138 Equilibrium Problems in Hilbert Spaces
Before the meal was finished, the two were forced to take a break. They were supposed to sing, but they couldn't sing anymore.
Lu Zhou settled the bill for Brother Fei first, and then he and Huang Guangming supported Liu Rui and dragged the boy back to the dormitory.
As for Brother Fei, there is a beautiful woman to take care of him. Tonight, probably because he was drunk, he half-pushed and refused to come back...
After returning to the dormitory, the two single dogs spread a mat on the ground for Liu Rui, and then covered him with a quilt, which was considered an arrangement.
Huang Guangming climbed up the ladder, lay down on the bed, and after a while, he let out a long sigh.
"It's hard, elbow."
He didn't drink much, and his mind was still clear. Lu Zhou, who was about to choose a topic for his graduation thesis, replied casually: "Why are you uncomfortable?"
"Hey, seeing that Brother Fei is out of order, don't you have any idea?"
"...What do you think?"
Huang Guangming sighed: "Forget it, there is no common language."
Lu Zhou: ...?
Nothing to say all night.
The next morning, Brother Fei hadn't come back yet, so he was probably still immersed in the gentleness and couldn't extricate himself.
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 lying on the bed, also got down tacitly.
Lu Zhou asked curiously, "Why are you working so hard today, all of you go to self-study?"
Huang Guangming yawned, and while walking to the balcony with a cup for brushing his teeth, he replied, "Otherwise? Wait until Brother Fei comes back to pretend to be aggressive?"
Lu Zhou imagined the scene, and his expression was a little subtle.
Well, that's it, got it.
...
After having breakfast in the cafeteria, Lu Zhou walked slowly to the door of the library.
At this moment, the open space in front of the library is already full of people.
The old postgraduate entrance examination army has been liberated, and a new batch of postgraduate entrance examination army is ready to go. Lu Zhou, who has been appointed by the school to graduate, may not have the chance to experience the feeling of thousands of troops crossing the single-plank bridge.
Hey, what a pity in life.
As the crowd poured into the library, Lu Zhou found a remote place to sit down, opened a blank document, and was about to start writing his graduation thesis.
He had already chosen the topic.
Mathematics is a scientific research tool. It is certainly useful to sharpen this tool, but if you only stay at the level of mathematics, it would be a waste of your talent.
Now that he has decided to step into the pit of mathematical physics, Lu Zhou decisively chose functional analysis as the direction of his graduation thesis. It's just that this time it's no longer the Fourier transform, 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 certain parameters are set to infinity, in order to prevent any physical state from running out of space, mathematically, the limit of any sequence needs to be still in the space, that is, the space is required to be complete.
The Hilbert space just meets this requirement of quantum mechanics.
A physical system can be represented by a complex Hilbert space, and the vectors in it are wave functions describing 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 are still at some superficial stages. In the frontier field of mathematics, the Hilbert space, like the Fourier transform, can be singled out as a research direction to discuss.
For this graduation project, Lu Zhou will not follow the standards of undergraduate students, but will follow the standards of journal submissions. Don’t care if you do well or not, it’s just a practice session!
Recalling the references he read some time ago, Lu Zhou put his hands on the keyboard and quickly typed out a line.
[Equilibrium Problems in Hilbert Space and Viscous Approximation Methods for Finite Nonstretchable Maps]
There is no need to exchange points for this thesis. When I was discussing the problem of Hilbert space with Senior Brother Luo, 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 the draft paper.
[Assume H is a complex Hilbert space endowed with an inner product, record L(H) as all bounded linear operators, T∈L(H), then the numerical field of operator T is defined as the following set: W(T)={
As time passed by, Lu Zhou felt that his thoughts were extremely smooth, and soon he filled the entire draft with eloquence, and reached out to the second draft paper.
It seems that just as he guessed when he challenged the twin prime number conjecture, the benefits of the improvement of mathematics level are not only unlocking the system's database permissions, but also improving his own thinking ability in this field.
Brain development?
or something else?
In short, he can clearly feel the changes that have happened to him.
"Let's get the thesis done in the past few days, and then do the system tasks."
Stretching his waist, he looked at the brothers and sisters who were preparing for the postgraduate entrance examination beside him, and Lu Zhou also became motivated.
In fact, it feels good to brush papers and read books in the library. With the improvement of the subject level, the speed of knowledge acquisition is accelerated, and he enjoys this process from ignorance to knowledge more and more.
I just don’t know why, but Lu Zhou, who is sitting here writing hard, always feels that something is missing...
...
Back in the dormitory, no accident, I heard Shi Shang pretending to be there again.
But this guy didn't talk about the very private topic of "what's the first time I'm grateful", but simply imparted a little life experience to the two single dogs, such as how to flirt with girls... and this is the most annoying thing. human!
Huang Guangming directly turned on the computer to watch variety shows. Liu Rui put on headphones and listened to music while doing abstract algebra. The two blocked this guy in unison.
"Yo, Elbow, are you back from self-study?"
"How did you feel yesterday? Is the quality of my wife's bedroom okay?"
"Do you want to go to WeChat? Don't be so shy, everyone is an adult, be straightforward, or tell me who you are interested in, and I will ask WeChat for you?"
Lu Zhou sighed: "Brother Fei, you are inflated."
Shi Shang touched his face: "Expansion? Am I inflated?"
Lu Zhou: "Yes, you make me feel like it's still Chinese New Year."
Shi Shang was stunned: "Chinese New Year? Why?"
"What you said just now, during the Chinese New Year, several menopausal aunts at my relative's house have 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 the variety show on Huang Guangming's computer, so he took a look.
"The strongest scholar?"
"yes."
Yes, have you started to find common topics?
Looking at Huang Xiaojian, Lu Zhou felt emotional.
It seems that 201's single dog camp has lost another brave little partner.
"What are they doing?" At some point, Liu Rui stopped doing the questions and came over to watch. From the outside, several men were gathered around a computer, and people who didn't know it thought they were looking at something.
"Sudoku!"
Sudoku?
Looking at the young man with a calm face on the stage, Lu Zhou's expression showed a hint of bewilderment.
This is the top student named Wu Yan?
But for some reason, he, who is also a top student, could smell the breath of a weak person through the screen. Of course, no matter what the reason is, it must not be because this guy is handsome, after all, there is still a gap compared to him.
As the Wu Yan group in the mathematics world, Lu Zhou felt that although he could not beat those old men in terms of academic achievements, he still could not lose to anyone in terms of appearance. No one would refute this, right?
At this moment, the person on the stage moved.
Lu Zhou was startled.
"Blind Sudoku?!"
Huang Guangming smiled cheaply: "Let's cheat...Brother Lu, can't you?"
Lu Zhou: "...If you can't be provoked, you can't be provoked."
Did the program group misunderstand the term Xueba? But having said that, and that player doesn't even need the calculation time?
This is too scary.
Next is a hundred academic problems, and the two sides stand in line to answer the questions on the spot. Some are physics, some are mathematics, and there are also topics such as biochemistry, which require division of labor and cooperation among members to solve. Lu Zhou could understand it, but Huang Xiaojian and Liu Rui had already started to look confused.
However, it doesn't seem to prevent these two from watching with gusto?
Liu Rui: "Elbow, do you understand?"
Lu Zhou nodded: "Basically understand it."
You can understand it, but you certainly can't do it so fast. Many of the topics are at the level of college students' professional knowledge and skills competitions. Even some professors may have to spend a little time thinking about it.
Although it is a multiple-choice question, unless you are blind, it is almost impossible to push it like this... Have the geniuses in this world become so perverted already?
Lu Zhou subconsciously looked at the four players of the opposite German team one by one, and found that Peter Schulz was not there. He looked at the Huaguo team, and there was no familiar face.
In less than fifteen minutes, all one hundred questions were solved 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 Huaguo who answered 79 questions correctly.
The total score of the two sides was 14:15, and the Tiger King temporarily took the lead, and the situation suddenly became tense.
At this moment, the hostess in an evening gown stepped forward to speak.
"We all know that the great mathematician Euclid proved the infinity of prime numbers, and the modern mathematician Hilbert proved it again by means of topology. The pursuit of the mysterious prime numbers in the mathematical world is Never ending."
"The next question is a world-class problem."
"The great mathematician Polignac proposed a general conjecture that for all natural numbers k, there are infinitely many pairs of prime numbers (p, p+2k). Our topic today is to carry out the weak conjecture of this conjecture. Ask for proof."
"Whoever can advance K to a smaller number will get the 3 points that determine the outcome!"
"Start answering the questions!"
The three friends in front of the computer were shocked instantly.
Huang Guangming: "Hold the grass? Such a society?!"
Liu Rui: "Can this fucker prove it on stage? I'll eat this computer...or not."
Lu Zhou:? ? ?