Omnipotent Data
Chapter 299
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.
Once again, Cheng Nuo, who is sleeping soundly, is awakened by Xu Jie.
By the bed, Xu Jie has already dressed up, "the plan of the day is in the morning, classmate Cheng Nuo. In the good morning, you can't go to sleep in vain. Come and play sports with me."
Cheng Nuo was forced to get up, he rubbed his sleepy eyes, "then we go downstairs for a morning run?"
"No, No Xu Jie shook his head. "Running is too low. We should have a unique way to do morning exercises."
Cheng Nuo: "so?"
Xu Jie scratched his head and laughed, "so I created a set of" function dance. "The "function dance" invented by Xu Jie is to construct various basic function curves with the body.
Cheng Nuo is forced to jump.
Y = SiNx, sine function, bending the arm and swinging the wave.
Y = x, linear function, one hand side up, one hand side down, 45 degrees.
Y = (1-x) ^ 2 + 3 √ x ^ 2, cardioid, bicenter!!!
…………
Sweating and panting.
After breakfast, Cheng Nuo and Xu Jie separate and join their respective teams, and take the bus to the final examination site.
The test time is the same as that of the preliminary contest. It starts at 9:30 and has three hours to answer questions.
However, in terms of test questions, the final questions are not only higher than the final in terms of difficulty, but also add two additional questions.
Each additional question is ten, the score is not much, but the difficulty is not small. The two questions are handled by two mathematicians themselves.
In the past years, candidates who were able to answer the last two additional questions correctly on the premise of answering the previous questions could only be described by the number of their fingers.
At nine o'clock sharp, more than ten people from Tsinghua University arrived at Mordo University, where the test site is located.
At half past nine, the examination begins.
At 10:10, Cheng finished all the previous questions, leaving only two additional questions.
Additional question 1: [for polynomial f (x), let D (f) denote the minimum real root distance represented by its maximum sum. Let n ≥ 2 be a natural number and find the maximum real number C such that for any real root 】
additional question 2: [suppose x1, X2 Xn is an independent and identically distributed random variable. It has a common distribution function f (x) and a density function f (x) Xn, reorder in order of size 】
sure enough, both the starting point and the operation process of the problem are more troublesome than the previous problems.
But still that sentence, to Cheng Nuo, this is not a matter.
The examination lasted for an hour.
Cheng Nuo came out of the examination room with a pencil bag.
Professor Lu was still sitting with Professor Liu, but this time he was smart and didn't make any bets with Professor Lu.
"Lao Lu, you are a very good student!" Seeing the coming Cheng Nuo, Professor Liu said with half emotion and half envy.
Professor Lu laughed and did not answer.
An hour later, Xu Jie returned from the examination room in advance.
Fortunately, Professor Cheng Nuo is still sitting next to him this year. Cheng Nuo, you just came out? "
Cheng Nuo said, "sorry, I came out an hour ago."
Xu Jie:
www.mylovenovel.com , the fastest update of the webnovel!
"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.
Once again, Cheng Nuo, who is sleeping soundly, is awakened by Xu Jie.
By the bed, Xu Jie has already dressed up, "the plan of the day is in the morning, classmate Cheng Nuo. In the good morning, you can't go to sleep in vain. Come and play sports with me."
Cheng Nuo was forced to get up, he rubbed his sleepy eyes, "then we go downstairs for a morning run?"
"No, No Xu Jie shook his head. "Running is too low. We should have a unique way to do morning exercises."
Cheng Nuo: "so?"
Xu Jie scratched his head and laughed, "so I created a set of" function dance. "The "function dance" invented by Xu Jie is to construct various basic function curves with the body.
Cheng Nuo is forced to jump.
Y = SiNx, sine function, bending the arm and swinging the wave.
Y = x, linear function, one hand side up, one hand side down, 45 degrees.
Y = (1-x) ^ 2 + 3 √ x ^ 2, cardioid, bicenter!!!
…………
Sweating and panting.
After breakfast, Cheng Nuo and Xu Jie separate and join their respective teams, and take the bus to the final examination site.
The test time is the same as that of the preliminary contest. It starts at 9:30 and has three hours to answer questions.
However, in terms of test questions, the final questions are not only higher than the final in terms of difficulty, but also add two additional questions.
Each additional question is ten, the score is not much, but the difficulty is not small. The two questions are handled by two mathematicians themselves.
In the past years, candidates who were able to answer the last two additional questions correctly on the premise of answering the previous questions could only be described by the number of their fingers.
At nine o'clock sharp, more than ten people from Tsinghua University arrived at Mordo University, where the test site is located.
At half past nine, the examination begins.
At 10:10, Cheng finished all the previous questions, leaving only two additional questions.
Additional question 1: [for polynomial f (x), let D (f) denote the minimum real root distance represented by its maximum sum. Let n ≥ 2 be a natural number and find the maximum real number C such that for any real root 】
additional question 2: [suppose x1, X2 Xn is an independent and identically distributed random variable. It has a common distribution function f (x) and a density function f (x) Xn, reorder in order of size 】
sure enough, both the starting point and the operation process of the problem are more troublesome than the previous problems.
But still that sentence, to Cheng Nuo, this is not a matter.
The examination lasted for an hour.
Cheng Nuo came out of the examination room with a pencil bag.
Professor Lu was still sitting with Professor Liu, but this time he was smart and didn't make any bets with Professor Lu.
"Lao Lu, you are a very good student!" Seeing the coming Cheng Nuo, Professor Liu said with half emotion and half envy.
Professor Lu laughed and did not answer.
An hour later, Xu Jie returned from the examination room in advance.
Fortunately, Professor Cheng Nuo is still sitting next to him this year. Cheng Nuo, you just came out? "
Cheng Nuo said, "sorry, I came out an hour ago."
Xu Jie:
www.mylovenovel.com , the fastest update of the webnovel!