I am not sure if I share your enthusiasm about impaling Prof. He regarding two issues:

1. There seems to be a "Chinese" rivalry between Dr. Liao and Dr. He about the homotopy method. The former calls it the homotopy analysis method and the latter calls it the homotopy perturbation method. Dr. Liao did not start with this name initially and switched to it after a few years. In my opinion the two methods share the same philosophy, namely, introducing a parameter p and varying p continuously from 0 to 1. For p = 0, the problem reduces to one which can be solved rather trivially, and of course, for p = 1 the solution to the original problem is recovered. Both Dr. Liao and Dr. He start with the same "original" idea. The idea itself does not belong to either of them. In 1970s the idea was extensively used by Prof. L.T. Watson and others to obtain the numerical solution of highly nonlinear problems using the homotopy method. What Dr. Liao and Dr. He did was to use the latest developments in the evolution of computer technology to derive the analytical solutions using computer algebra systems. Dr. Liao specialized by introducing auxiliary parameters, especially h, to control the convergence of the perturbation series in p. Dr. He on the other hand used more creative ideas of introducing parameters and optimizing them so that the convergence could be achieved in a very few number of iterations (3-4). Dr. Liao's technique uses many more iterations - to the order of 50 or so. In my opinion they are both very valuable ideas and there is no reason for putting down one and lauding the other.

2. You are angered by Dr. He extolling some not that well-known scientist [El Naschie] to be on par with Newton and Einstein. We ought to appreciate that researchers have their opinions about the work of their contemporaries and notwithstanding how much it may sound outrageous that should not affect the evaluation of that person's research. I am quite close to some of the researchers who rail against Dr. He, yet I do not judge them on their allegations against Dr. He, but rather on their own research.

I will look further at the links provided by you, but please bear in mind that my opinion about Dr. He will be solely determined by the quality of his work, and not on how he thinks about others or what others think about him.

And then this from the most recent email (Fernández background here, here and here; HAM and HPM background here):

You have mentioned about Prof. Fernández. I have read some of his papers. I suppose he has picked up on some of the contributions made in the name of HPM. Unfortunately there are some researchers who have employed the HPM without the discretion used by Dr. He and others and they came up with some really absurd results, which Prof. Fernández has rightly singled out for condemnation. I have also pointed out this fact to Dr. He in my emails to him, indicating that the HPM is being misused by some researchers. I have not printed my findings similar to that of Prof. Fernández as I felt that the offending people might think that I have something personal against them, which honestly speaking I don't. In fact I have rejected dozens of papers on HPM which have come to me for review because they were in Prof. Fernández's words "useless", but this was done anonymously. In any case I think I can better utilize my time and energies on something more constructive rather than indulging in time wasting polemics.

So Prof. Fernández's objections are well founded. However, I disagree with him that the three methods are useless. There ARE some problems for which the homotopy method (HAM or HPM) succeeds whereas other methods would fail. Besides these methods give analytical results which in general are superior in landing the physical insight into the problems. I somehow prefer HPM as it gives an analytical result in very few iterations, and it is a lot easier to draw meaningful conclusions from those tidy expressions than those derived from the HAM using 50 iterations or so.

Again, for me it is not a big issue what Dr. He thinks about this "great" scientist El Naschie. Frankly I have never heard about him, and I do not consider it worthwhile to pursue him.

Posts about Ji-Huan He:

- Status report on the Ji-Huan He project
- SIAM president attacks El Naschie and Ji-Huan He!
- Master list of Ji-Huan He's editorial positions
- Francisco M. Fernández on Ji-Huan He
- Another Fernández review of Ji-Huan He's papers
- A supporter of Ji-Huan He speaks up
- In defense of Prof. Ji-Huan He
- El Naschie, Ji-Huan He, and nanotechnology
- Guess who's looking for Ji-Huan He
- No.6=何吉欢=自己的杂志=极不光彩
- Can't pull the wool over Fred's eyes
- Another
*Chaos, Solitons and Fractals*liability - huān yíng nín, xiāng gǎng !
- Science prize prediction posted on the Internet
- Valentine

What Prof. Don Ariel said is particularly

ReplyDeleteneutral. I only concentrate on the methods

and ideas but not what his saying.

It's fairly even-handed but not quite neutral.

ReplyDeleteBetween He and Liao, Ariel prefers He's HPM for exact analytic results and fast convergence.

Ariel thinks it's unfair of me to criticized He for comparing El Naschie to Newton and Einstein. (But since Ariel admits not knowing anything about El Naschie, I think that's premature.)

It is a well-informed, reasoned, and politic response by Ariel, who must work with all parties.

Why always HAM discussed his solutions (almost papers)near the paremeter near h=-1? Whether the case(or HPM) is the "best" one?

ReplyDeleteHomotopy perturbation method and homotopy analysis method are just standard perturbation approaches with fancy names. Both the use of a dummy perturbation parameter that varies from 0 to 1 and the addition of adjustable parameters for improving the convergence properties of the series are known since long ago. Liao and He discuss about two perturbation approaches that are anything but original. Besides, their claims about the convergence of their approaches are ridiculous (to say the least). They have not provided any rigorous proof, except some numerical tests. I suggest that the readers have a look at some of the relevant studies on the application of perturbation theory to the quantum-mechanical anharmonic oscillator (Bender and Wu, Simon, etc) to have an idea of what I mean. Then the readers may compare those remarkable analytical results with the HAM main theorem in which the author obtains the coefficients of the perturbation series from the equation, as it is customary in ordinary perturbation theory, and then states that if the series converges then it is a solution to the equation. It is far obvious that if the coefficients are developed to match the equation the series should be a solution if it is convergent (unless one makes a mistake). The HAM users repeat this argument over and over again as if it were catechism. The main problem is to prove the convergence of the proposed perturbation series. I think that most of the recent applications of HAM and HPM are completely useless.

ReplyDeleteDear Francisco M. Fernández.

ReplyDeleteHAM group emphasizes in their papers their method is not based perturbation theory.

It's confused when I firstly read their papers.

Maybe Prof. Don Ariel will be convinced if Ji Huan he applies HPM to fiber wool or virus flatness. Even if this would happen, I think that Prof. Don Ariel would say that I don't care what Ji Huan is doing by his method in other fields (Fiber wool, virus, medicine,...)

ReplyDeleteIndeed, Zahy, Prof. Ariel in his emails only addressed the points he numbered 1 and 2. He didn't express an opinion about He's theories about wool and viruses. Nor did Ariel address He's cooking the books on IJNSNS impact factor. Many people think the impact factor shenanigans by themselves are enough reason to fire He.

ReplyDeleteJason wants to turn to another direction. It seems what he said is the truth. I dislike to discuss anything in this way.

ReplyDeleteAnonymous 7:28 PM (or "mathlike" which would be a nice alias to use since we have too many anonymouses) I'm not trying to change the subject. I'm happy to have Ariel's opinions on record here, and yours too. It's perfectly reasonable for me to point out that Ariel didn't address certain criticisms of He.

ReplyDeleteThe truth is that He and his colleagues are "suckups" (to each other) what is also symptomatic for the "new Einstein" El Naschie and his group.

ReplyDeleteTry to discuss these "love letters" between He and his his colleagues from Donghua University:

http://iopscience.iop.org/0143-0807/29/4/L02/pdf/0143-0807_29_4_L02.pdf

http://iopscience.iop.org/0143-0807/29/4/L03/pdf/0143-0807_29_4_L03.pdf

Amusingly, He sees his note "as a paradigm

for many other applications...". A note - a paradigm? OMG, he's even more narcissistic than his genius friend.

And his "sucking-up" friends from Donghua University confirm that with no shame:

"will, therefore, become a universal tool for dealing..."

In other words:

"We ought to appreciate that researchers have their opinions about the work of their contemporaries...", clearly. :I

Of course you're right, Shrink. Really, neither of those love letters deserved to be published in Eur. J. Phys. or any physics journal. They're not physics papers, they're just some trivial fiddling with differential equations.

ReplyDeleteEl Naschie, Rössler, He, and our Hans H. Diebner defender "Researcher" who called me an idiot all have this compulsion to describe any stupid thing they do using the word "paradigm". They are a bunch of incompetent, pretentious bozos.

I believe that HPM is more efficient and simple. It is totally wrong that HPM is another copy of HAM. Prof. He is a great researcher.

ReplyDeleteI totally agree with Prof. Ariel.

ReplyDeleteDevendra, thank you for commenting. I wish we got more comments in defense of He or El Naschie.

ReplyDeleteYou clicked around this blog a bit so you are aware that He and El Naschie are at the center of a mutual citation scandal that not only raised the Impact Factors of their journals to absurd levels, but also caused Times Higher Education/Thomson-Reuters to rate Alexandria University as fourth in the world in research impact, which is ridiculous. And you are aware that He rates El Naschie among the greatest scientists in history with Newton and Einstein. Surely that is reason enough to dismiss anything He says as unserious.

"Prof. He is a great researcher." Hahahahah.

ReplyDeleteHow about a little sampling of the epic failures of HPM/HAM?

"We discuss two recent applications of the homotopy analysis method and the homotopy perturbation method and conclude that the results are of no physical or mathematical utility at all." http://iopscience.iop.org/1402-4896/81/3/037002

"...we show that the author’s method is not able to reveal the basic and important features of the dynamics of the delay logistic equation, and gives misleading results." http://www.sciencedirect.com/science/article/pii/S1007570411000360

"...show that the approximate analytical solutions provided by the homotopy method must be used with caution." http://iopscience.iop.org/1402-4896/81/3/037001

Somehow, I hadn't seen the original post before. This struck me as particularly hilarious: "What Dr. Liao and Dr. He did was to use the latest developments in the evolution of computer technology to derive the analytical solutions using computer algebra systems."

ReplyDeleteYes, because making Maple or Mathematica compute a 50-page long power series is a tremendous advance. Liao and He truly are geniuses. Nobody could've ever though computer algebra systems could do mindless work of expanding things in power series. Wow.