On the other side, Chen Xuan was just about to go out at this time. Since immersing himself in the ocean of knowledge, Chen Xuan has felt that his life has become more regular, and early in the morning, he carried his Apple macBook Pro (MJLQ2CH/A) to the library.

It was still the old place, Chen Xuan opened the notebook, found a power supply by the wall and plugged it in, thought about it for a while, and knocked out a few big words on the ord document.

【Optimal calculus theory of NP complete problem】

This topic is one of the world's top seven mathematical problems. The seven "world problems" include: NP complete problem, Hodge conjecture, Poincaré conjecture, Riemann hypothesis, Young Mills theory, Neville-Stoke equation, and BSD conjecture.

These seven questions were all offered a reward of one million dollars, of course, Chen Xuan did not fancy the reward above, but wanted to solve the mystery of it.

He has been immersed in the ocean of knowledge for a month, and he doesn't know what level he has reached for theoretical knowledge. These seven problems happened to be seen last night, and since I don't know how huge my knowledge is, I can test it.

Based on the information on the Internet, NP is a non-deterministic polynomial problem, that is, a non-deterministic problem of polynomial complexity. Diagram of hypothetical P ≠ NP. If P = NP, then all three classes are the same. Diagram of hypothetical P ≠ NP.

If P = NP, then all three classes are the same. If any NP problem can be converted into an NP problem by a polynomial time algorithm, then the NP problem is called a Non-deterministic Polynomial complete problem. The NP complete problem is also called the NPC problem.

As an example, on a Saturday night, you attend a gala party. Feeling cramped and uneasy, you wonder if there are people in this hall that you already know.

The host of the banquet proposes to you that you must know the lady Roman, who is in the corner near the dessert plate. It doesn't take a second for you to glance there and see that the host of the banquet is correct. However, without such a hint, you have to look around the hall and look at each one one one to see if there is anyone you know.

It usually takes much more time to generate a solution to a problem than it does to validate a given solution. This is an example of this general phenomenon. Similarly, if someone tells you that a number 13717421 can be written as the product of two smaller numbers, you may not know whether you should trust him or not, but if he tells you that it can be broken down into 3607 times 3803, then you can easily verify that this is correct with a pocket calculator.

It has been found that all completely polynomial non-deterministic problems can be transformed into a class of logical operation problems called satisfying problems.

Since all possible answers to such problems can be calculated in polynomial time, people wonder if there is a deterministic algorithm that can directly calculate or search for the correct answer to this kind of problem in polynomial time. This is the famous NP=P? of conjectures.

Regardless of whether we are clever in writing a program, determining whether an answer can be quickly verified with internal knowledge or takes a lot of time to solve without such a hint is considered one of the most prominent problems in logic and computer science. It was stated by Steven Cork in 1971.

Chen Xuan was silently immersed in the operation of knowledge, but this hypothetical theory of knowledge was far beyond his imagination, and even with super-intensive brain calculations, there was still no way to crack it.

After an hour of high-intensity calculations, Chen Xuan did not feel tired, on the contrary, he became more and more energetic, but he knew that with his current knowledge, he could not solve the problems of this world.

This is also normal, if Chen Xuan has mastered the knowledge in a month, he will be able to solve the world's problems, which has already been solved by the big bulls in the mathematics world, how can it be Chen Xuan's turn.

Chen Xuan had some guesses that it should be that the knowledge he has mastered is not comprehensive enough, or there is a big blind spot in knowledge.

"Forget it, let's test another theory." Chen Xuan shook his head, his knowledge could not solve the problems of this world, and if he continued to think about it, it would only be a pure waste of time.

Chen Xuan sat by the wall, thought about it again for a while, and then re-typed a few big characters on ORD.

【Optimal Inversion Theory of Linear Operators and Linear Functionals】

[Abstract, this paper studies several types of inversion problems of linear functional and linear operators when giving all and part of the information, introduces the basic results of the optimal inversion theory, especially the construction of the optimal inversion method, and discusses the derivative problem of the inversion function when giving part of the Fourier coefficient as an example. 】

Chen Xuan silently calculated in his mind, a huge mathematical theory, from the simplest to the most complex process, step by step.

Slowly, Chen Xuan was completely immersed in the process of deducing the theory, and finally, "Unraveled? ”

It's really unraveled! If it weren't for the library, he would have cheered excitedly.

On the computer screen, from the process to the answer, every number, every symbol, and even every punctuation, it is so concise and full of mathematical beauty.

The only fly in the ointment is that this beauty is too skinny, and it needs to be enriched with language to turn it from a pure theory into a thesis.

"Yes, it seems that my theory of knowledge is quite strong." Chen Xuan showed a faint smile.

"Let's see if we can solve the physics puzzle." Chen Xuan thought about it, in addition to studying mathematics this month, he was also studying physics problems, but most of the time, he was immersed in mathematics, and there were very few physics books.

Chen Xuan thought for a while, and knocked down a few big words again, [Wave impedance inversion based on MPI parallel real number coding hybrid genetic algorithm]

[Abstract:The local linear method of geophysical inversion is easy to trap the solution into local extrema and relies heavily on the initial model, while the traditional genetic algorithm has problems such as weak local search ability and premature convergence in the optimization application.]

[To solve this problem, a Parallel Real Number Coding Hybrid Genetic Algorithm (MRCGA) was proposed to solve the geophysical inversion problem. In this method, the pseudo-grid method is used to implement the pseudo-grid initial population, the integrated crossover strategy and the linear operator, and the parallel real-code hybrid genetic algorithm is realized. The theoretical model proves the effectiveness of the proposed algorithm in inverting the impedance of seismic waves. 】

Chen Xuan continued to silently think about the key to knowledge, however, after half an hour, Chen Xuan could still only simply guess, but he could not directly solve this problem.

"Hey, it seems like I'm still too arrogant." Chen Xuan shook his head. He didn't even read many physics books, so he wanted to solve this problem, and he really thought too much.

At that moment, a ballpoint pen reached over and poked his arm gently.

"That, junior ......" Lu Yansheng blushed and asked embarrassedly, "Can I ask you another math problem?" ”

Originally, she didn't want to continue to look for Chen Xuan, a junior, because it was too faceless, to be honest, the problem that Chen Xuan helped him solve last month, she still hasn't sorted out the key to it.

And she was confident that she had mastered the key, and when she went to write a similar topic afterwards, she found that she didn't understand it at all. Then, after reviewing Chen Xuan's solution ideas, she found that she didn't know how to write the first step......

However, she has asked everyone before and after this question, and no one can solve it.

(End of chapter)