The Science Fiction World of Xueba

It's an amazing feeling.

Pang Xuelin never thought that Ponzi geometry, which was originally used to solve number theory problems, could be connected with nonlinear partial differential equations.

The sudden inspiration suddenly spread out, and in an instant, all kinds of wonderful ideas began to emerge in Pang Xuelin's mind.

...

"In the partial differential equations related to surfaces, the first thing that needs to be solved is the existence of complex structures! This point can be started from a classic old problem! That is: given a 2n-dimensional real differential manifold M A near-complex structure of J, when is this near-complex structure induced by the complex structure?"

...

"A given near-complex structure J is induced by a complex structure if and only if there are local real coordinates {x^1, x^2, x^3...x^2n-1, x^2n}, making J?xj=?x^j+n, J?x^j+n=-?x^j, because if there is such a local coordinate card set, the complex coordinate card set {x+ix The conversion function between ^n+1,...,x^n+ix^2n} is suitable for the Cauchy-Riemann equation system, so it is a holomorphic function; the inverse proposition is obviously established. Next, the problem can be attributed to finding such a good coordinate system, or solve some first-order linear differential equations."

...

"High-dimensional case: -Nirenberg's theorem. The near-complex structure M is a (1, 1) type tensor field, so it can be applied to the cotangent bundle. At each point p∈M, the complex tangent space TpMc can be decomposed into The direct sum of two subspaces corresponding to the eigenvalue ±i. According to the continuity, the direct sum decomposition of the complex tangent bundle can be obtained..."

...

"Lemma: Let M be a compact Riemann manifold. Consider the differential equation δu=f(x,u) on it, f: M*R→R is a smooth function. If u- exists, u+∈C^2(M ) so that u-≤u+, δu-+f(x, u-)≥0, δu++f(x, u+)≤0, then there exists a solution x∈C^∞(M) satisfying u-≤u≤u+ ..."

...

As the time passed by, lines of symbols like heavenly scripts quickly flowed out from Pang Xuelin's pen, filling one piece of manuscript paper after another.

Pang Xuelin wandered in the ocean of mathematics, perfecting the theoretical framework of Ponzi geometry step by step, enriching its flesh and blood.

The more he studied, the more Pang Xuelin felt that there was a vast space behind the Ponzi geometry theory he created.

This is like Galois, who created group theory back then, and raised algebra research to a whole new field.

Pang Xuelin even vaguely realized why Mr. Grothendieck wanted to study Far Abelian geometry back then.

Ponzi geometry was created on the basis of Far Abelian geometry. On the basis of Ponzi geometry, Pang Xuelin faintly felt that algebra and geometry were merging with each other.

From the era of Descartes, the organic combination of algebra and geometry through coordinate axes formed analytic geometry, and then Riemann created the theory of algebraic geometry. Algebra and geometry, two important branches of mathematics, have great differences. There is a deep inner connection between them.

However, in an era when the branches of various disciplines are becoming more and more narrow, it is almost an impossible task to unify the two propositions of algebra and geometry.

However, the Ponzi geometry theory proposed by Pang Xuelin has made algebra and geometry have a tendency to converge, and there is a real bridge of communication between the two.

Perhaps Mr. Grothendieck had similar ideas back then, but unfortunately he left early and only proposed a theoretical framework of Far Abelian geometry.

Today, the Ponzi geometry proposed by Pang Xuelin on the basis of Far Abelian geometry is fulfilling the unfulfilled wish of Mr. Grothendieck.

This set of theories can not only solve related problems in the field of number theory,

Even in the field of nonlinear partial differential equations, it also plays an important role.

It should be known that the main body of differential equation research is nonlinear partial differential equation (NLPDE).

Many significant natural science and engineering technology problems can be attributed to the study of nonlinear partial differential equations.

Mathematical models in many fields of real life can be described by NLPDE, and the basic equations of many important disciplines such as physics and mechanics are themselves NLPDE.

In addition, with the deepening of research, some problems that can be approximated by linear differential equations must also consider the influence of nonlinearity. Therefore, the research on NLPDE, especially the research on the exact solution of NLPDE has shown a very important theory. and application value.

However, no matter in reality or in the world of mathematics on the wandering earth, a generally effective method for finding the exact solution of nonlinear partial differential equations has not been provided.

The emergence of Ponzi geometry has made it possible for people to effectively solve the exact solution of nonlinear partial differential equations.

This also means that Ponzi geometry not only plays an important role in the field of mathematics, but also has very important significance in the fields of natural science and engineering.

This is a brand-new mathematical tool that can fundamentally promote the large-scale progress of human beings in the fields of natural science and engineering.

What Pang Xuelin has to do now is to further improve this theory.

One day, two days, three days...

One week, two weeks, three weeks...

Before I knew it, a month and a half had passed.

During this period, Pang Xuelin slept when he was sleepy, ate when he was hungry, and spent the rest of the time on research.

His hair began to grow longer, his face was covered with stubble, his clothes became more and more dirty, and his whole body began to emit a strong smell.

But he didn't seem to realize that, apart from thinking, the rest of the time was only spent resting and eating.

...

On this day, Liu Xin came outside Pang Xuelin's office again, and asked Li Yi, the technical secretary, "Xiao Li, Professor Pang hasn't come out yet?"

Li Yidao: "No, Secretary-General, Professor Pang has been staying there for more than a month. Now that the distance between the earth and Jupiter is getting closer and closer, if Professor Pang doesn't come out again, there will be no time for the final orbit change window." gone."

Liu Xin said: "I believe him, Xiao Pang is not a big talker, by the way, what about Xiao Xia?"

Li Yi said: "My sister-in-law went back to cook for Professor Pang. During this time, apart from cooking for the professor and going home to sleep, my sister-in-law waited here every day, and tried every means to cook all kinds of delicious food for Professor Pang."

Liu Xin sighed and said, "It's really embarrassing for her. When Xiao Pang comes out, remember to notify me immediately!"

As he said that, he turned around, and just as he was about to leave, he saw Yao Bingxia walking over with a food box.

"Xiao Xia, you girl, you still cook for Xiao Pang every day, are you afraid that we will starve him to death?"

Yao Bingxia forced a smile on his face and said, "Grandpa Liu Xin, brother Xiao Lin is used to the taste I make, I'm afraid he won't be used to it..."

"You guys!"

Liu Xin shook his head, and was about to speak, when he suddenly noticed something wrong with Yao Bingxia's expression. The food box in her hand fell to the ground with a slap, and then, Yao Bingxia ran past him like a wind...

Turning around, Liu Xin saw that Pang Xuelin, who had completely changed his appearance, came out of the office at some point, and was hugging Yao Bingxia, who was streaming down his face, into his arms.

Liu Xin waited for a while, and when the two of them were tender enough, he stepped forward and said, "Xiao Pang, have you been released?"

Liu Xin's eyes fell on Pang Xuelin's face.

Not seeing him for a month and a half, Pang Xuelin's hair became disheveled, his face was pale, and his face was full of stubble. He seemed to have lost weight, but his eyes became clear and bright like never before.

Pang Xuelin turned his head and smiled and said, "Master, it's a good luck not to disgrace your life!"