Tuesday, January 3, 2012

A new book by Ji-Huan He

Ji-Huan He reports on a new book he has coauthored with S.K. Elagan. His blog post is impressively cosmopolitan, being trilingual in English, Chinese and Arabic. The table of contents, shown below the fold, is hilarious.

First Edition: December 25, 2011
ISBN: 978-988-19132-2-7
Copyright Ó 2011 Asian Academic Publisher Ltd., Room 3208, Central Plaza, 18 Harbour Road, Wanchai, Hongkong, China


Preface -------------------------------------------------------------------v
1. Inequalities and Metric Spaces--------------------------1
1.1 Negative dimension----------------------------------------2
1.2 Inequalities--------------------------------------------------4
1.3 He Chengtian’s Inequality--------------------------------8
1.4 Modifications of He Chengtian’s Interpolation------13
1.5 Ancient Egyptian Fractions-----------------------------20
1.6 Two applications of inequality in nanotechnology --23
1.6.1 Electrospinning process-------------------------23
1.6.2 Asymptotic match of Rayleigh grain size distribution and Hillert grain size distribution--------26
1.7 Metric Spaces---------------------------------------------29
1.8 Bounded metric spaces----------------------------------38
1.9 Pseudo metrics--------------------------------------------40
1.10 Ultra –metrics-------------------------------------------42
1.11 Distances and Diameter--------------------------------43
1.12 Sequences------------------------------------------------46
1.13 Separable Metric Spaces-------------------------------48
1.14 Complete Metric Spaces-------------------------------57
1.15 Some examples of Incomplete Metric Spaces------74
1.16 Note on Lagrange multiplier method ----------------77
2. Normed Spaces--------------------------------------------86
2.1 Basic Concepts and Definitions------------------------86
2.2 Compactness and finite dimension---------------------95
2.3 Bounded Linear transformation and Duals----------100
3. Hilbert Spaces-------------------------------------------120
4. El Naschie Fractal Spacetime------------------------151
4.1 Three dimensional space---------------------------------151
4.2 Four dimensional spacetime-----------------------------151
4.3 E-infinity spacetime--------------------------------------152
4.4 The Hausdorff dimension of El-Naschie spacetime--------------------------------------------------153
4.5 Infinite dimensions in E-infinity spacetime -----------155
4.6 Why does our world appear as if it were four-dimensional? ---------------------------------------155
4.7 Faster-than-light particles in 5 dimensions------------157


Functional analysis is a branch of mathematical analysis, it focuses on mainly metric spaces with special structures. This textbook, beginning with everyday sensual experience, is for students who have never studied the subject, and introduces them to touch the frontiers of modern science including negative spacetime (negative dimensions), fractal space time, faster-than-light particles, and optimization without Lagrange multipliers. In order to confirm the beginners what they have learned is useful, two examples arising in modern textile engineering(nanofibers and nanocrystalline materials) are given, which can be used as paradigms for further applications of mathematics into practical problems. Furthermore, the textbook gives a brief but heuristic introduction of ancient Chinese mathematics and ancient Egyptian mathematics, making the textbook unique in its sense. Yes, every knowledge works for ever, ancient mathematics when revisited in the light of new developments may reveal hidden pearls. The inequality used by He Chengtian(369?~447AD) for Chinese lunar calendar can be used to solve nonlinear differential equations much effectively, while the ancient Egyptian fractions can be used for solving nonlinear algebraic equations much easily.


يعتبر التحليل الدالي فرع من التحليل الرياضي., حيث انه يلقى الضوء بصورة أساسية على الفضاء المتري مع مجموعة من الهياكل الخاصة. هذا الكتاب, والذي يعتبر أساسيا, هو للطلاب اللذين لم يدرسون التحليل الدالي قط, كما انه يضع إقدامهم على حدود العلم الحديث والذي يحتوى على : الفضاء الزمني السلبي (الإبعاد السلبية) , الفضاء الزمني الكسرى, الجسيمات الأسرع من الضوء, والمثاليات بدون مضروبات لاجرانج. ولكي نؤكد على أهمية ما يتعلمه المبتدأين في هذا المجال , سوف نقوم بتقديم مثالين مستخرجين من النسيج الهندسي وهما النانو الضوئي و المواد النانو بلورية واللذان يستخدمان كنماذج للتطبيقات المستقبلية الرياضية للمساهمة في حل المشاكل العملية. بالإضافة إلى أن هذا الكتاب يعطى ليس فقط نبذة ولكن مقدمة إرشادية لرياضيات القدماء الصينيين والمصريين والذي يجعله مميزا في حسه. نعم, أن المعرفة لا تموت فمن الممكن أن يكون المشاركة الطفيفة لرياضيات القدماء في التطورات الجديدة مساهما في اكتشاف خبايا جديدة. كما أن المتباينات التي استخدمت بواسطة

He Chengtian(369?~447AD)

للتقويم القمري للصينيين من الممكن استخدامها في حل المعادلات التفاضلية الغير خطية بطريقه أكثر كفاءة بينما يمكن استخدام الكسور المصرية القديمة في حل المعادلات ألجبريه الغير خطية.

Translate English to Arabic
محمد النشائى El Naschie Watch محمد النشائي El Naschie News محمد النشائى محمد النشائي All El Naschie All The Time محمد النشائى


  1. Wow. (What else can I say?)

  2. I don't understand why he didn't include a chapter about golden functional analysis.
    Especially Huan almost a whole chapter about E-infinity and Elnaschie's fractal space time.

  3. And we thought He is disassociating himself from the Great Man. Not in this universe. :D

  4. My peer review of this work is as follows:


  5. Also, my peer review of this work is as follows:
    "haha haha haha haha haha haha haha haha haha"

    It is interesting that in chapter four which is devoted to Elnaschie fractal space time, there is a section titled "Faster-than-light particles in 5 dimensions"

    I expect soon that when Elnaschie knows about the OPERA experiment for measuring the velocity of the neutrino and found to be greater than the velocity of light. The great man would attribute this to the fractal space time since the notation of spatial separation of points is fuzzy in the sense of what we consider far separated is actually nearby and this could account the measured velocity of neutrino greater than the speed of light.
    Of course this due the obvious consequence of the VAK conjecture and Fermat last theorem and trivial consequence of Golden differential geometry.

    I put this link that could help Elnaschie to read something simple at the level of popular science. http://www.guardian.co.uk/science/2011/nov/18/neutrinos-still-faster-than-light

    I hope the great man will acknowledge Elnaschie watch for drawing his attention to this experiment.

  6. Zahy, I want very much to get a PDF of this book, at least chapter 4, and post it. Chapter 1 has some funny parts too. Unfortunately I can't find it anywhere, even for sale. There is no mention of it on Asian Academic Publisher's website. http://www.nonlinearscience.com/index.php

  7. It seems this book:


    was edited by He.