Chapter 110 Others participated in the competition, and I became a judge
An important idea in studying an equation is to study the properties of the solution, and the theory of Monge-Ampere equation is no exception.

So far, mathematicians have mainly studied the existence, uniqueness and smoothness of solutions.

The existence and uniqueness of it have been proven.

The research on smoothness still remains at the stage of many years ago, that is, when two regions are uniformly convex and the density function is smooth, the optimal transmission solution is smooth.

There are two essential conditions here.

Compared with the proof of the existence and uniqueness of solutions to the Monge-Ampere equation under natural boundary conditions, there are still flaws.

The smoothness of the solution is also called regularity, which is usually used to describe the smoothness of a function.

If a function is smooth, it is infinitely differentiable by mathematical definition.

Unfortunately, after all these years, no one has been able to fully prove the two necessary conditions of removing the two regions' uniform convexity and smooth density function.

Xu Yuan's research on the Monge-Ampere equation is to truly prove the smoothness of the solution.

If it can succeed.

This was a huge improvement on the Monge-Ampere equation.

It is equivalent to expanding the scope of a theorem to a wider field.

It is helpful for the study of partial differential equations.

However, it is not easy to eliminate these two conditions. The process requires a lot of complex calculations, as well as the emergence of clever inspiration and ideas.

Friday, August 2004, 10, School of Mathematics, Qinghua University.

In the discussion room, Xu Yuan was leaning over the table with a focused expression, with a lot of draft papers filled with mathematical formulas scattered around him.

If you continue to move your eyes to the side, you can see Chen Yuran, who is still wearing a side ponytail, sitting at the computer. She seems to be revising her press release, but her eyes are on Xu Yuan for forty seconds in one minute.

Xu Yuan did not go to the library these days, but stayed in the discussion room reserved for him in the department.

Occasionally, Chen Yu Ran would come over and they would study together, but every time Chen Yu Ran’s efficiency was very low.

"No wonder Professor Tang advised me that before. It's really not easy to completely prove the overall smoothness."

At this time, Xu Yuan casually crumpled up the discarded draft in front of him, and felt a little emotional when he thought of what Tang Shihong had said before. Especially when his eyes stayed on the light screen panel in front of him, he couldn't help but sigh.

-

Task: Proof of Monge-Ampere equation

Subject: Mathematics

Progress: 5%
Result: Not completed
After studying for so many days, the progress bar not only did not rise, but even dropped twice due to calculation errors.

It is no exaggeration to say that the remaining 5% is not a small amount.

This is because he can enter a deep learning state at any time, and his thinking is more sharp and active than usual. Otherwise, if he only relies on his usual state, he may not even be able to enter the door of proof.

Then his attention was no longer highly focused and Xu Yuan came out of the deep learning state.

I looked at the time and found that it was almost twelve o'clock, so I simply stopped working and filled my stomach first.

After being busy in deep learning for so long, I was really hungry.

The thought stayed here. He raised his eyes, put down his pen and shouted to Chen Yuran who was sitting beside the computer.

"Let's go to the cafeteria to eat."

Chen Yuran had long stopped working on her press release and was secretly observing Xu Yuan from behind with the help of the screen. After all, she liked Xu Yuan's serious look.

So much so that as soon as he heard the voice, he immediately responded: "Then let's go."

As soon as she said this and before she completely stood up from the chair, she suddenly thought of something and took the initiative to express her concern.

"Have you got any ideas for your graduation thesis?"

She naturally knew that Xu Yuan was writing his graduation thesis and was about to pursue a doctorate in science.

"Not yet, but I'm sure I can find a way." Xu Yuan answered confidently.

The smoothness of Monge-Ampere's equation is indeed difficult to prove thoroughly, but it did not daunt him. Instead, facing the challenge inspired him to fight hard.

The key is that he can see the changes in progress, which is equivalent to having confidence that he is not just floating on the ocean.

Even if the progress increases by 1% in a few days, at least he knows that the proof is moving forward. As long as he is given time, the solution will be proven sooner or later.

"I believe you."

Looking at Xu Yuan's confident expression, Chen Yuran immediately smiled and said affirmatively.

Then the two of them locked the door of the discussion room and went to the school cafeteria.

Not long after.

Xu Yuan and Chen Yuran walked to the cafeteria door and were about to go in when they were interrupted by the sudden ringing of a cell phone.

"Wait a moment."

"I'll take a call first."

When Xu Yuan saw that it was his cell phone, he turned around and said something to Chen Yuran, and they both moved to the side to make way, then he took out his cell phone and prepared to answer the call.

"Professor Qi?"

When the name of the note displayed on the screen came into view, Xu Yuan felt a little surprised.

Unexpectedly, the other party was Professor Qi Tongxiang from the Department of Mathematics at HKUST.

Actually, he hadn't seen the other party since the end of the mathematics academic conference. So the sudden call must mean something's going on.

The thought stayed here, and my hand had already pressed the answer button and put the phone to my ear.

"Hello, Professor Qi." Just as I opened my mouth to greet him politely, I heard a familiar voice coming from the other end of the phone.

"I won't waste your time. I'll make it short. You should know about this year's undergraduate mathematical modeling competition. The preliminary review and defense will begin in a few days. This time, our provincial competition area has chosen our university for the defense, so I would like to invite you to serve as a preliminary review judge for this competition area's organizing committee."

"I have already contacted Old Tang and learned that you did not sign up for this Mathematical Modeling Contest."

Qi Tongxiang really didn't waste any time and went straight to explaining the matter in detail.

After hearing everything, Xu Yuan was quite surprised. He didn't expect that the other party would invite him to be a preliminary judge.

He even contacted Tang Shihong in advance to ask if he had time to go to USTC.

The so-called preliminary judges are those who listen to the paper defense of the group winning the provincial first prize on site, select the best ones and send them to the national organizing committee to participate in the selection of the national award and the final Higher Education Press Cup.

He thought that since he did not sign up for the Mathematical Modeling Competition, he would not have anything to do with this Higher Education Society Cup.

In the end, I still had to find a different way to participate.

Qi Tongxiang was the first professor who taught him mathematics. He had previously attended an academic conference on number theory. Now that he had received a phone call and invitation, he felt embarrassed to refuse.

Plus, he hasn't made much progress on his graduation thesis these days, so he might as well join in the fun and change his mindset.

But the words came out of his mouth with a certain degree of modesty: "Is it not appropriate for a student like me to serve as a judge?"

"Other students can't solve the Carmichael number interval problem. We have arranged your tickets and itinerary." Qi Tongxiang said this with a smile and hung up the phone without waiting for Xu Yuan to refuse.

Hearing the busy tone coming from the other end of the phone, Xu Yuan was at a loss whether to laugh or cry and had to run over.

"Are you going to be a judge for the Higher Education Press Cup Mathematical Modeling Competition?" Chen Yuran asked Xu Yuan with a look of surprise on her face.

Xu Yuan did not avoid Chen Yuran in the phone call just now, so there was no need to keep it a secret.

Without any pause, he nodded and replied, "I'm just a judge for the competition area. I was invited by a professor I know."

"This is a good thing."

"Others have signed up for the competition, but you have directly become a judge. If you meet classmates you know..." Chen Yuran smiled and was happy for Xu Yuan to get this opportunity.

"Let's go eat first. I'm almost starving." Xu Yuan reached out and rubbed Chen Yuran's head to end the topic.

……

Because Xu Yuan had promised Professor Qi Tongxiang to serve as a preliminary review judge at USTC, he had to separate from Chen Yuran and return to the dormitory after dinner.

However, before they reached the door, they heard the excited cheers of Li Zhenya, Wang Haitao and others inside.

"Liu Yang, you can do it."

"We must celebrate properly tonight and treat everyone to dinner."

"Our dormitory is really full of hidden talents."

When I pushed the door open, I immediately saw Li Zhenya and Wang Haitao surrounding Liu Yang with excitement and joy on their faces.

When Li Zhenya saw Xu Yuan first, he immediately turned around and shared his eager explanation.

"Xu Yuan, you're back just in time. Liu Yang offered to treat us. We were just discussing where to eat tonight."

"Are the results of the Mathematical Modeling Competition out?" Xu Yuan asked casually.

From the phone call from Qi Tongxiang inviting him to be a judge, to the performance of several people in the dormitory, it is obvious that the competition results have been announced and Liu Yang's group has achieved good results.

He was not surprised by this, after all, Liu Yang was a member of the national team who competed in the Olympics with him.

Even if you have two bronze teammates, the results won't be too bad.

"It was just announced today that our group has qualified for the preliminary review and defense." Liu Yang nodded and said to Xu Yuan.

There was obvious joy in his words.

He has always regarded Xu Yuan as his target to catch up with. Although the gap is becoming more and more obvious and they are no longer on the same track, he is somewhat comforted by the excellent results he achieved in the Higher Education Society Cup this time.

Xu Yuan knew that with Liu Yang's level, if he was able to participate in the defense, he would definitely be sent for the national award, which was indeed quite good in this level of competition.

The next second Xu Yuan expressed his sincere blessing to Liu Yang: "Congratulations, Liu Yang."

"Thank you."

"I'll treat you tonight, let's have some fun together."

Liu Yang's face was filled with joy, and he immediately spoke in an unusually generous tone.

This made Li Zhenya and Wang Haitao cheer immediately.

"Yoko is generous."

"Then let's go back to the place we went to last time. We have to have a few drinks tonight."

Although Xu Yuan didn't want to ruin the atmosphere after hearing this, he still took the initiative to explain the situation in order not to delay the trip.

"I may not be able to participate this time. Professor Qi from HKUST invited me to serve as a judge for the preliminary defense of the Mathematical Modeling Contest at their school."

Almost at the moment Xu Yuan finished speaking, the dormitory fell into an extremely quiet silence.

After about two seconds of being stunned, the shock suddenly burst out.

"Fuck."

"No wonder you didn't sign up, turns out you want to be a judge!"

"Brother Yuan is awesome."

Compared with the excitement of Li Zhenya and Wang Haitao, Liu Yang sighed in his heart.

I thought I could narrow the gap with Xu Yuan a little this time, but Xu Yuan actually became a judge of the competition area organizing committee. We were not on the same level at all. There was no chance for comparison.

(End of this chapter)