Chapter 137: The Problem of Equilibrium in Hilbert Space
Before the meal was finished, I forced two to stop, and I was going to sing, but I couldn't sing anymore.
Lu Zhou settled the account for Fei Ge first, and then dragged the kid back to the bedroom with Huang Guangming and Liu Rui.
As for Fei Ge, he has a beauty to take care of, and most of the time tonight he is drunk, half pushing, half pushing, and can't come back......
After returning to the dormitory, the two single dogs laid a mat on the ground for Liu Rui, and then took a quilt to cover him, which was arranged.
Huang Guangming climbed the ladder and lay down on the bed, and after a while, he let out a long sigh.
"It's uncomfortable, elbow."
I didn't drink much, my mind was still clear, and Lu Zhou, who was about to choose a topic for his graduation thesis, replied casually: "What's uncomfortable?" β
"Hey, seeing that Fei Ge has taken off the list, don't you have any ideas?"
ββ¦β¦ What's the idea? β
Huang Guangming sighed and said, "Forget it, there is no common language." β
Lu Zhou: ......?
Nothing was said all night.
The next morning, Fei Ge hadn't come back yet, and it was estimated that he was still immersed in Gentle Township at this time.
Lu Zhou got out of bed and went to the balcony to brush his teeth and wash his face.
When he came back, he happened to find that Liu Rui, who was lying on the ground, got up, and Huang Guangming, who was originally lying on the bed, also climbed down with tacit understanding.
Lu Zhou asked curiously: "Why are you so diligent today, and you all go to self-study?" β
Huang Guangming yawned, walked to the balcony with his toothbrushing cup, and replied, "Otherwise? Waiting for Fei Ge to come back and pretend to be forced? β
Lu Zhou imagined the picture for a moment, and his expression was a little subtle.
Well, I see, got it.
β¦β¦
After breakfast in the cafeteria, Lu Zhou slowly swayed to the door of the library.
At this moment, the open space in front of the library is already crowded with people.
The old army of postgraduate entrance examinations has been liberated, and a new batch of postgraduate examination troops are ready to go. This feeling of thousands of troops crossing a single-plank bridge, Lu Zhou, who has been approved to graduate from the school, is afraid that he will not have the opportunity to experience it.
Hey, it's a big regret in life.
As the crowd poured into the library, Lu Zhou found a remote place to sit down, opened the blank document, and prepared to start writing his graduation thesis.
He had already chosen the topic.
Mathematics is a scientific research tool, and it is useful to sharpen this tool, but if you only stay at the level of mathematics, it will be too wasteful of your talent.
Now that he has decided to step into the big pit of mathematical physics, Lu Zhou decisively chose functional analysis as the direction of his graduation thesis. Only this time it is no longer aimed at the Fourier transformation, but at 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 as infinity, in order not to let any physical state run out of space, so the limit of any sequence is still in space, that is, space is required to be complete.
Hilbert space, on the other hand, meets this demand for quantum mechanics.
A physical system can be represented by a complex Hilbert space, and the vectors in it are the wave functions that describe the possible states of the system.
Although the concepts related to Hilbert space have been introduced in the functional analysis at the undergraduate level, they have only stayed at a superficial stage. In the frontier field of mathematics, the Hilbert space is a separate research direction that can be discussed as a separate research direction, just like the Fourier transform.
This graduation project, Lu Zhou will not follow the standards of undergraduates, but will do it according to the standards of journal submission.
Recalling the references he read some time ago, Lu Zhou put his hands on the keyboard and quickly typed out a line of words.
γViscous approximation method of equilibrium problem and finite non-stretch mapping in Hilbert spaceγ
This time, the paper does not need to be exchanged for points, and when he was communicating with Senior Brother Luo about the Hilbert space problem before, Lu Zhou just had some ideas in his head, and he just wrote it at this time.
Picking up the pen, Lu Zhou wrote on scratch paper.
[Let H be the complex Hilbert space given to the inner product, and L(H) is the whole of the bounded linear operator, and TβL(H), then the numerical domain of the operator T is defined as the following set: (T)={<Tx,x>|xβH,||.] x||=1}β¦β¦γ
As time passed, Lu Zhou only felt that his thoughts were extremely smooth, and he soon filled the entire draft with joy and stretched out his hand to the second scratch paper.
It seems that as he had previously guessed when challenging the twin prime conjecture, the benefits of increasing his mathematical level were not only unlocking the system's database privileges, but also improving his own thinking skills in the field.
Brain domain development?
Or something else?
In short, he could clearly feel the changes that had happened to him.
"Let's get the paper done in the next few days, and then get the task of the system."
Stretching his waist and looking at the senior brothers and sisters beside him who were preparing for the graduate school entrance examination, Lu Zhou also raised his motivation in his heart.
In fact, it is also a good feeling to brush up on papers and read books in the library. As the level of the subject increases, the speed of knowledge acquisition accelerates, and he also enjoys this process from ignorance to knowledge more and more.
It's just that I don't know why, Lu Zhou, who is sitting here and writing hard, always feels that something is missing......
β¦β¦
When I went back to the dormitory, I heard Shi Shang pretending to be there.
However, this guy didn't say "what to be grateful for the first time" This very private topic, just simply taught a little life experience to the two single dogs, such as flirting with girls or something...... And this is also the most infuriating!
Huang Guangming directly turned on the computer to watch variety shows, Liu Rui put on headphones and brushed abstract algebra while listening to songs, and the two of them coincidentally blocked this guy.
"Yo, elbow, you're back from self-study?"
"How did you feel yesterday? The quality of my wife's bedroom is okay, right? β
"Do you want to go to WeChat? Don't be so shy, everyone is an adult, be direct, or you tell me who you are interested in, I'll help you ask> Lu Zhou sighed: "Brother Fei, you are inflated." β
Shi Shang touched his face: "Swelling? Do I have bloat? β
Lu Zhou: "Yes, you make me feel like I'm still celebrating the New Year." β
Shi Shang was stunned: "New Year? Why? β
"What you just said, at the time of the Chinese New Year, a few menopausal aunts from my relatives' family had already said it again."
Shi Shang: "......"
Throwing the computer bag on the table, Lu Zhou was about to go to the balcony to wash his hands, and happened to see a variety show on Huang Guangming's computer, so he glanced twice.
"The strongest student?"
"yes."
Yes, have you started looking for common topics?
Looking at Huang Xiaobei, Lu Zhou sighed in his heart.
It seems that the single dog camp of 201 is missing a brave little friend.
"What are they doing?" I don't know when, Liu Rui stopped brushing the questions, and came over to watch. From the outside, several men gathered in front of a computer, and those who didn't know thought they were looking at something.
"Sudoku!"
Sudoku?
Looking at the young man with a calm face on the stage, Lu Zhou's expression appeared a hint of abruptness.
This is the scholar named Wu Yan?
I don't know why, he is also a top student, and he smells a weak breath through the screen. Of course, no matter what the reason is, it's definitely not because this product is handsome, after all, it's still a bit of a gap compared to him.
As a Wu Yan group in the mathematics community, Lu Zhou feels that although he can't beat those old men in terms of academic achievements, he still doesn't lose to anyone in terms of appearance, no one should refute this, right?
Just then, the man on the stage moved.
Lu Zhou was shocked.
"Blind Sudoku?!"
Huang Guangming smiled cheaply: "It's a cheat...... Anyway, Brother Lu, can't you? β
Lu Zhou: "...... I can't afford to mess with it. β
Does this program team have any misunderstanding of the word Xueba? But then again, doesn't that player even need to calculate the time?
It's also terrifying.
Next is a hundred subject problems, and the two sides stand in line to answer the questions on the spot. Some are physics, some are mathematics, and some are biochemistry, which require the division of labor and cooperation between members to solve them. Lu Zhou can understand it, but Huang Xiaobei and Liu Rui are already confused.
However, it doesn't seem to prevent these two from watching with relish?
Liu Rui: "Elbow, do you understand?" β
Lu Zhou nodded: "I can basically understand it." β
I can understand it, but I definitely can't do it so quickly, many of these topics are at the level of professional knowledge and skills competition for college students, and even some professors may have to spend a little time thinking about it.
Although it is a multiple-choice question, unless it is blind, it is almost impossible to push flat like this...... Anyway, the genius of this world has changed so much. Is it stated?
Lu Zhou subconsciously looked around the four members of the German team on the opposite side one by one, and found that Peter Schultz was not inside, and looked at the Chinese team, but there were no familiar faces.
In less than fifteen minutes, all 100 questions were completed and the answers were announced. The Tiger King team from Germany answered 83 questions correctly and scored 8.3 points, temporarily leading the transcendence team from China that answered 79 questions correctly.
The total score of the two sides was 14:15, and the Tiger King team temporarily took the lead, and the situation became tense.
At this moment, the hostess, who was wearing an evening dress, stepped forward to speak.
"We all know that the great mathematician Euclid proved the infinity of prime numbers, and the modern mathematician Hilbert used topology to prove it again. The pursuit of mysterious prime numbers in mathematics is never-ending. β
"The next problem is a world-class problem."
"The great mathematician Polygnac came up with the general conjecture that for all natural numbers k, there are infinitely many pairs of prime numbers (p, p+2k). Today's topic is to verify the weak conjecture of this conjecture. β
"Whoever can push K to a smaller number will get the three points that will determine the outcome of the game!"
"Start answering questions!"
The three friends in front of the computer were instantly shocked.
Huang Guangming: "Hold the grass? So social?! β
Liu Rui: "Can this Nima be proven on stage?" Why the hell am I going to eat this computer...... Still don't eat it. β
Lu Zhou: ???