Chapter 299 (1/2)
Chapter 302
”students, are you kind enough to help Xu Jie put his hands together and made a petition.
Cheng Nuo rubbed his eyebrows, ”OK, I'll help you to have a look, but after reading, you should go to bed immediately. If you don't sleep well, even if you review more fully, it won't be of any use.”
”Of course.” Xu Jie handed Cheng Nuo the book ”complex function and operational differentiation preliminary” in his hand.
He turned the book to a page, pointed to one of the topics and said, ”well. That's the question. ”
[it is proved that if f ∈ s, then in Δ: | Z | ≤ 1, there is | Z | (1 + | Z |) ^ 2 ≤| f (z) | ≤| Z | (1 - (x)) ^ 2.]
Cheng Nuo glances at the topic and says, ”eh? Isn't this the koebe deviation theorem? ”
Xu Jie was confused. ”What is that?”
”Koebe deviation theorem is a bounded theorem used to describe univalent functions on the unit disk. If I remember correctly, the stem of this problem should be the content of koebe deviation theorem. In 1944, it was deduced by the mathematician Kebei Cheng explains.
”Why do you know so much?” Xu Jie then asked.
Cheng Nuo shrugged. ”I've read more books. I've read about one-third of the books about functions of complex variables in the school library.”
One third, that's at least dozens.
Xu Jie has a little admiration in his heart and some unconvinced spirit, but it doesn't show on his face.
He said, ”the key is that you know what it is and there is no theorem. The question is about the steps of proof.”
Cheng Nuo smiles, ”this is simple.” He reached out. ”Do you have a pen and paper?”
Xu Jie hands Cheng Nuo paper and pen and looks at Cheng Nuo quietly.
Instead of writing in a hurry, Cheng asked, ”you should know the debranges theorem?”
”This is nature.” Xu Jie proud head, ”although the class did not say anything about this theorem, but according to looking up some extracurricular information, I can still say one or two.”
”Debranges theorem, its predecessor is Bieberbach conjecture, was completely solved by mathematician debranges in 1912, so it was renamed debranges theorem.”
”Its main content is that if the power series of a function is expanded to f (z) = Z + A2Z ^ 2 + a3z ^ 3 +...” If and only if the function Z (1-z) ^ 2 or its rotation. ”
Bingo!
Cheng Nuo snapped his fingers. ”It's true, but what you haven't mentioned is that 30 years later, mathematicians will deduce koebe deviation theorem through debranges theorem.”
”How to deduce?” Although Cheng Nuo has told Xu Jie the necessary theorem, he has no clue.
Cheng Nuo raises his pen and swims on the paper.
”First, by using the debranges theorem, we derive the range of F (z) when | Z | 1. Because f (0) = 0 Using the above, we get | f (z) | = |∫ f (ζ) d ζ | ≤| Z | (1-z) ^ 2 Finally, the koebe deviation theorem is obtained
At this time, Xu Jie suddenly realized that his right hand became a fist, and suddenly placed in the palm of his hand, ”sikuyi, it is so. Taking debranges theorem as the breakthrough point, the general bounded range of | Z | 1 is obtained. Finally, it is proved by reasoning
”Classmate Cheng Nuo, you've been taught!” Xu Jie's face was full of joy. ”Although we are not students of the same university, I still hope you can enter into marriage with me Ah, bah, we'll be on the first prize list together. ”
Cheng Nuo put the pen and paper into Xu Jie's hand, ”come on, put away your blessing buff. It was stable to take the first prize, but don't be milked to death by you.”
”I'll see you tomorrow.” ”By the way, remind me again, remember to wake me up!”
Cheng Nuo yawned and fell asleep again.
”I am not poisonous milk!” Seeing Cheng Nuo, who has already started to snore slightly, Xu Jie whispered in his neck.
……
The next day. It's just dawning.
”Xu Jie, are you crazy? It's not until six o'clock now!” In Room 203 of the hotel, Cheng Nuo's voice reverberates.