The books once interested me

coolboy

Bennett, A. F., 2002: Inverse Modeling of the Ocean and Atmosphere. Cambridge Univ. Press, Cambridge, 234 pp.
Brown, R. G., and P. Y. C. Hwang, 1997: Introduction to Random Signals and Applied Kalman Filtering with MATLAB Exercises and Solutions. Third Edition. John Wiley & Sons, New York, 484 pp.
Chong, E. K. P., and S. H. Zak, 2001: An Introduction to Optimization. Second Edition.  John Wiley & Sons, Inc., New York, 476 pp.
Daley, R., 1991: Atmospheric Data Analysis. Cambridge Univ. Press, Cambridge, 457 pp.
Gordin, V., 2000: Mathematical Problems and Methods in Hydrodynamic Weather Forecasting. Gorden and Breach Sci. Pub., Amsterdam, Netherlands, 824 pp.
Haltiner, G. J., and R. T. Williams, 1980: Numerical Prediction and Dynamic Meteorology. Second Edition. John Wiley & Sons, New York, 477 pp.
Kalnay, E., 2003: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge Univ. Press, Cambridge, 341 pp.
Landau, L. D., and E. M. Lifshitz, 1976: Course of Theoretical Physics. Vol. 1: Mechanics. Third Edition. Pergamon Press, New York, 169 pp.
Marchuk, G. I., 1995: Adjoint Equations and Analysis of Complex Systems. Kluwer Academic Pub., Boston, 466 pp.
Menke, W., 1989: Geophysical Data Analysis: Discrete Inverse Theory. Revised Edition. Academic Press, Inc., 289 pp.
Morel, P., 1973: Space and Time Meteorological Data Analysis and Initialization. In "Dynamic Meteorology" (P. Morel, editor) Reidel, Dordrecht, Netherlands, pp. 469-512.
Parker, R. L., 1994: Geophysical Inverse Theory. Princeton Univ. Press, 386 pp.
Rodgers, C. D., 2000: Inverse Methods for Atmospheric Sounding, Theory and Practice. World Scientific, London, 238 pp.
Spall, J. C., 2003: Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control.  John Wiley & Sons, Inc., New York, 595 pp.

不久前我做了一个关于“资料同化”（Data Assimilation）的讲座。对象是对“资料同化”这一概念或这一词有一定了解，但对实际操作的数学步骤以及这一技术或工具在一般数值模拟过程中的作用不是十分清楚一些科学家。在讲座的参考文献中，除了列出相关的重要论文之外，还列出了我书架上有的相关的书籍，也就是上面所列的书单。
上列书籍中值得一提的是Vladimir Gordin关于数值天气预报数学基础的专著：

Gordin, V., 2000: Mathematical Problems and Methods in Hydrodynamic Weather Forecasting. Gorden and Breach Sci. Pub., Amsterdam, Netherlands, 824 pp.

这本书的写作形式是相当地理论化、数学化。尤其，书的约1/3篇幅是由11个相关数学背景知识的附录组成。例如，附录4就介绍了哈密顿流体动力学。从所含内容的难度及写作体裁，这本专著在很大程度上与前面14楼中所列的另一本中文专著很相近：
曾庆存，1979：数值天气预报的数学物理基础，第一卷，543页，科学出版社。

Vladimir Gordin的专著包含了数值天气预报的三大部分：（1）“数学基础”，（2）“资料同化”，（3）“计算数学”。
曾庆存的专著是他原写作计划中的第一卷。所包含的内容就是“数学基础”。第二卷计划是“计算数学”的内容。当时我还听说在准备第二卷的同时，作者还打算把他的第一卷翻译成英文出版。但似乎至今为止，也还是停留在第一卷的中文版。

coolboy

在另一论坛上说到了计算尺。晒一下我自己曾经用过的计算尺。那把小的计算尺是高一时我自己掏钱买的。那把大的是我叔叔原来用的，后来他买了新的，就在高二时送给我了。上大学时也带上用了。直到大四时才看到有同学用上了计算器，当时很新奇。

周华

我原来也有一个计算尺，但一直没用上，主要原因也是计算器普及了，计算尺就自动被淘汰了。

coolboy

It has been a while since I updated this thread last time. Let me add an interesting and important book that was cited in one of my recent papers:

Gonzalez, W., and E. Parker (editors), 2016: Magnetic Reconnection – Concepts and Applications. Springer, Switzerland, 542 pp.

coolboy

上一本书的第二个编辑是尤金·帕克（Eugene N. Parker）。关于他的成名有一个流传很广的传说或故事。我在本主题帖子的117楼中也说到了这个故事。他最近逝世了（2022年3月15日，尤金·帕克逝世，享年94岁）。有人写了一篇关于他的纪念文章，其中自然也提到了这一个故事。该纪念文章在“数学中国”网转载了：
他的姓名值 15 亿美元：天才少年的传奇人生
http://www.mathchina.com/bbs/for ... ead&tid=2051172

我对文章中的故事作了如下的评论：
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审稿人说：“好吧，我建议帕克在尝试写论文之前，先到图书馆读读相关学科（的论著），因为这篇论文完全是在胡说八道。” [3] 原文为：“Well I would suggest that Parker go to the library and read up on the subject before he tries to write a paper about it, because this is utter nonsense.”
更悲催的是，编辑部找的第二个审稿人也拒绝了这篇稿子。
-----------------------

这是一桩历史疑案。即使在目前，也不能说在学术界已经令人信服地被完全解开了或解决了。

在当时的学术背景以及只针对帕克论文所论述以及给出的结果来看，上述评价其实并没有问题。上述评价也同样可以在本论坛上出现的许多帖子中照搬使用。

根据我对问题以及当时学术背景的了解，我一直猜测那两个审稿人是 J. W. Chamberlain 和 S. Chapman。但一直没有直接的证实，以后应该也不会再有了。
   

liyqxtu2

向大佬学习

coolboy

“Magnetic Reconnection” is a physical process that is unique to the field of plasma physics. The importance, difficulty and popularity of this subject are nearly the same as “turbulence” in the field of traditional fluid mechanics for the neutral fluid. However, in both the traditional fluid mechanics and plasma physics, there are common or similar physical processes such as “transportation”, “turbulence”, “instability”, etc. that are important and popular to both fields. It is noted that there is a tiny difference between “turbulence” and “instability”. “Turbulence” generally refers to a physical process associated with the observed phenomena whereas “instability” generally refers to a physical process associated with a hypothetical mechanism. Likewise, “magnetic reconnection” that is unique to plasma physics is a process associated with an observed phenomenon.

Because of its importance, difficulty and popularity, there are many researches including papers and books focused on the subject of “magnetic reconnection”. The above book edited by Gonzalez and Parker is one example. I have another book on my bookshelves focused on the same subject as one can see from its book title:

Hones, E. W. Jr. (editor), 1984: Magnetic Reconnection in Space and Laboratory Plasmas. Geophysical Monograph 30, AGU, Washington, DC, 386 pp.

coolboy

Add a book on “Artificial Neural Networks”:

Haykin, S., 1994: Neural Networks: A Comprehensive Foundation. Macmillan College Pub Com., New York, 696 pp.

The above book was cited in the following link that discusses the subject of “Machine Learning for Computational Fluid Dynamics (ML for CFD)”:
【视频】机器学习与CFD
http://www.cfluid.com/forum.php?mod=viewthread&tid=214405

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我的理解，机器学习其实就是传统统计学里的一些方法（如分类法）加上人工神经网络的组合体，再加上了一个好听一点的名称。在这个流体应用的讲座中，机器学习似乎就是指人工神经网络。那么，人工神经网络又是什么呢？我感到人工神经网络就是对数据的一种非线性回归或即非线性拟合的技术。由于对数据进行统计学回归或拟合是一种静态的处理技术而对（计算）流体力学（CFD）的描述则是已知的动态/动力学系统或即已知的演变型（即随时间变化）方程组（即纳维-斯托克斯方程组），机器学习显然不能对流体力学提供有效的帮助。

这里，我们可以举一个类似的例子。假如我们知道描述某质点的位置及其变化的方程是F=ma，我们该如何求得它的位置呢？方法一：根据给定的初、边条件求解方程F=ma。方法二：根据大量不同初、边条件求解方程获得的数据（以及加上实际观测值）构建一个人工神经网络模型来拟合那些数据，再从这个人工神经网络模型来获取所需之解。很难想象方法二本质上会优于方法一。

在上面视频讲座的结尾部分，其实作者的观点或评价也并不乐观。他意思说，机器学习对CFD的应用需要很聪明的人花费很大的努力才能获得一些（个例上的）有意义的结果。他把这一现象归结为机器学习才发展了很短的时间而CFD领域则早已有了很长的发展历史。我则认为主要原因是一个静态型的数据拟合（统计回归）方法并不适合于解决一个已知动力学方程组的动态变化问题。

许多年以前，人工神经网络刚刚成为热门学科，本人也曾进修了这门课。当时所用的主要课本即是下面的这本书：

Haykin, S., 1994: Neural Networks: A Comprehensive Foundation. Macmillan College Pub Com., New York, 696 pp.

coolboy

在“数学中国”论坛上看到一个有意思的帖子，发了一个相关的回帖：

++++++++++++++++++++++++++
几个印度数学家与统计学家
http://www.mathchina.com/bbs/for ... ead&tid=2053692
[bold]
1. Mahalanobis
...............
Mahalanobis 认为统计学是一门新兴的科学领域, 从分析各种数据, 可以得到新的资讯, 提供决策参考。从1920 年代初期, Mahalanobis 把统计学应用到许多领域,如：人类学、气象学、农学、经济学。他的物理实验室慢慢地有一些人对统计学产生兴趣, 有人戏称他们是统计实验室。
++++++++++++++++++++++++++

“统计气象学”里有两个专题就是所谓的“分类分析”和“聚类分析”。其中的“Mahalanobis距离”也可认为是研究这两个专题的基架。随着计算机的蓬勃发展，“分类分析”和“聚类分析”等“统计气象学”里的一些方法也就演变成了更时髦的“人工智能”统计学方法（如“人脸识别”等）。后来再加上了“神经网络”的算法也就形成了现在又称之为“机器学习”的又一新学科。

下面的一本专著就是现代“统计气象学”的经典教科书：

Wilks, D. S., 2006: Statistical Methods in the Atmospheric Sciences. Second Edition. Academic Press, New York, 627 pp.

coolboy

这两天海外一个中文网上出现了一个热门帖子：
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南京路新华书店和里面的漂亮营业员
https://blog.creaders.net/u/8699/202307/467114.html
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说的是上世纪七、八十年代新华书店的运作形式。作者经常去上海新华书店偷瞄一个新到的漂亮营业员。若干年后，他在加拿大一超市中发现那个漂亮营业员成了超市的试吃服务员，......。此外，帖子中作者晒出了一张1982年的购书发票。
+++++++++++++++++++++++++++++++++++

我也在评论中，晒出了本帖94楼中我的1980年的一张购书发票：


也来秀一张1980年的购书老发票。在南京读书。中山东路上有一家南京外文书店。书店正门里面柜台上展出的外文书很贵，普通人根本买不起。但书店有一后门，凭学生证才可进入，上楼。二楼很大，所有的外文书都是开架供读者浏览选择。当然都是盗版书，比较便宜，一般的学生也能负担得起。
书名是：Richtmyer, R. D., 1978: Principles of Advanced Mathematical Physics. Vol. I. Springer-Verlag, New York, 422 pp.
美国出版才两年的书就可在中国书店买到。说明当时在中国盗版传播的速度就已经非常快了。

[有人又评论了上海外文书店]我说的是南京外文书店。上海的外文书店后来（多年之后回国时）也去过，福州路听起来有印像。看来当年各地外文书店的设置和操作运营是统一的。二楼出售或仅仅出售盗版书。出入需要查证查包。

coolboy

转发我在数学中国论坛上发的一个帖子：
+++++++++++++++++
http://www.mathchina.com/bbs/for ... &extra=page%3D1

与其阅读或翻译牛顿的《自然哲学之数学原理》，不如阅读或翻译诺贝尔物理学奖得主S. Chandrasekhar对牛顿《自然哲学之数学原理》结合现代物理学知识的解读：

Chandrasekhar, S., 1995: Newton's Principia for the Common Reader. Oxford Univ. Press.

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Representing a decade's work from one of the world's most distinguished physicists, this major publication is, as far as is known, the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breathtaking economy of Newton's methods. This book will stimulate great interest and debate among the scientific community, illuminating the brilliance of Newton's work under the steady gaze of Chandrasekhar's rare perception.
-----------------------

coolboy

转发我在数学中国论坛上发的一个帖子：
+++++++++++++++++
http://www.mathchina.com/bbs/for ... &extra=page%3D1

才发现玻尔兹曼的导师原来是斯忒藩。学物理的同学应该都非常熟悉热辐射公式中有一个“斯忒藩-玻尔兹曼常数”。该常数的值为5.67×10^-8[W m^-2 K^-4]。这应该是大家现在都还记得或知道的斯忒藩的一个重要贡献了。斯忒藩还做出了什么有意义被大家很长时间内一直都使用着的贡献呢？

斯忒藩求解了热传导方程并给出了（一百多年前只可得的）热传导方程存在相变条件下的解析解。不同（固、液）相态的物质具有不同的热传导系数，热流经过固-液态的界面时会导致潜热的释放或吸收，界面的位置也会随时间变化。斯忒藩在不同边界条件下给出了这类问题的解析解。

列出一个含有热传导方程大量解析解的经典参考书：

Carslaw, H. S., and J. C. Jaeger, 1958: Conduction of Heat in Solids. Second Edition. Oxford Univ. Press, 510 pp.

周华

coolboy 发表于 2023-8-26 21:42
转发我在数学中国论坛上发的一个帖子：
+++++++++++++++++
http://www.mathchina.com/bbs/forum.php?mod= ...

好书，可惜看不到

coolboy

It has been a while since I updated this thread last time. Let me add a useful book on numerical calculations of special functions:
size=3]
Zhang, S., and J. Jin, 1996: Computation of Special Functions. John Wiley & Sons, Inc., 717 pp.

A classic book in this field was the one by Abramowitz and Stegun (1965). However, in the book by Zhang and Jin (1996), the authors picked useful schemes and wrote the FORTRAN programs to evaluate the functions among various expressions listed in Abramowitz and Stegun (1965). For example, the adopted one for evaluating the error function in its FORTRAN program was much more accurate than other expressions shown in Abramowitz and Stegun (1965). All the FORTRAN programs also came with the book in a disk.

Another good feature of the book is that the programs are mostly self-contained. Again, for example, one can just simply understand and use one subroutine to calculate the error function. On the other hand, in another similar and popular book by W. H. Press et al (1992, Numerical Recipes) that also contained FORTRAN code, one first needs to understand and call a much more complicated incomplete gamma function in order to evaluate just a simple error function.

This important feature of self-contained programming apparently was reflected in the book as a general rule: “..., although many special functions can be expressed in terms of the confluent hypergeometric functions, it is often not desirable to evaluate these special functions using the confluent hypergeometric functions, simply because each special function has some special properties that can be employed to simplify it evaluation.”