Research starts with PhD students

Chapter 192 We have already proved it, what else is there to discuss?
Li Weihua and Luo Yongjun quickly went upstairs and entered the office.

Zhang Shuo was writing something at the table. He put a manuscript aside, greeted the two people, and then said, "I just thought about that question carefully, and I'm here to discuss it with you."

Li Weihua and Luo Yongjun looked at each other and breathed a sigh of relief together.

Although the two people said different things, they actually felt the same. They felt that a problem that had been bothering them for half a month was solved by Zhang Shuo in just half an hour. This was really incomprehensible and at the same time they felt deeply shocked.

Now when I hear Zhang Shuo say "let's discuss it together", I suddenly feel a lot more relaxed.

They moved chairs and sat at the table.

Zhang Shuo started to talk, "We need to do a comprehensive certification, or more precisely, a demonstration of limited values ​​under natural boundary conditions, whereas before we only did certification for special value points."

"The argument is an analysis that starts from the position of the three-dimensional projection point, but due to the influence of boundary conditions and mapping functions, the values ​​can only be limited to fixed parameter conditions..."

Previous studies have all focused on the values ​​of "points", such as the transition point from laminar flow to turbulent flow, which can correspond to fixed physical phenomena. Some parameters are also determined.

The NS equations are very complex, and their component forms are even more complex.

It is obviously a very complicated task to conduct a comprehensive argument for such a complex equation, but if the parameters can be fixed, the argument will be relatively simple.

Zhang Shuo briefly summarized it and then began to talk about the method, "So we have to find other methods, and the original argument can only serve as a condition for the argument of the new method."

"We need to analyze it from a holistic perspective. We need to start our research from the boundary function and the reference function. We need to study the common problems of taking values ​​in a large area..."

This is the breakthrough in the research.

The previous research is the condition for the new demonstration direction. Using the comparison function and boundary function demonstration as a breakthrough is the "right way" for analytical demonstration of partial differential equations. It is impossible to carry out a complete coverage demonstration with some sophisticated directions and methods, and we can only do some special proofs.

Luo Yongjun and Li Weihua are both professional students in the field of partial differential equations. They understood the next direction after listening for a while.

They also read the content of the materials written by Zhang Shuo, which is the general direction of the next step of the argument.

After listening to everything, Li Weihua continued to stare at the manuscript and asked thoughtfully, "What you just said, and these, are the results of your half an hour's work?"

"Uh~~~"

Zhang Shuo was stunned for a moment, then explained, "I already had some ideas about this problem, and I just summarized them just now."

Li Weihua pursed his lips tightly.

Luo Yongjun had the same expression. Both of them stared at Zhang Shuo very seriously, but in the end no one said anything.

They walked out of the office with complicated expressions, holding the manuscripts.

When they first entered the office and heard Zhang Shuo say that they wanted to discuss the issue together, they felt relieved. But now, they found that Zhang Shuo was actually "comforting people".

discuss?

There was no discussion at all during the whole process. Zhang Shuo was just talking about his own ideas and the next direction of the argument. They wanted to express their own opinions, but there was no chance at all, and they couldn't think of anything at all.

In just half an hour, I came up with a new direction for the argument.

Both Li Weihua and Luo Yongjun felt quite shocked, and even Luo Yongjun shrugged his head.

The two walked to the first floor.

Li Weihua stopped at the corner of the stairs and sighed deeply, "Zhang Shuo... I feel now that ordinary people and geniuses are really not of the same race, just like mortals and gods..."

“I can’t understand it!”

"Yes."

Luo Yongjun stopped boasting and sighed, "Mathematics is like this. Some students can learn it once they are taught, and they understand it immediately. Some students cannot understand it no matter how much you teach them. Even if you give them the answer, they still cannot understand it."

"Same foundation, but the gap is so huge."

"I always thought this would only happen to students, but now I realize..."

"In fact, we are no different from stupid students."

Li Weihua nodded solemnly.

They walked out of the high school building together, and suddenly felt much more relaxed. Li Weihua said, "Yes, the good news is that we have found the next direction, and I have even seen the results."

"We will complete the proof of the bounded value of the NS equation under natural boundary conditions."

"There is also bad news, it is bad news for others, their work may become meaningless."

Luo Yongjun frowned and thought for a while, "Are you talking about... Teacher Tong Jietong?"

"It's just one of them." said Li Weihua.

Luo Yongjun nodded solemnly. They all knew that Tong Jie had applied for a small project on incompressible fluids, which was about proving the smoothness of specific positions in the NS equations.

This study is a continuation of the demonstration of the smoothness of the turbulence transition position of the NS equations.

If their research proves the smoothness of the solution set within a bounded range of values ​​under the natural boundary conditions of the NS equations, the arguments near special points will be included therein, and the relevant research will naturally lose its meaning.

Luo Yongjun thought about it and said, "I'll tell her to change her research direction."

"It can only be the."

……

If the argument for the bounded value of the NS equation can be completed, Tong Jie will not be the only one affected.

After the International Congress of Mathematicians, many scholars in the field of partial differential equations considered referring to Zhang Shuo's demonstration of the smoothness of the turbulent transition position to prove the solution set problem of other special points of the NS equations.

In the argumentation in this direction, the closer the parameters are to the turbulence transition position, the more reference value Zhang Shuo's paper will have and the lower the difficulty will be.

Bill McIver's demonstration of a square channel in Cartesian coordinates is not a special case; it is just one of many.

The difference is that he has a higher academic influence, his argument for the Cartesian coordinate system is more difficult, and more importantly, the result of his argument is the existence of a singularity in the square channel.

There are also many other related papers, and the results all prove the smoothness of the solution set of the NS equation corresponding to special positions.

If they had completed the argument, all finite values ​​would have been included and the studies would have lost their meaning.

This is the conflict of academic research.

For other scholars, this is of course a sad thing, but if you think about it carefully, their research speed is too fast.

There is a rule in mathematical research that after a certain difficult problem has made qualitative progress, there will be no further progress for a long time.

For example, the Goldbach conjecture.

After Chen Jingrun completed the "1+2" ​​demonstration, there has been no progress until now.

Zhang Yitang proved the weakened twin prime conjecture, and subsequent research continued to narrow the scope, eventually narrowing it to '246'. However, more than a decade has passed, and there has been no other progress.

The Monge-Ampere equation achieved a breakthrough in the 90s, but stagnated for more than two decades until Professor Chen's team completed research on expanding the boundary conditions.

Because of this, Luo Yongjun and Zhang Shuo's research on "boundary expansion" shocked international mathematicians. Zhang Shuo's demonstration of the smoothness of the turbulent transition position made a qualitative breakthrough in the NS equation demonstration. According to normal rules, there will be no major breakthroughs for a long time. Related research is based on this and conducts demonstrations at special points.

That's why many people apply for research projects.

Now their next step is to complete the comprehensive proof. If they can complete it, it will mean that the proof of the NS equation will make another qualitative breakthrough. Who could have thought of this?
When Li Weihua and Luo Yongjun joined the project team, they could not imagine that there would be such a big breakthrough so soon. Looking back, they found it incredible and could only sigh that doing research with Zhang Shuo was indeed different.

This kind of research conflict will definitely make the affected party very depressed, and it will affect others...

Very comfortable!

Li Weihua and Luo Yongjun both felt very motivated, and they couldn't wait to go back and start their research.

……

When research sees a goal, it can bring great motivation to people and greatly enhance their work enthusiasm.

This is the case with Li Weihua and Luo Yongjun.

Zhang Shuo focuses his main energy on experiments related to the theoretical correlation between electromagnetic force and gravity. He hopes to obtain numerical values ​​more quickly to analyze and study mathematical models.

Halfway through, we discovered that Luo Yongjun and Li Weihua were extremely efficient at work. They would make a small report about once every two days and a large report once a week, and each report would show great progress.

In just half a month, the progress of the 'singularity proof of the NS equation' has increased by nearly '5%'.

Zhang Shuo was very surprised by this feeling.

'Proof of the singularity of the NS equation' is an A-level task that requires 7000 research coins. Each point of progress represents '70 research coins'. Five points of progress can be completed in half a month, which makes Zhang Shuo feel that the research is about to be completed.

So during the intervals between experiments, he simply studied and discussed the issues with Luo Yongjun and Li Weihua.

They found it inconvenient to work and communicate separately, so they decided to work in a large office on the first floor.

When there are no classes, Luo Yongjun and Li Weihua will come to the office at 8 o'clock in the morning, take a break after 11:30 in the afternoon, and start research and discussion again at 1 o'clock in the afternoon. They will be busy until after 6 o'clock in the evening. Occasionally, when there is progress, they will even discuss until 8 o'clock in the evening.

This is the case on weekdays, and work enthusiasm will be higher on weekends because you won’t be affected by classes and you can stay in the office the whole time.

This also puts pressure on others in the High Court.

When Luo Yongjun and Li Weihua decided to work on the first floor of the High Court, Wang Hui, Qi Zhixiang and others thought it was a good idea. The High Court building was always very quiet, and it was not easy to find someone to chat with. They always gathered in the large office on the first floor, and the people who talked did not change.

Now that there are more people, it feels more interesting.

As a result, every time they went to the office where Luo Yongjun and Li Weihua worked, they found that the two were discussing issues and doing research seriously, and there was no way to disturb them. The most important thing was that they could not wait for the two to stop.

This makes them feel very anxious, as if the extra comma makes them feel like they are doing nothing while others are working hard and seriously.

Sometimes, Wang Hui would stand in the corridor and listen to the discussions inside and wanted to shout, "You are mathematics professors and scholars, can you please not work so hard and be so competitive!"

Then, they also have to 'roll' because they feel they will fall behind if they don't work hard.

This is when the difference comes.

Luo Yongjun and Li Weihua have a clear direction. Their daily research and discussions will make progress, and progress will boost their enthusiasm for work.

It's different for other people.

When problems arise in mathematical research, working longer hours is meaningless and may even have a counterproductive effect.

Inspiration is really hard to describe.

Maybe you don't work for a long time, and then you get inspiration from something you see by chance, and then you solve a big problem. Conversely, even if you continue to work hard, you will not make any progress if you can't find inspiration.

Volume, it makes no sense at all.

Tan Youming also noticed the situation in the High Court. He thought it was pretty good at first. Everyone was working very hard, and he also "pretended" to work hard in his office.

In fact, the office door was always closed and no one knew what he was doing in there.

The biggest impact on Tan Youming was that he felt embarrassed to come out and chat with others, or to go out and relax.

This feels very depressing.

Tan Youming felt a headache when he thought about the situation. He didn't quite understand why Luo Yongjun and Li Weihua were so eager. Two mathematics professors voluntarily worked overtime together and even came to work on weekends?

Are they trying to study?

Tan Youming felt very anxious when he thought about it. He even felt that he would be eliminated if he didn't work hard, but working hard was of no use.

How to do?
While thinking, he opened his mailbox and suddenly noticed an email from Donggang Mathematics Center.

The Donggang Mathematical Center initiated a "Partial Differential Equation Theory Seminar" and invited scholars from the Soochow University Institute of Advanced Studies to participate. The signature of the dean "Jiang Weizhi" was also on it.

Jiang Weizheng also sent him a private message, hoping that Tan Youming would help persuade Zhang Shuo to participate.

After reading the email, Tan Youming went directly to the work offices of Luo Yongjun and Li Weihua.

Zhang Shuo was also inside, and the three of them were discussing a boundary function problem.

After entering, Tan Youming stood by the door waiting.

About two minutes later, Zhang Shuo stopped and turned around to ask, "Dean Tan, what's the matter?"

Tan Youming smiled and said, "I just received an invitation letter from the Donggang Mathematical Center. They organized a theoretical seminar on partial differential equations. One of the important topics of the demonstration is the NS equation. You are doing research on this. Do you want to participate?"

After he finished speaking, he asked Zhang Shuo, "You should have received the email as well, right?"

"Let me see."

When Zhang Shuo opened his mailbox, he found two emails, one of which was a standard invitation letter from the Donggang Mathematics Center.

The other letter was from Li Jianfeng, expressing his hope in a private tone that he could attend the seminar, and explained that many well-known domestic scholars had been invited, even including Qiu Chengwen from Shuimu University.

Zhang Shuo pondered and said, "Let's not talk about whether to attend the meeting. There should be no point in discussing the coverage proof of the ns equation at the meeting, right?"

"No point? Aren't you doing this research?" Tan Youming asked doubtfully.

Zhang Shuo nodded and said, "That's why it's meaningless. We're almost done."

Tan Youming was stunned for a moment and immediately turned to look at the other people.

Li Weihua also nodded and said, "We are indeed going to finish it."

"Yes."

Luo Yongjun smiled and said, "We have already proved it. What is there to discuss? If we go there... wouldn't it be the same as ruining the place? Telling them that there is no point in discussing it?"

"You can't do this kind of thing. Let them discuss it happily!"

(End of this chapter)