The Science Fiction World of Xueba

This feeling is wonderful.

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

Suddenly, the sudden inspiration radiated out. Instantly, all kinds of whimsy began to emerge in Pang Xuelin's mind.

Uh ...

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

Uh ...

"The 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 in a neighborhood of each point, x ^ 2n} such that J? xj =? x ^ j + n, J? x ^ j + n =-? x ^ j, because if such a local coordinate card set exists, the complex coordinate card set {x + ix The conversion function between ^ n + 1, ..., x ^ n + ix ^ 2n} is suitable for the Cauchy-Riemann equations, so it is a holomorphic function; the inverse proposition is obviously true. Next, the problem can be reduced to finding this Good coordinate system, or solving some first-order linear differential equations. "

Uh ...

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

Uh ...

"Lemma: Let M be a compact Riemannian manifold. Consider the differential equation δu = f (x, u) above, f: M * R → R is a smooth function. If u- exists, u + ∈C ^ 2 (M ) Such 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 + ... "

Uh ...

Time passed by every minute and every second, like symbols of heavenly books, flowed out quickly in Pang Xuelin's pen, filling one sheet after another.

Pang Xuelin In the ocean of mathematics, he gradually perfected the theoretical framework of Ponzi geometry and enriched his flesh and blood.

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

This is like Galois, who pioneered group theory, and promoted algebraic research to a whole new field.

Pang Xuelin even faintly realized why Master Grothendieck had to study Far Abel geometry.

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 Cartesian era, algebra and geometry were combined organically through the coordinate axis to form analytic geometry, and then Riemann pioneered the theory of algebraic geometry. Algebra and geometry, two important branches of mathematics, have great differences. There is a deep inner connection between each other.

However, in the era when the branches of branches of each university are getting thinner, it is almost impossible to unify the two major propositions of algebra and geometry.

But this Ponzi geometry theory proposed by Pang Xuelin has made the algebra and geometry vaguely converge, and there is really a bridge between the two.

Perhaps Grandfather Grothendieck had a similar idea at the time, but unfortunately, the grandfather left early and only proposed a theoretical framework of far Abelian geometry.

Today, Pang's geometry, proposed by Pang Xuelin on the basis of Far Abel's geometry, is fulfilling the endless wish of Mr. Grothendieck.

理论 This theory can not only solve related problems in the field of number theory, but also play an important role in the field of nonlinear partial differential equations.

It is important to know that the main body of current 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.

数学 Mathematical models in many areas of real life can be described by NLPDE. The basic equations of many important physics, mechanics and other disciplines 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 non-linearity. 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 in the wandering earth, a universally effective method for obtaining accurate solutions 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 solutions of nonlinear partial differential equations.

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

This is a brand-new mathematical tool, which is enough to 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 perfect this theory.

One day, two days, three days ...

One week, two weeks, three weeks ...

Unconsciously, one and a half months passed.

During this period, Pang Xuelin fell asleep when he was sleepy, and ate when he was hungry. The rest of his time was spent on research.

His hair began to grow, his face was covered with stubble, his clothes were getting dirty, and his entire body began to exude a strong smell.

But if he didn't realize it, apart from thinking, the rest time was just for rest and eating.

Uh ...

On this day, Liu Xin once again came outside Pang Xuelin's office and asked the technical secretary Li Yiyi, "Xiao Li, Professor Xiao Pang has not come out yet?"

Li Yiyi said: "No, the Secretary-General ~ www.readwn.com ~ Professor Pang has been in it for more than a month. Now the distance between Earth and Jupiter is getting closer and closer. If Professor Pang does not come out again, the last The derailment window is gone. "

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

Li Yiyi together, "Xunzi went back to cook for Professor Pang. During this time, in addition to cooking for the professor and going home to sleep, the sister-in-law is waiting here every day, but also trying to make various delicious things for Professor Pang.

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

He said, he turned around, and as soon as he was about to leave, he saw Yao Bingxia carrying the food container over.

"Xiao Xia, you girl, cook your own meal for Xiao Pang every day, afraid he will not be hungry for us?"

Yao Bingxia barely smiled on his face and said, "Grandpa Liu Xin, Brother Xiaolin is used to my taste, I'm afraid he won't be used to eating ..."

"You!"

欣 Liu Xin shook her head and was about to speak. Suddenly she found that Yao Bingxia's face was a bit wrong. The food container in her hand fell to the ground.

欣 Liu Xin turned around and saw that Pang Xuelin, who had completely changed his vice appearance, did not know when to come out of the office, and was hugging Yao Bingxia with tears in his arms.

欣 Liu Xin waited for a while, when the two of them were gentle enough, they came forward: "Xiao Pang, did you solve it?"

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

After not seeing for a month and a half, Pang Xuelin became disheveled, pale, and stubble. His whole body seemed to be thin, but his eyes became clearer and brighter than ever before.

Xi Pang Xuelin turned her head and smiled, "Grandpa, thank you for your life!"