Orion Crest, Series_1

Chapter 59: Graduation Ceremony by oneself

　　After a long preparation, it was finally the day of the defence.

　　Orion followed the process and after introducing himself, he started to describe his thesis and briefly reported the main ideas and conclusions he got from the thesis.

　　The process was rather short, just fifteen minutes.

　　The next questioning session was the most important part of the defence!

　　Professor Nelson's eyes were sharp, and he asked in a single question.

　　"On the fifth page of the thesis, line 11, I noticed that you mentioned, let C be a non-empty closed convex subset in the Hilbert space, for a class of proposed non-expansive mappings T: C → C, a modified Halpern-type iterative algorithm is introduced, what is the significance of this, can you explain it in detail?"

　　If it was an ordinary undergraduate's graduation defence, the defence judges would definitely not ask such tricky questions, but the person standing on the podium was not an ordinary one, and the one sitting below the podium was not an ordinary defence judge as well.

　　Naturally, the questions asked would not be ordinary.

　　Without even bothering to turn the page of the thesis, Orion naturally wrote for himself what was written at the beginning of the fifth page.

　　"The sequence {xn} converges strongly to some immovable point on T which is the unique solution of the variational inequality V. Can I use the blackboard if I explain in detail?"

　　Professor Nelson smiled and said, "Sure."

　　Picking up the chalk.

　　[x1 ∈ C, x(n+1) = αn·f·xn + βn·xn + γn·T·xn, n ≥ 1. where f:C→C is a compressed image and where T:C→C is a non-stretched image ......]

　　Nelson narrowed his eyes and nodded approvingly, "Not bad."

　　Even when held to the standards of a doctoral student, this respondent's qualifications were quite high.

　　This answer, at least, satisfied him.

　　Standing next to him, Professor Stewart spoke slowly, "I'll ask a few questions as well."

　　Orion respectfully said, "Please."

　　Prof Stewart: "I noticed that you mentioned in your paper that the application of this viscous iterative algorithm can be used to study the pre-solutions of the 'maximal monotone operator' in the 'Banach space' as well, and that this could be a tool for the study of quantum mechanics. This is similar to that algorithm mentioned by Prof Kohsaka in Japan when he introduced non-stretching images in 2008, but you did not make any further derivations based on it, why?"

　　The question did make Orion freeze for a couple of seconds.

　　Where was the why?

　　Because that's not the point of this thesis!

　　Orion coughed lightly and said, "Because further derivation would allow for another paper, and this paper discusses just the maths, and while there are references to applications in quantum mechanics, it doesn't go into specifics."

　　The problems of academia are endless, and deriving a little bit of everything makes this paper a very weird thing to write. Including the possible applications of his set of viscous iterative algorithms in quantum mechanics, he had only mentioned it a little.

　　Professor Stewart shook his head and preached in a serious tone, "This is not the mindset that a scholar should have, one should strive for perfection when doing scholarship, since you have already discovered this possibility, why don't you continue to go deeper along this line of thought?"