Volume 1: Student Life Chapter 130 Clifford Analysis
Chen Zhou looked at Wu Xiping's serious expression, and suddenly he felt as if it was himself who was knocked, not Shen Jing.
After letting the student think for a while, Wu Xiping said, "Is there any direction?"
Chen Zhou didn't say anything, but found an A4 draft paper and a pen and quickly wrote a line of words.
[Properties of holomorphic functions and related operators in Clifford analysis]
After a pause, Chen Zhou continued writing:
[Clifford analysis is one of the main branches of function theory. It studies various analytical properties, functional properties, operator theory and various boundary value problems of functions defined in real (or complex) high-dimensional Euclidean space and whose values are Clifford algebras whose multiplication is non- ...]
Wu Xiping watched with interest and nodded slightly: "Clifford analysis is a natural extension of classic unit complex analysis, quaternion analysis and multivariate complex analysis in high-dimensional space."
Chen Zhou put down his pen and continued Wu Xiping's words: "In Clifford analysis , one of the hot research issues is to study the properties of various holomorphic functions under Euclidean and non-Euclidean metrics, as well as the properties of various integral operators related to holomorphic functions."
"The main research objects of single-unit complex analysis and multivariate complex analysis are holomorphic functions, and the corresponding functions of holomorphic functions in Clifford analysis are called regular functions."
Wu Xiping looked appreciative: "How did you come up with the idea of studying this issue?"
Chen Zhou explained: "I have been thinking about this for a long time, and I just happened to see this aspect when I was reading a book."
Wu Xiping nodded: "At present, there is indeed not much theoretical research on canonical functions and related operators in complex Clifford analysis. This is a good research direction."
After a pause, Wu Xiping asked again: "Do you have any specific ideas?"
Chen Zhou looked at Wu Xiping, who was looking at him with a smile.
After thinking for a while, Chen Zhou organized his words a little: "The Cauchy integral formula plays a pivotal role in both classical single-unit complex analysis and multivariate complex analysis. It is not only the integral expression of a holomorphic function, but also an important tool for studying the various properties of holomorphic functions."
"In addition, the Cauchy integral formula also plays a very important role in Clifford analysis. It is a tool for studying the properties of regular functions, and it can provide a variety of integral operators."
After hearing Chen Zhou's words, Wu Xiping praised: "This is a very good idea. We can use the Cauchy integral formula to study the good properties of various integral operators."
"Hmm..." After a brief pause, Wu Xiping continued, "This idea can be further expanded. For example, the good properties of integral operators play a key role in solving partial differential equations. You can establish a theoretical basis for solving complex partial differential equations based on some functional properties of related operators."
"Partial differential equations..." Chen Zhou chewed over Wu Xiping's words over and over again. Following this line of thought, related knowledge kept emerging in his mind.
Chen Zhou stood beside Wu Xiping's desk, lost in thought.
Sometimes he looked surprised, sometimes he frowned.
Wu Xiping saw the changing expression on Chen Zhou's face and smiled silently.
In order not to interrupt Chen Zhou's train of thought, he tried to move as slowly as possible, took out the draft paper and pen, and wrote the formula on the draft paper.
For a moment, the only sound in Wu Xiping's office was the rustling sound of pen tips scratching on paper.
After a long time, Chen Zhou came back to his senses from his trance. He said softly, "Teacher, thank you."
Wu Xiping smiled at Chen Zhou and said, "You won't say that I favor you, my senior?"
"Ahem..." Chen Zhou coughed twice, "Teacher, you must have misunderstood something. Why do I feel this way..."
After a pause, Chen Zhou continued, "Teacher, if we go deeper into this topic, it will be a bit difficult, don't you think?"
Wu Xiping looked up at Chen Zhou and said slowly, "It's okay. I believe you can do it. Well, how did you say that?"
Chen Zhou: "Which sentence?"
Wu Xiping smiled and said, "I'm optimistic about you!"
Chen Zhou: “…”
When I came out of Wu Xiping's office, it was almost 4 o'clock in the afternoon.
Chen Zhou also took out the draft paper he had just written, folded it and put it in his pocket.
Then he took out his cell phone and took a look. Yang Yiyi had sent him several messages.
【Why did you take so long? 】
【Are you coming to the library yet? 】
[If you don't come, someone else will take your seat. ]
[Okay, there's no more space, so don't come...]
Chen Zhou smiled and replied with a message [I'll be there soon, but Professor Wu kept me here].
When Chen Zhou arrived at the library, the seat next to Yang Yiyi that originally belonged to him was indeed occupied by someone.
Chen Zhou had also met this person once. Yang Yiyi's other roommate was named You Yurou, who, like Li Jing, was in the astronomy department.
There are only two girls in the Astronomy Department of the Physics School: Li Jing and You Yurou.
Of course, there is only one girl in the Physics Department, Yang Yiyi.
"Isn't it difficult to take back the position?" Chen Zhou walked towards Yang Yiyi and the others hesitantly.
When she was about to reach the two of them, You Yurou looked up at him, smiled, then stood up, packed up her books, and gave her seat to Chen Zhou.
Chen Zhou said softly: "Thank you."
Yang Yiyi heard Chen Zhou's voice and looked up.
Seeing that You Yurou gave up her seat to Chen Zhou, she shook her head slightly and then looked at You Yurou.
You Yurou smiled at her and said, "I'd better not disturb you two."
After saying that, You Yurou walked to a seat not far away holding a book.
Yang Yiyi looked at Chen Zhou and said, "You pushed my little sister away."
Chen Zhou replied: "Then should I call her back?"
"Forget it." Yang Yiyi shook her head, "Why are you here so late?"
Chen Zhou explained: "I was detained by Professor Wu and given a beating."
"Knocked over? Were you beaten by the professor?" Yang Yiyi looked at Chen Zhou in surprise.
Chen Zhou smiled and said, "No, I just talked about something. Why are you so cute? How could the professor hit me?"
Yang Yiyi replied: "You didn't explain it clearly. I don't care. You made me wait for so long, and you even pushed my sister away. What do you think we should do?"
Chen Zhou thought for a moment and said, "Well...I'll treat you to a meal?"
Yang Yiyi asked: "What to eat? "
Chen Zhou: "What do you want to eat?"
Yang Yiyi: "Whatever, it's all right."
Chen Zhou pondered and said, "Uh...rice with toppings?"
"..." Yang Yiyi glanced at Chen Zhou, "You are so insincere..."
An impatient cough interrupted their conversation. Chen Zhou and Yang Yiyi looked at each other and quickly fell silent.
Yang Yiyi snorted, picked up the pen again and started reading her book.
Chen Zhou took out the folded draft paper, and his eyes unconsciously stopped on the "Clifford Analysis".
He needs more relevant literature and books to recharge himself.
