Research starts with PhD students

Chapter 33 Let me see what the specific problem is!
"Senior, excuse me!"

"We were discussing a topic and happened to see you."

Deng Xiao looked at Liu Chengjie and asked, "The senior over there is alone, is that okay? How about calling him over as well?"

Zhang Shuo turned his head and took a quick look, and found Liu Chengjie staring at the ceiling with his fists clenched on his chest...

Is this some kind of prayer ritual?

He thought about it, shook his head and said, "It doesn't matter. He enjoys it."

Zhong Yijing and Deng Xiao nodded in agreement.

Zhong Yijing said, "It's like this. My instructor gave me a question, and I've been thinking about it for a few days, but I have no idea where to start. I want you to help me see if you have any ideas?"

She said this with a depressed pout.

Deng Xiao said indifferently, "Your tutor is pretty good. My tutor didn't give me anything and asked me to figure it out on my own."

"What question?"

Zhang Shuo asked while eating.

Zhong Yijing took a draft book, opened a page and handed it to Zhang Shuo, "It's this equation..."

Zhang Shuo looked up and took a quick look. He immediately put down his chopsticks and took the draft book. He looked at it carefully and raised his head. "Nonlinear Schrödinger wave function equation?"

"Correct."

Zhong Yijing was suddenly delighted, "Senior, did you know?"

Zhang Shuo nodded, "I know a little bit."

More than just a little!
This is his area of ​​expertise!
The Schrödinger equation uses the wave function (or quantum state) as the basic variable, and uses this wave function to calculate the probability distribution of particles at different positions and times.

It is a fundamental method in quantum mechanics.

This type of equation has very wide applications in quantum physics and particle physics.

In his previous life, Zhang Shuo was doing research in particle physics. The main content of the experiment was to use strong electromagnetic interference to measure the energy of particles, which naturally involved a lot of particle analysis, and he encountered problems with the analysis and calculation of the Schrödinger equation.

"I'll show it to you after I finish my meal." Zhang Shuo took the draft book and put it aside.

Zhong Yijing hurriedly said, "Eat slowly, I'm not in a hurry!"

Zhang Shuo finished his meal in a few bites, pushed the plate aside, took out the pen from his pocket and started writing on the draft book.

The linear Schrödinger equation is relatively simple to solve, but it becomes much more complicated when nonlinearity is involved.

Some nonlinear Schrödinger equations require proving the existence of solutions, and studying their properties can be considered a small topic.

But it was nothing for Zhang Shuo. He just looked at the equation and knew how to solve it.

"Make the transformation first..."

“Derivation, separation.”

"Expand it, and then use the balancing method..."

The pen in my hand never stopped moving as I analyzed the process step by step, writing page after page.

Zhong Yijing and Deng Xiao were watching from the opposite side. They wanted to understand, but they found that they couldn't understand it at all.

Deng Xiao said with exaggerated mouth shape, "You really have an idea?"

"can't read!"

Zhong Yijing pursed her lips tightly.

Zhang Shuo wrote for nearly twenty minutes in one breath, filling up five pages of draft paper. He put down his pen, stood up straight, and examined his masterpiece from front to back.

"good!"

“This equation is still very familiar!”

He nodded with satisfaction and handed the draft book to the other party. "I have solved it. Take a look. If you don't understand anything, you can ask me."

"Solved it?"

Zhong Yijing's expression was a little exaggerated. "Senior, you're not going to tell me that you found the exact solution, right?"

“There’s only one set, and I’m not sure how many exact solutions there are.”

Zhang Shuo explained, "In fact, this equation is a special case."

"Many of these nonlinear partial differential equations do not have exact solutions. Even if they do, they still require computer-assisted calculations."

"If we want to determine the number of exact solutions, we have to analyze the properties of the equation, which makes the research very difficult."

"You guys are studying for a master's degree, the requirements won't be that high, right?"

He was a little unsure.

"No no!"

Zhong Yijing quickly shook her head, her expression still exaggerated.

Deng Xiao's expression wasn't much better.

The two of them stared at Zhang Shuo in a daze.

"Then try to understand it first, and ask me if you have any questions." Zhang Shuo nodded and said, then he found that he had received a message on his phone.

I clicked on it and saw that it was a message from the bank.

Your bank card account has a new transfer income of 500...

"The project bonus has arrived."

Zhang Shuo was delighted and said immediately, "I have something to do, so I'll leave first. Go back and try to understand it. If there's anything you don't understand..."

"Tell you next time!"

With that, he quickly walked out of the cafeteria.

Zhong Yijing and Deng Xiao stared at Zhang Shuo's back together, their expressions remained the same as before.

After a long while, Deng Xiao finally reacted and asked in shock, "He figured it out?"

"really?"

"How is this possible? Your instructor just asked you to study the existence of the solution, right?"

"And then he found the exact solution?"

Zhong Yijing was also very surprised. The topic given by the instructor was to study and prove the existence of the solution. In other words, it was to study whether the solution exists or not.

This is the direction of the master's thesis given by my supervisor.

She wanted to ask Zhang Shuo if he had any ideas for the proof, and she fully expected that Zhang Shuo would be able to give an exact solution directly, and it only took him 20 minutes to complete the calculation.

Or, calculate manually!
For a moment, Zhong Yijing didn't know how to react. Suddenly she came to her senses and put the draft book into her backpack. "I'll go ask my tutor!"

"Look what he said!"

……

After Zhang Shuo walked out of the cafeteria, he first received a call from Wang Duoju.

Wang Duoju called specially to inquire whether the project bonus had arrived, and then congratulated on the official completion of the project settlement.

Wang Duoju wants to have a good relationship with Zhang Shuo.

In her opinion, Zhang Shuo is a very capable person. As a doctoral student, he can get a million-level project in cooperation with the Institute of High Energy Physics. If he stays at the school to teach in the future, he will definitely be able to take on big projects.

Such talents who can raise funds on their own are treasures in any university. If every professor is like this, her job will be much easier.

Zhang Shuo and Wang Duoju exchanged a few polite words and went to the computer room to find Luo Yongjun and asked about the bonus issue.

Zhang Shuo personally received 500,000 yuan for the project, plus 1 million yuan in personal funding from the Institute of High Energy Physics, for a total of 1.5 million yuan.

The rest all belong to Luo Yongjun.

The finance department will transfer the money to Luo Yongjun in two installments, one is a whole amount of 200,000, and the remaining uncertain amount will be transferred to another new card.

“It’s in the account!”

Luo Yongjun said happily, "A total of 215,000."

As soon as he finished speaking, he came over and whispered, "If anyone asks you, just say I only took 20."

"Must remember!"

"Why? Who would ask this?" Zhang Shuo was a little confused.

"Maybe?"

Luo Yongjun said while operating his mobile phone, "I'll teach you a way to save some private money. Maybe you can use it in the future."

He said to transfer all the more than 10,000 yuan on the new card to the financial management platform attached to the communication software, and then set the icon of the financial management platform to not be displayed.

The next step is to set up SMS to refuse to receive messages from financial management platforms.

Zhang Shuo was stunned.

Luo Yongjun said seriously, "When saving private money, you must be cautious. This is my experience."

"Otherwise, if you check your phone, you'll know everything!"

Zhang Shuo forced himself to hold back his laughter and gave a thumbs up, "Teacher Luo, you are the best. You do things perfectly!"

“It’s all experience.”

Luo Yongjun said happily, and reminded Zhang Shuo, "You should also save some money so that you can have your own small treasury like me in the future."

"Uh~~"

Zhang Shuo looked at the seven-digit number displayed on the bank card and pursed his lips. "At least now, money is just a number to me."

Luo Yongjun's face darkened when he heard this, "Call someone!"

"Call Gao Xiaohong, Liu Chengjie, and a few other professors. We're going to have a celebration banquet today. We're going to have a seafood feast!"

"We've already agreed on this!"

"no problem!"

at the same time.

Max Planck Institute for Mathematics, Bonn, Germany.

Friedrich Jost, who is nearly 60 years old, came to the office early. He is the deputy director of the institute and was appointed honorary professor of Bonn University. He has won the Leibniz Prize and is an internationally recognized top mathematician. The textbook "Partial Differential Equations" he wrote is widely used in the field of international mathematics education.

In short, Friedrich has achieved success.

But he is still very hardworking and comes to the office early every day. Of course, it is also related to his hobbies.

Friedrich is a guest review editor for the academic journals Advances in Mathematics and Mathematical Computing and Information Engineering.

Every day when he arrives at the office, the first thing he does is to make a cup of black coffee, and then open his email to see if there are any papers sent by the two journals. The papers that are sent to him for review are often difficult and innovative.

So, the content will be interesting.

Same today.

Friedrich took a sip of black coffee, sipped his lips to savor the rich aroma, then opened his email and started reading.

He immediately saw two papers sent to him from the editorial department of New Advances in Mathematics.

There was also a message on it, "Hello, Mr. Yost, these two papers have the same author, the content is very innovative, and the method logic involved is very novel and complex. We cannot decide."

Friedrich first glanced at the author's introduction, then frowned, "Mr. Zhang Shuo? Is he affiliated with the Institute of High Energy Mathematics of Soochow University?"

After a moment of thought, he realized that the person who submitted the paper was a doctoral student.

When submitting a paper, you need to fill in the title, which is divided into Professor, Doctor, Ms. and Mr.

If you fill in Ms. or Mr., it means you do not have a doctoral degree, and your institution is a university or research institute, so you can only be a doctoral student.

In addition, the corresponding author and first author of the paper are the same person.

"So, this Mr. Zhang Shuo completed the research alone and submitted two papers to Advances in Mathematics?"

"The first article is about methods, and the second one is about 'General Algorithms for Elliptic Equations', which should be applications?"

Friedrich rubbed his eyes vigorously to make sure he was not seeing things, but the content of the research was still surprising.

He took a deep breath and thought, "If he can pass the initial review, there shouldn't be any obvious problems."

"But general algorithms for nonlinear equations..."

Friedrich took a deep breath, still a little bit unbelieving.

He took a big sip of coffee, put down the cup, his eyes gleaming with interest, "Let me take a look, what's the problem!"

(End of this chapter)