Chapter 311

In Professor Fang's apartment, when Cheng Nuo pushed the door and entered, Su Xuanqi and the other two seniors of the second graduate school, Zhang Chumen and Gu Shi, were sitting on the sofa in the living room chatting with laughter.

As for Professor Fang, Cheng Nuo did not find him in the living room.

Seeing Cheng Nuo come in, Su Xuanqi got up, walked to Cheng Nuo's side, and said with a smile, "Did you bring the research report?"

Cheng Nuo nodded.

Su Xuanqi glanced in the direction of the study, "The teacher is in the study, you just go in and hand over the research report to the teacher." ”

Cheng Nuo took out the project report with more than a dozen pages of A4 paper from his schoolbag, walked to the door of the study, and knocked lightly.

"Please come in. Professor Fang's voice came.

"Professor, this is the report you asked me to write about the research direction of the project. In the study, Professor Fang wore reading glasses, lowered his head, and carefully reviewed a project report on the desk.

Cheng Nuo subconsciously glanced at it and found Gu Shi's name on it.

"Oh, classmate Cheng Nuo, just put your report on the table, and I'll look at you after reading a few of them in a while. Professor Fang glanced up at Cheng Nuo and smiled and motioned for Cheng Nuo to just put the research report on the table.

"That'...... Professor, I'll go out first?" Now that the report has been delivered, Cheng Nuo is embarrassed to continue to stay in the study and disturb Professor Fang.

Professor Fang nodded with a smile, "Okay." ...... By the way, Cheng Nuo, don't be in a hurry to leave, wait for me outside for half an hour, and after I finish reading the reports of the four of you, I will finalize the position of the deputy team leader. ”

"Oh, okay. ”

Cheng Nuo tiptoed the door shut, exited the study, and stayed in the living room with the other three waiting for the final result.

Half an hour later, Professor Fang opened the door and walked out of the study. In his hand, he held four documents.

It was a study submitted by each of the four of them.

Professor Fang leaned on Cheng Nuo without the slightest shelf and sat among several people.

Su Xuanqi diligently poured Professor Fang a cup of tea, and Professor Fang took a sip.

He raised the four reports in his hand and said with a smile, "I have read all four of these research reports." ”

"In general, so-so. Professor Fang looked at Su Xuanqi, Zhang Chumen, and Gu Shi, "The report of the three of you did not disappoint me, but it also did not surprise me. ”

Professor Fang took one of the four reports, "Gu Shi, this is your research report. ”

"You said here that you can use the fractional integral operator as a research direction to deduce the monotonicity method of hyperbolic nonlinear differential equations of generalized p-Laplacian operators through the non-monotonicity theorem of the Lipschitz function?" Professor Fang turned to the first page of the report and spoke slowly.

"Teacher, this method should be ...... It should be feasible, right?" Gu Shi, who was originally full of confidence in the report, was not very convinced in his heart when Professor Fang said this.

All roads lead to Rome, and there is no single research topic, only one research direction.

This is especially true in the field of pure mathematics.

At the last meeting, Professor Fang had already vaguely pointed out the feasibility of the research direction proposed by Cheng Nuo: that is, to take the Banach space as the starting point, and further deduce the p-Laplacian operator by constructing subsets existing in the Banach space and non-Banach space.

If stability is required, Gu Shi can directly follow the ideas proposed by Cheng Nuo to diffuse and write a perfect paper.

But the pride in his heart made Gu Shi reject this practice that bordered on plagiarism.

After going back, Gu Shi spent two whole days, 48 hours of sleepless night, and read a lot of materials before he came up with this plan to put the entry point in the sub-integral operator.

However, reality is destined to pour cold water on Gu Shi.

Facing Gu Shi's question, Professor Fang just shook his head slightly, "Although your report is very carefully written and the steps are very detailed, what I want to tell you is that your plan is not feasible. ”

Gu Shiru was struck by lightning, and his lips trembled.

At this time, Cheng Nuo also quietly picked up Gu Shi's research report on the coffee table and looked at it page by page.

Gu Shi was silent for a long time before he slowly exhaled a breath of turbidity, his gaze returned to his usual calmness, he looked at Professor Fang, and his tone was sincere, "Teacher, can I know where I went wrong?"

It just so happened that Cheng Nuo closed the last page of the report. Before Professor Fang could speak, Cheng Nuo smiled and said,

"It is true that by fractional integrals, and by applying some properties of the Lipschitz function, an operator called a generalized Toeplitz operator can be formed, and the p-Laplacian operator and properties are indeed like similar triangles, with almost no difference. ”

Cheng Nuo looked at Gu Shi with a calm gaze, "But, senior, what you overlooked is that all the properties of the Toeplitz type operator are only available under the condition that the operator is in the Qi space. ”

Gu Shi defended, "What I clearly said in the research report was that it was discussed in a Qi space. ”

Cheng Nuo smiled and shrugged, "Senior, you should remember what the definition of Qi space is, right?"

"The homogeneous space ( X , d , μ) refers to a symmetrical pseudometric d and a non-negative, regular Borel measure on the set X...... There is μ(B(x, 2r))(B(x, r))<∞. where B ( x , r ) = { y∈X : d ( x ,y )}. Gu Shi said very skillfully.

Cheng Nuo snapped his fingers, "That's it, Qi space, which refers to a space with symmetrical quasi-measurements. However, for the p-Laplacian operator, there is no condition to limit the space in which it is located as a symmetric quasimetric space. ”

That's it.

Cheng Nuo has already explained the reason very clearly, and Gu Shi's IQ will not be incomprehensible.

Sure enough, after Cheng Nuo said this, the expression on Gu Shi's face changed for a while, and he glanced at Cheng Nuo with a wry smile, "I've been taught." ”

Then, he looked at Professor Fang with apologetic eyes, "Teacher, this time it was indeed my inconsiderate and made a mistake that I shouldn't have made. ”

Professor Fang waved his hand, "Don't say that, although the research direction mentioned in your report is not likely to be implemented, there are still many things in it that have reference significance, and it is estimated that they will be used in the future research projects." ”

Then, Professor Fang commented on the project reports of Zhang Chumen and Su Xuanqi, which, like Gu Shi, are not likely to be implemented.

In the end, Professor Fang glanced at Cheng Nuo with satisfaction.

"Cheng Nuo's dissertation is a report on the research process of the entire project based on the Banach space as the starting point, which is the best among the four of you in terms of feasibility and simplicity. ”

"So, I decided to let Cheng Nuo take the position of deputy leader of this research group, do you have any opinions?" Professor Fang asked.

"Nope. This time, the three of them replied very simply.

Even Gu Shi, who was the most unconvinced by Cheng Nuo, did not have the slightest objection.

Although it is a bit embarrassing to let a junior who is only one year older and four or five years younger than them serve as his immediate boss.

But in the academic world, all positions are filled by capable people.

The strength is not as good as others, and they lose convincingly.