I just want to be a quiet scholar

Chapter 251 Enrich product layout and intensively cultivate market segments

"I really can't find a weak * closed convex set that is a close set, so as to get the Hosdaff topology. I believe that no mathematician in the world can prove that every ω * closed convex set of X * The set is close to the Chebyshev set." Shen Qi was not too depressed, but was full of interest: "At first I didn't realize that this was a dead end, because I didn't reach the end of the dead end."

"So you have a good solution?" Mueller asked.

Shen Qi already has an answer: "My solution is to set up a new subject for assertion (3). I temporarily named it 'Muller-Shen Jinming Theorem'. This theorem needs to be further verified. It can be regarded as 'Mueller A corollary of Le-Chen's theorem."

"Then the new 'Muller-Sink Theorem' contains (1) and (2), which is enough. We will complete the revision within a few days and publicly release the research results of the 'Muller-Sink Theorem' .” Shen Qi gave a solution.

"Actually...we are equivalent to launching a 'reduced version' of the 'Muller-Shen Theorem'." Professor Muller quickly understood Shen Qi's new plan.

Shen Qi nodded: "Professor Muller's metaphor is very appropriate, yes, the reduced version. In fact, the so-called reduced version is the standard version, because the argument (3) can be regarded as a new product."

"Actually, two bodies with different lengths but roughly the same exterior shape are equipped with the same powertrain system, and then sold separately. Well, Volkswagen often does this." Professor Muller is indeed German, and he hit the nail on the head.

"Haha!" Shen Qi laughed loudly and said, "That's why I bought a Chevrolet."

As soon as Muller and Shen Qi came together, they did just that, launching a low-profile version of the "Muller-Shen Theorem" first, to meet the basic needs of the market, and to occupy this segment of the market first.

The high-end version of "Muller-Shen theorem" will be launched in the near future. At that time, it will be given a new name. -Shen"'s market share and brand effect in this market segment.

The revision of the "Muller-Shen Theorem" was completed quickly.

"...After the proof, we get the following theorem:

Let X be a Banach space, then the following assertion is equivalent to:
(1) If x*∈S(X*) reaches its norm on S(X), then x* is the ω*concave point of the unit ball B(X*);
(2) X is a strongly smooth space. "

After checking the paper for the last time, Professor Muller uploaded the paper to arVix for pre-recording.

The task of formally delivering the thesis was given to Shen Qi.

The title of the thesis is "Problems of Concavities and Strongly Smooth Spaces in Banach Spaces", and both Muller and Shen Qi are the first authors.

The length of the paper is 24 pages, which contains a complete proof of the "Muller-Sink theorem".

Of course, the "Muller-Shen theorem" was unilaterally declared by Muller and Shen Qi. As for whether it can be loaded into the IMU's mathematical theorems in the end, it is up to the IMU to decide.

Shen Qi believed that the quality of this paper was very high, and it belonged to the four major journals, so he submitted it to the "Annual Journal of Mathematics".

At the same time, the work of proving the "Muller-Shen Jinjun theorem" was carried out simultaneously. This work was mainly completed by Shen Qi, because it was proposed by Shen Qi.

In a blink of an eye, it was another Wednesday.

This morning, Faltins habitually browsed arVix and found a paper titled "Problems of Banach Space Concavity and Strong Smooth Space", the author of the paper is his colleague, and the Department of Mathematics of Puda University A doctoral student.

"Oh, this proof...'Muller-Shen theorem' is applied to close closed convex subsets that are close to compactness, as well as the RNP properties of Banach spaces and martingale theory. It seems that old Allen can finally publish a paper this year Already." Faltings read the paper in its entirety and felt that there was nothing wrong with it.

Gerard Faltings is a German. He became famous very early. In 1983, he proved the sensational Model's conjecture. At that time, Faltings was only 29 years old.

When he won the Fields Medal in 1986, Faltins was only 32 years old. His wife was also a mathematician, and his teacher was Grothendieck, the godfather of mathematics in the 20th century.

A disciple of a famous teacher, married a mathematician wife, and the people around Faltings in this life are all related to mathematics.

As a top mathematician today, Faltins is the editor-in-chief of the most authoritative mathematics journal "Annual Mathematics".

In the afternoon, in the coffee shop on the third floor of the Department of Mathematics Building, there is a routine coffee time.

Holding a coffee cup, Faltings walked to Mueller and Shen Qi's small table and sat down.

"ass@@, *helü@*ful." Faltings said something in German to Muller, and his expression seemed to be teasing.

"daf@@aeü, @@l!" Mueller said to Faltings unhappily.

Shen Qi was confused: "Can the two professors speak English?"

"Old Allen, you finally published your paper." Faltings said.

"You're a year older than me, old Greed!" Muller repeated his previous expression.

These two German old men are very cute...Shen Qi was secretly amused, a learned person reaches the stage of an old man in his 70s and [-]s, and sometimes he is as naughty as a child of [-] or [-] years old.

"Alan, you don't seem to have published a paper or published any academic monographs throughout this year," Faltings said.

Princeton has 1200 professors or adjunct professors, who publish or publish more than 2300 papers (books) each year, with an average of nearly two papers (books) per capita.

It is now October, and Muller has not published a single paper, nor has he published a single monograph.

In Princeton, although the quantity and quality of theses or academic monographs are not linked to housing or professional titles, it is a place where academics are supreme after all, and theses or academic monographs occupy an important position in the hearts of most professors.

"Wait, Grad, you just said I finally published the paper, so soon?" Mueller asked.

"It should be pre-recorded, Alan, didn't you upload the paper "Problems of Concave Points and Strongly Smooth Spaces in Banach Spaces" to arVix?" Faltins was surprised, and then looked at Shen Qi: "Is that you, Shen Qi?"

Shen Qi said: "Professor Muller operated the pre-recording, and I operated the formal delivery of papers."

Professor Faltings sent a congratulatory message: "Then I should congratulate you, Alan, Shen Qi. In my opinion, there is no problem with the proof of the 'Muller-Shen Theorem'. I believe that in the near future, with your The theorem named after the two surnames will be widely cited in the research on topics related to Bachna space."

"Grade, it seems that you are not that annoying." Mueller said.

"Professor Faltins said there is no problem, so it should be no problem." Shen Qi felt that the problem was not too big. The review experts hired by IMU could not be more professional than Professor Faltins, at most they were equal.

"Which journal did you submit to?" Faltings asked.

Shen Qi smiled: ""Annual Journal of Mathematics."

"Really?" Faltings was a little surprised.

Faltins is the editor-in-chief of this journal, and the manuscript should still be in the process, and it has not yet reached the procedure for his final approval of admission.

"That has to be formally reviewed according to the rules. I need to go back and study this paper again." Faltings said seriously.

"Old Grad, didn't you just say that there is no problem?" Professor Muller was unhappy again.

"It doesn't count if I say it, but it counts if the reviewer says it. I'm not a reviewer." Faltins walked away with a coffee cup.

"Annual of Mathematics" is a mathematical journal jointly sponsored by the Department of Mathematics of Princeton and the Institute for Advanced Study of Princeton, ranking first among the four major journals.

At the beginning of the establishment of the Institute for Advanced Study in Princeton, the research building was under construction, and the first batch of researchers such as Einstein and von Neumann had no place to study, so they stayed in the Princeton Department of Mathematics building for several years.

The Department of Mathematics, Department of Physics, and the Institute for Advanced Study in Princeton have a good relationship. The researchers of the two often move around. Faltings also stayed in the Department of Mathematics of the Institute for Advanced Study in Princeton for several years before.

The editorial office of "Annual Journal of Mathematics" is located in the Department of Mathematics Building of Pudong University, just above the floor where Shen Qi drinks coffee.

(End of this chapter)