universal data

Chapter 308 Position Determination
311 chapter

In Professor Fang's apartment, when Cheng Nuo pushed the door open, Su Xuanqi and two other second-year graduate students, Zhang Chumen and Gu Shi, were sitting on the sofa in the living room, chatting and laughing.

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

Seeing Cheng Nuo coming in, Su Xuanqi got up, walked to Cheng Nuo, 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, just go in and hand over the research report to the teacher."

Cheng Nuo dug 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 on the door lightly.

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

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

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

"Oh, Cheng Nuo, just put your report on the table. I'll read yours after I finish reading them." Professor Fang looked up at Cheng Nuo, smiled and signaled Cheng Nuo to just put the research The report is on the table.

"Then...Professor, I'll go out first?" Now that the report had been delivered, Cheng Nuo felt embarrassed to stay in the study and disturb Professor Fang.

Professor Fang nodded with a smile, "Okay. By the way, student Cheng Nuo, don't rush away, wait for me outside for half an hour. After I read the reports of the four of you, I will give the position of the deputy team leader to you." Make it final."

"Oh, okay."

Cheng Nuo tiptoed and gently closed the door, exited the study, and stayed in the living room with the other three to wait for the final result.

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

That was the research report submitted by the four of them.

Professor Fang leaned against Cheng Nuo without any airs, and sat among them.

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

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

"Generally speaking, so-so." Professor Fang looked at Su Xuanqi, Zhang Chumen, and Gu Shi, "The reports of the three of you didn't disappoint me, but they didn't surprise me either."

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

"You said here that fractional integral operators can be used as the research direction, and the monotonicity method of the hyperbolic nonlinear differential equation of the generalized p-Laplacian operator can be deduced through the Lipschitz function non-monotonicity theorem?" Professor Fang Turn the report to the first page and speak slowly.

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

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

Even more so in the field of pure mathematics.

At the last meeting, Professor Fang had vaguely pointed out the feasibility of Cheng Nuo's research direction: that is, to use Banach space as the entry point, and to construct subsets that exist in Banach space and non-Banach space to conduct Further deduction of p-Laplacian operator.

If he wanted to be stable, Gu Shi could directly follow Cheng Nuo's ideas and spread them out, writing a perfect thesis.

But the pride in his heart made Gu Shi reject this approach that was close to plagiarism.

After returning home, it took Gu Shi two full days and 48 hours of sleepless nights to read a lot of information before he came up with this plan of putting the entry point in the sub-integral operator.

However, reality is doomed to pour a basin of cold water on Gu Shi.

Facing Gu Shi's question, Professor Fang just shook his head lightly, "Although your report is written very seriously 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, his lips trembled.

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

Gu Shi was silent for a long time before he let out a breath of foul breath, his eyes returned to his usual calm, he looked at Professor Fang with a sincere tone, "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,

"From fractional integration, and then using some properties of Lipschitz function, it is indeed possible to form an operator called a generalized Toeplitz type operator, and the p-Laplacian operator and properties are indeed similar to similar triangles, and there is almost no difference."

Cheng Nuo looked at Gu Shi calmly, "But, senior, what you overlooked is that all the properties of a Toeplitz-type operator are only available under the condition that the operator is in a homogeneous space."

Gu Shi defended, "What I clearly said in the research report is to discuss in the homogeneous space."

Cheng Nuo shrugged with a smile, "Senior, you should still remember the definition of a homogeneous space, right?"

"A homogeneous space ( X , d , μ) means that a symmetric quasi-measure d and a non-negative, regular Borel measure are endowed 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 it skillfully.

Cheng Nuo snapped his fingers, "That's it. A homogeneous space refers to a space that has a symmetric quasi-quantity. However, for the p-Laplacian operator, there is no condition to limit the space it is in to a symmetric quasi-quantity space." .”

That's all for now.

Cheng Nuo had already explained the reason very clearly, Gu Shi's IQ would not fail to understand.

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."

Afterwards, he looked at Professor Fang with apologetic eyes, "Teacher, it's true that I didn't think carefully this time and made a mistake that shouldn't be made."

Professor Fang waved his hand, "Don't say that, although the research direction mentioned in your report is not possible to implement, there are still many things in it that can be used for reference, which will probably be used in future research projects. .”

Then, Professor Fang commented on the project reports of Zhang Chumen and Su Xuanqi. Like Gu Shi, they were not likely to be implemented.

Finally, Professor Fang gave Cheng Nuo a satisfied look.

"Student Cheng Nuo's thesis is a report on the research process of the whole project based on Banach space as the starting point. It is the best among the four of you in terms of feasibility and simplicity."

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

"No." This time the three answered very simply.

Even Gu Shi, who was the most dissatisfied with Cheng Nuo, didn't 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 be his immediate boss.

But in academia, all positions are reserved for those who can.

The strength is not as good as others, and they are convinced to lose.

(End of this chapter)