函数（代表利益） 达到极大。目标函数也可代表损失，于是要求它达到极小。这
类问题往往化为求目标函数的条件极值，或 者化为变分问题。优选法、线性规划、非线性规划、
最优控制等，都致力于研究优化问题。如果有好几件 工作要做，便发生如何合理安排，以使收效
最大（时间最短、劳力或成本最省等），这是统筹（或运筹学 ）的研究对象。70年代，华罗庚
教授登高一呼，并且亲自动手，率领研究小组，深入到工厂、农村、矿 山，大力推广优选法与统
筹法，足迹遍及23个省市，成果遍及许多行业，解决了许多问题。例如，纺织 业中提高织机效
率与染色质量，减少细纱断头率；电子行业中试制新的160V电容器，使100万米废 钼丝复活；
农业中提高加工中的出米率、出油率、出酒率等等。目前张里千、陈希孺教授等正在开展的现 场
统计，对国家经济建设也起了很好作用。

由于改善数学模型，运用最优控制理论 和改进计算方法，生产过程和工艺参数的优化已在钢铁、
冶金、电力、石油化工中取得很好效果。武汉钢 铁公司、上海石油化工总厂、南京炼油厂、燕山
石化公司通过上述优化技术，提高生产率最高可达20％ ，一套装置每年可增加几百万元的经济
效益。攀枝花钢铁公司建立了提钒工艺流程系统优化的数学模型， 进行全面调优后使钒的回收率
达到国际水平，使我国从钒进口国一跃而为钒出口国。云南大学统计系运用 多元回归分析研究钢
eelings survey, by looking up public sentiments to find problems. Problems will increase its special supervision, set up accounts, hold on to it. We should conscientiously implement the leading contracting matters, secured, had an answer to everything, then settles rate of 100%. Have an impact on some of the outstanding issues, supervision departments and information components together, play the supervisory role of the news media to promote problem solving. Investee 3. insist on a daily run, around the practice of truth catching efficiency, focus specification. To give full play to the party Office around connecting, coordinating internal and external features, contact, rally at all levels, to motivate every aspect, adhere to the truth, strengthening standardized management to achieve coherent, efficient and effective functioning of the daily work of the Party Committee. Is processing messages should strive to streamline, standardize and quality. Streamlining is to control the number of
messages, compress messages, reducing procedures, improve message handling efficiency. Specifications, is to strictly enforce the ban issued by the Communist party authorities in document handling regulations and provincial and municipal regulations, conscientiously strengthen and improve communications management to ensure that party documents orderly. High quality, is to improve the quality of message processing, it is necessary to accurately implementing the intention of the Party Committee, clearance, good communications, policy program closed, ensuring that there is no error. Second meeting scheduled to ensure thorough, safe and efficient. Any arrangements for the meetings and events, carefully arranged, item-by-item interface implemented, sure. o vigorously streamline meetings, activities, number of pressure reduction, scale to ensure that leadership emerged from the General Conference and entertainment services, focus on big things, matters. Third, reception services
should lay stress on humane, personal, cultural and human. Reception and work directly with people, reception services directly affecting the Office of party Committee The image of the region. At the same time strengthening the construction of library, improve the reception conditions, more human- oriented, personal, cultural work into the reception, a little more human needs, a little more human care more humane atmosphere, and constantly improve the service, improve the quality of service. Meanwhile, to further pay special attention to the daily work of the other Office System. Confidential work responsibility system for leading cadres to implement security as a leader, to improve the confidentiality of classified personnel, especially leading cadres, strengthening party and Government focus on vital sectors of security management, to advance privacy management standardization, modernization of security techniques as a means of administration according to law and security
enforcement, ensure the safety of the party and State secrets. Confidential work to meet the demands of new technology development
out city created, and care masses life, focus work, in-depth investigation, more out boutique masterpiece, makes we of research results more to into led of decision vision, more to in national some has effect of newspaper Shang published, for advance work, and publicity changde play due of role. Third, information submitted to be pragmatic. Quick and timely. The ancients said: for the time system; statement back for the time being, nothing. Therefore, the submission of information to do ourng, send and read faster approval and feedback to implement quickly. To be true and accurate. True mainly reflect the full picture of events, one is one, two, this is the life of the information. Accuracy is primarily qualitative and quantitative questions, quantitative objective of publicQualitative logic. To be reliable and useful. We submit information to have access to decision-making, to guide and promote the work and solve practical problems. Mixed cum.
On the negative information and emergency information, rapid escalation in strict accordance with the procedures, firm, newspaper, newspapers, never late, fail to report, false claim and skimming. Investee 2. supervision and insist on, around and protecting their interests to touch the truth, seek practical results. Adhere to people-oriented, the most important thing is to realize, safeguard and develop the fundamental interests of the overwhelming majority of the people. We carry out inspection, so must go deep among the masses, go deep into the realities, always pay attention to the people's livelihood, to grasp the public sentiment, and earnestly safeguard the benefit, addressing the masses are most concerned about and reflecting the strongest issues, efforts to solve the problem of decisions implemented and not implemented. One is to stick to principles. Right of inspection is one of the most important powers of the Office, should not only dare to use, but also with caution. So-called
dared to use, is to hold a number of important issues, bold supervision over supervision, track inspection, problems are not solved do not pass, the blame does not hold did not miss, dissatisfaction of the masses did not miss, the real right of supervision authority, with the benefits. Call with caution, is supervising departments should strengthen the consciousness of authorized strictly according to procedure, preventing the supervision and excessive to prevent adding burden to grass-roots. To this end, the supervision Department of the Party Committee of supervision must be under city and County party Committee Secretary-General (Office). Second, we should focus on. Is the Governor, those related to the globalEvent, Governor the protracted difficult, strong Governor during emergency urgent. Not having special departments in charge of the General Governor, under the normal procedure can do good things not Governor, not authorized by County leaders, not the Governor. Third is to solve
the problem. The purpose of supervision, to resolve the problem. To adhere to and further improve the
的 成份与性能关系，使昆明钢铁厂甲类镇静钢的合格率由原来的40％～81％提高到95%以上。
华东师 大数学系与上钢五厂合作，利用自适应技术，使力学蠕变炉温度调节由6～7小时减少为
2～3小时，控 制精度由±4℃提高到±2℃，并使罩式退火的保温时间缩短5％～20％，提高了炉
温控制精度，保证 了退火质量。上海科技大学数学系用最优化数学，制成“E型电源变压器计算
机优化设计系统”，可缩短 设计周期，节约生产成本。

现代大型工业是多线路的联合作业，成为一完整的系统，因而产 生系统的控制问题，在化工联合
企业，半导体集成电路、电力传输系统、电话网络、空间站等方面都有此 问题。上海石化总厂采
用网络优化，建立了用电子计算机编制共四级（总厂、分厂、车间、机台）设备的 大型网络计划
体系。清华大学关于电力系统过渡过程的研究，相当巧妙地运用微分几何，取得了很好的经 济效
益，在国际上领先，曾荣获国家自然科学奖二等奖。

曲阜师范大学自动化研究 所应用数学方法，对汽车发动机调温器进行了研究，提高了调温器的质
量，从而延长发动机的寿命，并节 约耗油量。他们还采用随机线性模型及定积分近似算法，提高
了碘镓灯晒版机的质量，产品进入了国际市 场；此外，他们制成智能广义预测鲁棒控制器，可用
于生产过程中温度、压力的控制；他们还将山东机床 附件厂的车间、生产、财务、销售、人事、
动力等八个点实行计算机联网，进行优化管理。

运筹学起源于二战中军需供应管理，主要应用于工商经营部门和交通运输以对生产结构、管理关
系、人事组合、运输线路等进行优化。应用数学所运用运筹学指导全国原油合理分配和石油产品
合理调运 ，年增效益2亿元；另外，他们所发展的下料方法可节省原材料10％-15％。上海石油
化工总厂、镇 海石化总厂等运用运筹方法，每年可增加利税数百万乃至千万元。华南理工大学和
甘肃外贸局合作，建立 新的存贮数学模型和管理决策原则，每年可节省存贮费用近百万元。

2．设计与制造 工程 的设计与建造、产品的设计与制造是国民经济的重要支柱，也是数学大可
用武之领域。随着电子计算机技 术的飞速发展，数学在制造业中的应用进入了新阶段。波音767
飞机的成功设计，与应用数学家Gar abedian对跨音速流和激波进行的计算密切相关，由此设计
出了防激波的飞机翼型。目前以CAD 和CAM技术为标志的设计革命正波及整个制造业。CAD
是数学设计技术和计算机技术相结合的产物。 我国在老一辈数学家苏步青教授的亲自开拓和大力
倡导下，许多数学家在几何造型方面做了大量的工作， 所取得的成果已成功地应用于飞机、汽车、
船体、机械、模具、服装、首饰等的设计。南开大学吴大任、 严志达教授等在船体放样及齿轮设
计上也做了很好的工作。

复旦大学数学系与工程 人员合作，对内燃机配气机构建立新的数学模型，发展了新的数学方法，
使用此方法可以省油、降低噪声 和抑制排污，有很好经济效益，曾获国家科技进步奖一等奖。上
海应用数学咨询开发中心等开发研制服装 CAD系统，为服装行业创汇提供了基础。

3．质量控制 提高产品质量是国民经济中的一 个关键问题。二战中由于对军用产品的高质量要
求，特别是对复杂武器系统性能的可靠性要求，产生了可 靠性、抽样检查、质量控制等新的数学
方法，这些方法在美国、日本等国家取得了巨大成功。从60年代 中期开始，我国应用推广质量
控制等统计方法到工业、农业等部门，收到良好的效果，以手表、电视机为 代表的机电产品的质
量得到明显提高。清华大学、天津大学等研究了裂纹的扩展过程，有助于改善产品。 同时，我国
还制定了一系列质量控制的国家标准，对产品的质量提出了明确的要求。

eelings survey, by looking up public sentiments to find problems. Problems will increase its special supervision, set up accounts, hold on to it. We should conscientiously implement the leading contracting matters, secured, had an answer to everything, then settles rate of 100%. Have an impact on some of the outstanding issues, supervision departments and information components together, play the supervisory role of the news media to promote problem solving. Investee 3. insist on a daily run, around the practice of truth catching efficiency, focus specification. To give full play to the party Office around connecting, coordinating internal and external features, contact, rally at all levels, to motivate every aspect, adhere to the truth, strengthening standardized management to achieve coherent, efficient and effective functioning of the daily work of the Party Committee. Is processing messages should strive to streamline, standardize and quality. Streamlining is to control the number of
messages, compress messages, reducing procedures, improve message handling efficiency. Specifications, is to strictly enforce the ban issued by the Communist party authorities in document handling regulations and provincial and municipal regulations, conscientiously strengthen and improve communications management to ensure that party documents orderly. High quality, is to improve the quality of message processing, it is necessary to accurately implementing the intention of the Party Committee, clearance, good communications, policy program closed, ensuring that there is no error. Second meeting scheduled to ensure thorough, safe and efficient. Any arrangements for the meetings and events, carefully arranged, item-by-item interface implemented, sure. o vigorously streamline meetings, activities, number of pressure reduction, scale to ensure that leadership emerged from the General Conference and entertainment services, focus on big things, matters. Third, reception services
should lay stress on humane, personal, cultural and human. Reception and work directly with people, reception services directly affecting the Office of party Committee The image of the region. At the same time strengthening the construction of library, improve the reception conditions, more human- oriented, personal, cultural work into the reception, a little more human needs, a little more human care more humane atmosphere, and constantly improve the service, improve the quality of service. Meanwhile, to further pay special attention to the daily work of the other Office System. Confidential work responsibility system for leading cadres to implement security as a leader, to improve the confidentiality of classified personnel, especially leading cadres, strengthening party and Government focus on vital sectors of security management, to advance privacy management standardization, modernization of security techniques as a means of administration according to law and security
enforcement, ensure the safety of the party and State secrets. Confidential work to meet the demands of new technology development