Shen Qitou's first four papers, the expert review opinions are similar: "The author is right, you wrote very well, but the fly in the ointment is XXXX...... Of course, the flaws are not hidden, and I hope you can revise it. ”

The reviewers of the first four papers have their own characteristics, some write several pages of review comments, and some write one or two sentences. But the meaning passed to Shen Qi is the same, two words, minor repair.

Regardless of how many pages a reviewer writes or a one-sentence review, they will eventually tell the author of the paper two words, major or minor repair.

Some reviewers write a few pages or even a dozen or dozens of pages of review suggestions, and it is possible to tell the author in the end that minor repairs are fine. In this case, the reviewer's review comments can be sorted out, and a new paper can be written. The author of the paper is lucky to meet this kind of reviewer.

Some reviewers only write one sentence, pure text description, without any mathematical formulas or symbols, and the final thing to tell the author may be: overhaul.

When encountering this kind of reviewer with one sentence + overhaul, more than 90% of the authors of the paper will disarm and surrender, and the society cannot afford to provoke them, disturb the big guy, and retreat.

Shen Qi revised the first four papers, oh, and the co-signed one was by Ou Ye Xiaoxiu.

However, in the fifth paper, which is also the most complex, "Analysis of Generalized Nonlinear Complementarity Problems Constrained by Linear Inequality", the reviewers' comments can be summed up in one sentence: "Overhaul!"

Based on the generalized Jacobian matrix of semi-smooth equations composed of generalized complementarity problems, it is the core logic of Shen Qi's argument to find a linearized quadratic model with ellipsoidal constraints.

Focusing on this core logic, Shen Qi completed a 15-page paper.

The reviewer takes a different view, he or she argues that F,G:Χ⊂R^n→R^n are continuously differentiable, Χ contains a constrained set of n-dimensional inequalities, and that the use of approximate Newton and generalized quasi-Newtonian does not involve global convergence.

Obviously, the reviewer's point of view is contrary to Shen Qi's logic.

As for who is right and who is wrong, Shen Qi thinks he is right.

Shen Qi didn't know who the reviewer was, which university or research institution was a math expert, and under the single-blind process, Shen Qi only knew the editor.

In fact, I haven't met with the editor to drink tea or anything, and the knowledge here only exists on the Internet, in the email.

The editor of "Math Review" is called Xu Weini, Shen Qi knows such a name, and the name may be a female editor.

Shen Qi certainly has ideas about the reviewers' overhaul review opinions.

In order to write the paper "Analysis of Generalized Nonlinear Complementarity Problems Constrained by Linear Inequality", Shen Qi almost went crazy, and now you tell me that what I am doing is basically useless work, overhaul? No, I Shen Qi is not convinced!

Defy?

Then be reasonable.

Reasoning.

Shen Qi created a new LaTeX document in his laptop and began typing, writing mathematical formulas, supplemented by text explanations.

He was going to be clear about what he was doing, proving that his argument was logically correct and pointing out logical errors in the reviewers' comments.

▽Φ(x)=V^TH(x)=▽F(x)(A(x)-I)H(x)+▽G(x)(B(x)-I)H(x)

Here A(x) and B(x) satisfy the diagonal array of Eq. (7).

Considering the vector (A(x)-I)H(x), it can be seen from its construction that its i-th component is non-zero equivalent to Hi(x)≠0.

That is, one of the following conditions is satisfied:

(1) Fi(x)≠0 and Gi(x)≠0

(2) Fi(x)=0 and Gi(x)<0

(3) Fi(x)<0 and Gi(x)=0

……

It can be proved that if ▽G(x)^-1▽F(x) is a P-matrix defined in linear algebra.

Then ▽G(x)^-1▽F(x)(A(x)-I)+(B(x)-I) is non-singular.

Old......

Shen Qi quietly coded words, stubbornly reasonable.

Ou Ye quietly looked at Shen Qi's code words, and from time to time she also coded a few formulas on her computer, she was inspired, she and Shen Qi were studying the same paper, the same topic.

When he first wrote his thesis, Shen Qi had no opponents, and he could justify the logic of his thesis.

And now, Shen Qi has an opponent, and the opponent says that he has a wrong logic and needs to be overhauled.

An academic paper, especially a mathematical paper, is not afraid of errors in details and local calculation biases, and is afraid of being accused of core logical errors.

The author's core logic is overturned, which is equivalent to a total rejection, the paper is written in vain, and the overhaul is equivalent to writing a new paper.

Overhaul a wool, it's about to be the New Year, who is in the mood to overhaul with you?

In order not to overhaul, Shen Qi needs to use sharper and sharper mathematical language to prove that his logic is not wrong, and impress and conquer the reviewers.

The work lasted all morning.

Coo, Shen Qi's stomach made a muffled sound, hungry.

"Waiter, replenish the water and provide some more food. Shen Qi called the waiter.

The waiter's nose was sore, tears were about to flow out, it was not easy, this man and woman came to our house to drink boiled water and became a VIP member, and finally willing to eat once.

"What do you need to order?" the waiter handed the menu to Shen Qi and said, "Package B is also a double couple package, enjoy a discount on lunch, and it is very cost-effective, I recommend you to order this package." ”

Package B is a combination of steak + spaghetti + bread + salad + coffee, Shen Qi said: "Then order this package, we only drink pure water, we don't want coffee, and we don't need it, so it's less money." ”

"It's so much money to not want coffee. The waiter said politely.

Shen Qi: "Then don't order a set meal, carry it, it's all young people who can't starve to death." ”

"Okay, okay, let's not coffee, count less money, I'll explain to the store manager when I go back, after all, you are a VIP member of the store and enjoy privileges. "The waiter knows that you can't lose a set meal because of two cups of coffee.

"Can the discount of the VIP card be weighted to the discount of package B?" asked Shen Qi again.

The waiter didn't understand: "What's weighted?"

Shen Qi explained: "The full-time discount value of the VIP card and the lunch discount value of package B will calculate a final value, which is the actual value we need to pay when we pay. I mean, is the actual amount we pay for a weighted average? It's better to ask clearly, so as not to cause disputes. ”

Shen Qipu gave a round of weighted averages, the waiter didn't understand it too thoroughly, but he probably understood, he said: "If you enjoy the package discount, you can no longer enjoy the VIP discount, and the one with the higher discount is the one with the higher discount between the two." ”

Shen Qi shook his head: "This is not scientific, then what is the use of me doing a VIP card, I can only enjoy the discount of pure water, the water card? ”

"6% off by 8% off is really unfair to you, a 4.8% discount may make your store lose money, but considering the weighting factor, everything is reasonable. Don't argue with me, that's how the National Bureau of Statistics calculates. Shen Qi said.

"I ...... I'll ask the store manager, please wait. "The waiter with a secondary school education retreated, and he couldn't afford to provoke him.

After a while, package B was delivered to Shen Qi and Ou Ye's booths, excluding coffee.

"This is a weighted package, please use it slowly. "The waiter maintained a polite attitude, and today he learned a knowledge point, the weighting algorithm.

"So your store manager knows math?" Shen Qi asked the waiter.

"The store manager graduated from college and is educated. The waiter said, and then left, receiving the other guests.

"The spaghetti is yours, the rest of the food is mine, eat it, move the fork. Shen Qi put the spaghetti in front of Ou Ye, he solved the steak first, replenished his strength, and continued to fight.

The amount of Ouye rice is not large, and one serving of spaghetti is enough.

The two people from the Department of Mathematics of Yan University ate a working meal and discussed two math problems from time to time, never taking their eyes off the computer.

At two o'clock in the afternoon, Shen Qi finally finished writing the "appeal draft", and he showed the draft to Ou Ye: "What do you think?"

Ouye studied it for a long time and concluded: "Fat." ”