Chapter 137: Equilibrium Problems in Hilbert Space

I had two breaks before the meal was finished. I had to sing, but I could n’t sing.
Lu Zhou first settled the account for Feige, and then, with Huang Guangming and Liu Rui, dragged the boy back to the bedroom.
As for Fei Ge, there is a beautiful person to take care of it. Mostly tonight, while drunk, half push and half, I can't come back ...
After returning to the dormitory, two single dogs laid Liu Rui with a cushion on the ground, and then covered him with a quilt, which was considered as arranged.
Huang Guangming climbed up the ladder and lay down. After a while, he sighed.
"Uncomfortable, elbow."
He didn't drink much, and his head was still sober. Lu Zhou, who was preparing to choose a topic for his graduation thesis, replied casually: "What's wrong?"
"Hey, seeing Fei Ge take off the bill, do you have no idea?"
"... What's the idea?"
Huang Guangming sighed: "Forget it, there is no common language."
Lu Zhou: ...?
speechless.
The next morning, Feige had not returned yet, and it was estimated that he was still immersed in Wenrou Township and could not help himself.
Under Lu Zhou, brush your teeth and wash your face on the balcony.
When he came back, he happened to find that Liu Rui, who was lying on the ground, climbed up, and Huang Guangming, who had been lying on the ground, climbed down very well.
Lu Zhou asked curiously, "I'm so diligent today, I'm going to study by myself?"
Huang Guangming yawned, walking to the balcony while holding his brushing cup, and said, "Why not? Wait for Fei to come back to pretend?"
Lu Zhou imagined the picture with a subtle expression.
Well, that's it, understand.
...
After having breakfast in the cafeteria, Lu Zhou slowly moved to the entrance of the library.
At this moment, the open space in front of the library was crowded.
The old postgraduate army has been liberated, and a new batch of postgraduate army is being prepared. This kind of feeling of crossing the wooden bridge with thousands of horses, has been selected by the school, Lu Zhou, I'm afraid I have no chance to experience it.
Hey, a big regret in life.
As the crowd rushed into the library, Lu Zhou found a remote place to sit down, opened the blank document, and began to write his graduation thesis.
He had already chosen the topic.
Mathematics is a scientific research tool. It is useful to sharpen this tool, but if it only stays at the level of mathematics, it is too wasteful of your talent.
Now that he has decided to move his feet toward the big pit of mathematical physics, Lu Zhou decisively chose functional analysis as the direction of his graduation thesis. It is just that the Fourier transform is no longer aimed, but the unpredictable Hilbert space.
In quantum mechanics, there are infinitely many states, so the dimension of the inner product space is infinite. Infinity involves the problem of convergence. When some parameters are taken to infinity, in order to prevent any physical state from running out of space, mathematically the limit of any sequence is still in space, that is, the space is required to be complete.
And Hilbert space just meets this demand of quantum mechanics.
A physical system can be represented by a complex Hilbert space, and the vector in it is a wave function describing the possible states of the system.
Although the concepts related to Hilbert space have been introduced in functional analysis at the undergraduate level, they have only stayed in some superficial stages. In the frontiers of mathematics, Hilbert space is the same as the Fourier transform, and can be separately identified as a research direction to discuss.
This graduation design, Lu Zhou will not follow the standards of undergraduates, but will do according to the standards of journal submissions. Do not do well and do not care, right should be a practice!
Recalling those references I read a while ago, Lu Zhou put his hands on the keyboard and quickly typed a line of words.
[Equilibrium Approximation Problem and Finite Non-Stretch Mapping in Hilbert Spaces]
There is no need to exchange points for this thesis. When I previously exchanged Hilbert space issues with Brother Luo, Lu Zhou had some ideas in his head.
Picking up the pen, Lu Zhou wrote on the draft paper.
[Let H be the complex Hilbert space given the inner product, let L (H) be the entire bounded linear operator, and T∈L (H), then the numerical range of the operator T is defined as the following set: W (T) = { & amp; lt; Tx, x & amp; gt; x∈H, x = 1} ……]
Time passed by every minute and second, Lu Zhou only felt that his thoughts were extremely smooth, and soon he filled the whole draft with ease, and reached out his hand to the second draft paper.
It seems that as he guessed before when challenging the twin prime conjecture, the benefit of the improvement of the mathematical level is not only to unlock the database permissions of the system, but also to improve his own thinking ability in this field.
Brain domain development?
Or something else?
In short, he can clearly feel the change that happened to him.
"Get the papers done these days, and then work on the system."
Stretching a lazy waist, looking at the brothers and sisters preparing for the postgraduate entrance examination, Lu Zhou was also motivated.
In fact, brushing papers in the library and looking at books, this feeling is also very good. As the subject level increases and the speed of knowledge acquisition increases, he also enjoys this process from ignorance to knowledge.
I just do n’t know why, sitting on the land boat that is struggling to write something, I always feel something missing ...
...
Back in the bedroom, no accident, and heard Shi Shang pretending to be there.
However, this guy didn't say the very topic of "grateful for the first time", but simply passed on a little bit of life experience to the two single dogs, such as my sister's experience ... and this is also the most irritating of!
Huang Guangming directly turned on the computer to watch the variety show. Liu Rui put on the headset and listened to the song while brushing the abstract algebra. The two people inadvertently blocked the guy.
"Yo, elbow, are you back from self-study?"
"How did you feel yesterday? The quality of my wife's bedroom is okay?"
"Want to get to WeChat? Don't be so shy. Everyone is an adult. Just be direct, or if you tell me who is interested, can I help you ask WeChat?"
Lu Zhou sighed, "Fei, you're inflated."
Shi Shang touched his face: "Swell? Do I have it?"
Lu Zhou: "Yes, you make me feel Chinese New Year."
Shi Shang stunned: "New Year? Why?"
"The words you just said, at the time of the New Year, several menopausal aunts from my relative's house had already said it."
Shi Shang: "..."
Throwing the computer bag on the table, Lu Zhou was about to go to the balcony to wash his hands. He happened to see the variety show on Huang Guangming's computer and glanced at it.
"The strongest learner?"
"Yes."
Yes, have you started looking for common topics?
Looking at Huang Xiaoxian, Lu Zhou felt with emotion.
It seems that the single dog camp of 201 lacks another brave little friend.
"What are they doing?" I don't know when Liu Rui stopped asking questions and came over to watch. From the outside, several men surrounded a computer, and people who didn't know thought they were looking.
"Sudoku!"
Sudoku?
Looking at the calm young man on the stage, Lu Zhou's expression appeared a faint expression.
This is the school fighter named Wu Yan?
But I don't know why. He, who is also a school bully, smelled a weak breath across the screen. Of course, no matter what the reason, it is definitely not because the goods look handsome, after all, there is still a little gap compared to him.
As a member of the Wu Yan group in the mathematics world, Lu Zhou felt that although he did not win those old men over academic achievements, he still wo n’t lose to anyone if he compares his value, should n’t anyone dispute it?
Just then, the man on the stage moved.
Lu Zhou was shocked.
"Blind Sudoku ?!"
Huang Guangming smiled indifferently: "Let's go wrong ... Can you not say Lu brother?"
Lu Zhou: "... can't mess with it."
Does this show group have any misunderstanding about the term Xue Ba? But having said that, does the player need even the time for calculation?
This is too scary.
Next is a hundred subject problems, both sides stood in line to answer the questions. Some are physics, some are mathematics, and some topics like biochemistry require the division of labor and cooperation between members to solve. Lu Zhou can understand, but Huang Xiaoxi and Liu Rui have begun to look aggressive.
However, it does not seem to hinder the interest of these two?
Liu Rui: "Elbow, do you understand?"
Lu Zhou nodded: "Basically understand."
You can understand it, but you ca n’t do it so fast. Many of these topics are at the level of professional knowledge and skills competition for college students. Even some professors have to take a moment to think.
Although it is a multiple-choice question, unless it is blind, it is almost impossible to push like this ... It is said that the genius in this world has changed so much.
Lu Zhou subconsciously looked at the four members of the opposite German team one by one, and found that Peter Schultz was not inside, looked at the Chinese team, and did not have a familiar face.
In less than fifteen minutes, all 100 questions were solved and the answers announced. The Tiger King team from Germany answered 83 questions correctly and scored 8.3 points, temporarily leading the surpassing team from China who answered 79 questions correctly.
The total score of the two sides was 14:15. The Tiger King team was temporarily ahead, and the situation became tense.
Just then, the hostess in an evening gown came forward to speak.
"We all know that the great mathematician Euclid proved the infinity of prime numbers, and modern mathematician Hilbert once again proved it using topology. The mathematical world's pursuit of mysterious prime numbers is Never ending. "
"The next problem is a world-class problem."
"The great mathematician Polignac put forward the general conjecture ~ EbookFREE.me ~ For all natural numbers k, there are infinitely many pairs of primes (p, p + 2k). And our topic today is to solve this A conjectural weak conjecture is verified. "
"Who can push K towards a smaller number, who will get 3 points for this decision!"
"Start answering!"
The three friends in front of the computer were shocked.
Huang Guangming: "Grass holding? So social ?!"
Liu Rui: "Can Nima prove this on the stage? Did I give this computer to eat ... or not to eat anymore."
Lu Zhou :? ? ?
...
Welcome to the latest chapter of Blackmaster System of Xueba, updated by
This article address:
Welcome to read.
...