universal data

Chapter 299 I'm Sorry

302 chapter

"Classmate, would you be kind enough to help me?" Xu Jie clasped his hands together in a prayer gesture.

Cheng Nuo rubbed his brows, "Okay, I'll take a look for you, but after reading it, you have to go to bed right away. If you don't sleep well, no matter how much you review, it's useless."

"Of course." Xu Jie handed the book "Complex Variable Function and Preliminary Calculation Differentiation" to Cheng Nuo.

He turned the book to a certain page, pointed to one of the questions and said, "Hmm. That's the question."

【证明：若f∈S，则在Δ:|z|≦1内，有|z|/（1+|z|)^2≦|f(z)|≤|z|/(1-(x))^2.】

Cheng Nuo briefly glanced at the title, and let out a little surprise, "Huh? Isn't this Koebe's deviation theorem?"

Xu Jie was confused, "What is that?"

"Koebe's deviation theorem is a bounded theorem used to describe the single-leaf function on the unit disk. The stem of this question, if I remember correctly, should be the theorem content of Koebe's deviation theorem. In 1944, Mathematics It was deduced by Ke Bei." Cheng Nuo explained.

"Why do you know so much?" Xu Jie asked immediately.

Cheng Nuo shrugged, "I just read a lot of books. I have read about one-third of the books in the school library related to complex variable functions."

One-third, that is at least dozens of books.

Xu Jie had a little admiration in his heart, and some dissatisfaction, but it didn't show on his face.

He said, "The key is that you don't know what theorem it is. The question is about the proof steps."

Cheng Nuo smiled, "That's easy." He stretched out his hand, "Do you have any paper and pen?"

Xu Jie handed Cheng Nuo a pen and paper, and looked at Cheng Nuo quietly.

Cheng Nuo didn't start writing in a hurry, but asked, "You should know de Branges' theorem, right?"

"This is natural." Xu Jie raised his head proudly, "Although I haven't taught anything about this theorem in class, I can still tell you a thing or two based on looking up some extracurricular materials."

"The de Branges theorem, its predecessor was the Bieberbach conjecture, was completely solved by the mathematician de Branges in 1912, so it was renamed the de Branges theorem."

“它的主要内容，是讲如果有一个函数的幂级数展开为f(z)=z+a2z^2+a3z^3+……，则|an|≦n且等号成立当且仅当函数z/(1-z)^2或它的旋转。”

bingo!

Cheng Nuo snapped his fingers, "That's true, but what you haven't mentioned is that more than [-] years later, mathematicians derived Koebe's deviation theorem from the de Branges theorem."

"How to deduce?" Although Cheng Nuo had told Xu Jie the theorems needed to deduce, but he had no clue.

Cheng Nuo raised his pen and scribbled on the paper.

"First, use the de Branges theorem to deduce the range of f(z) when |z|<1. Since f(0)=0,..., using the above mentioned, get |f(z)|=| ∫f(ζ)dζ|≤|z|/(1-z)^2... Finally, Koebe's deviation theorem is obtained."

At this time, Xu Jie suddenly realized that he formed a fist with his right hand and slammed it into the palm of his hand, "Scuy, so it is like this. Taking de Branges theorem as an entry point, we can obtain the universal bounded range when |z|<1, The final reasoning proves."

"Student Cheng Nuo, you've been taught!" Xu Jie's face was filled with joy, "Although we are not students in the same university, I still hope that you and I can enter into marriage together... Ahhhhhhhhhh, step into the first class together. list of awards."

Cheng Nuo stuffed the pen and paper into Xu Jie's hands, "Come on, put away your bless buff, it's safe to win the first prize, so don't be fooled by you."

"Sleep, see you tomorrow." "By the way, remind me again, remember to wake me up!"

Cheng Nuo yawned and fell asleep again.

"I'm not poisonous milk!" Seeing Cheng Nuo who was already grunting slightly, Xu Jie whispered, poking his neck.

……

the next day.It was just dawn.

"Xu Jie, are you crazy? It's only half past six o'clock!" Cheng Nuo's roar echoed in room 203 of the hotel.

Once again, Cheng Nuo, who was soundly asleep, was woken up by Xu Jie.

Beside the bed, Xu Jie had already dressed and packed up, "The day's plan starts in the morning, classmate Cheng Nuo, you can't waste the good time in the morning while sleeping. Come and exercise with me."

Cheng Nuo was forced to get up, rubbed his sleepy eyes, "Then let's go downstairs for a morning run?"

"No no." Xu Jie shook his head, "Running is too low, we Xueba should have the unique way of morning exercise."

Cheng Nuo: "SO?"

Xu Jie scratched his head and smiled, "So, I created a set of 'function dance'"

The "function dance" invented by Xu Jie is to use the body to construct various basic function curves.

Cheng Nuo was forced to jump together.

y=sinx, sine function, bend the arm and swing the wave.

y=x, linear function, one hand is raised sideways and the other hand is raised sideways, making a 45 degree angle.

y=(1-x)^2+3√x^2, heart-shaped line, heart-to-heart! ! !
…………

After a meal, I was sweating profusely and panting again and again.

After breakfast, Cheng Nuo and Xu Jie separated to meet up with their respective teams and drove to the final exam site.

The test time is the same as the preliminary round, starting at 09:30, with three hours of answering time.

However, in terms of test questions, the final test questions are not only more difficult than the final test questions, but also two additional questions will be added.

Each additional question is [-] points, and the score is not much, but the difficulty is not small.The two questions were written by two masters in the field of mathematics.

In previous years, there were only a handful of candidates who could answer all the last two additional questions correctly on the premise of answering the previous questions.

At nine o'clock sharp, more than a dozen people from Tsinghua University arrived at Modu University, where the examination center is located.

At 09:30, the exam officially starts.

At [-]:[-], Cheng Nuo finished answering all the previous questions, leaving only two additional questions.

Additional question 1: [For polynomial f(x), write down d(f) to represent the minimum real root distance represented by its maximum sum, let n≥2 be a natural number, find the maximum real number C, so that for any real root...]

Additional question 2: [Assume that X1, X2...Xn are independent and identically distributed random variables, which have a common distribution function F(X) and a density function f(x). Now for random variables, X1...Xn, press Rearrange the order of size, ...]

Sure enough, whether it is the entry point of solving the problem or the calculation process, it is much more troublesome than the previous problem.

But again, to Cheng Nuo, this was nothing.

Exam time is one hour.

Cheng Nuo walked out of the examination room with a stationery bag.

Professor Lu still sat with Professor Liu, but this time he was smart and didn't make any bets with Professor Lu.

"Old Lu, you are an amazing student!" Seeing Cheng Nuo approaching, Professor Liu said with half emotion and half envy.

Professor Lu laughed, but did not answer.

One hour later, Xu Jie also walked out of the examination room after handing in the papers ahead of time.

He came to Professor Liu, saw Cheng Nuo sitting beside him, and greeted him with a smile, "Not to mention, this year's questions are really difficult, but fortunately, they are all done. Cheng Nuo, you just came out, right?"

Cheng Nuo said, "Sorry, I came out an hour ago."

Xu Jie: "..."

(End of this chapter)