Work Lunch
The expert reviewers' comments on Shen Qi's first four papers were largely the same. "You're absolutely right, you wrote very well, but there's a slight flaw in XXXX... Of course, the flaws don't detract from the overall merit, and we hope you can revise it."
The reviewers for the first four papers each had their own characteristics; some wrote several pages of review comments, while others wrote only one or two sentences. But the message they conveyed to Shen Qi was the same: two words, minor revisions.
Regardless of whether the reviewers write several pages or just a sentence in their comments, they will ultimately tell the paper authors two words: major revision or minor revision.
Some reviewers write several pages, or even dozens of pages, of review comments, only to tell the author that minor revisions are all that's needed. This does happen; the reviewers' comments could be compiled into a whole new paper. Authors are lucky to encounter such reviewers.
Some reviewers write only one sentence, a purely textual description, without any mathematical formulas or symbols, and may ultimately tell the author: major revision.
When faced with a reviewer who demands a single sentence followed by major revisions, over 90% of paper authors will surrender. They'll think, "This is too much to handle. I've disturbed a big shot; I'm retreating."
Shen Qi made minor revisions to the first four papers; oh, one of them, co-authored, was revised by Ou Ye.
However, the fifth and most complex paper, "Analytical Problems of Generalized Nonlinear Complementarity with Linear Inequality Constraints," received the reviewers' comments summarized in one sentence. "Major revisions required!"
The core argument of Shen Qi is to derive a linearized quadratic model with ellipsoidal constraints based on the generalized Jacobian matrix of the semi-smooth equation system formed by the generalized complementarity problem.
Based on this core logic, Shen Qi completed a 15-page paper.
The reviewer held a different view, arguing that F, G: ΧR^n→R^n is continuously differentiable, Χ contains an n-dimensional set of inequality constraints, and that using the approximation Newton method and the generalized quasi- Newton method does not involve global convergence.
Clearly, the reviewers' views contradicted Shen Qi's logic.
As for who is right and who is wrong, Shen Qi believes he is right.
Shen Qi didn't know who the reviewers were, or which university or research institution's mathematics experts they were. Under the single-blind process, Shen Qi only knew the editor.
I've never actually met the editor in person or had tea with them; our acquaintance exists only online and through emails.
The editor of the journal * Mathematical Herald * is named Xu Weini. Shen Qi only knew this name; judging from the name, she was probably a female editor.
Shen Qi certainly had his own thoughts on the reviewers' comments regarding the major revisions.
In writing this paper, "Analysis of Generalized Nonlinear Complementary Problems with Linear Inequality Constraints," Shen Qi almost went mad. Now you're telling me that what I did was basically a waste of time? A major overhaul? No, I, Shen Qi, refuse to accept that!
Disagree?
Then let's talk about reason.
Persuade with reason.
Shen Qi created a new LaTeX document on his laptop and began typing, writing mathematical formulas and adding textual explanations.
His task was clear: to prove the logical correctness of his argument and to point out the 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 matrix of equation (7).
Consider the vector (A(x)-I)H(x). By its construction, we know that its i-th component is non-zero, which is equivalent to Hi(x)≠0.
That is, one of the following conditions must be met:
(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 proven 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 nonsingular.
Therefore...
Shen Qi quietly typed, stubbornly explaining his reasoning.
Ou Ye watched Shen Qi type away quietly, occasionally typing out a few formulas on her own computer. She was inspired; she and Shen Qi were researching the same paper and the same topic.
When Shen Qi first started writing his thesis, he had no rivals, and he only needed to be able to justify the logic of his thesis.
Now, Shen Qi has an opponent who says his logic is flawed and needs major revision.
An academic paper, especially a mathematical paper, is not afraid of minor errors or local calculation deviations; what it fears is being criticized for core logical errors.
The author's core logic has been overturned, which is tantamount to a complete rejection. This paper was written in vain, and major revisions are equivalent to writing a new paper.
Major overhaul my foot! It's almost Chinese New Year, who's in the mood for a major overhaul?
In order to avoid major revisions, Shen Qi needs to use sharper and more incisive mathematical language to prove that his logic is correct and to impress and win over the reviewers.
This job lasted all morning.
Gurgle, Shen Qi's stomach rumbled; he was hungry.
"Waiter, please replenish the water and bring some food," Shen Qi called to the waiter.
The waiter's nose tingled, and tears almost welled up in his eyes. It hadn't been easy for this man and woman to come to our house and drink plain water until they became VIP members. Finally, they were willing to order a meal.
"What would you like to order?" The waiter handed the menu to Shen Qi and said, "Set meal B, which is a couple's set meal, comes with a lunch discount and is very cost-effective. I recommend you order this set meal."
Set meal B is a combination of steak, pasta, bread rolls, salad, and coffee. Shen Qi said, "Let's order this set meal. We'll only drink water, so we'll skip the coffee and charge less."
"It's the same price even without coffee," the waiter said politely.
Shen Qi: "Then let's not order the set meal, we'll just carry it. We're all young people, we won't starve."
"Okay, okay, we won't take the coffee. We'll charge you less. I'll explain to the manager later. After all, you're our VIP members and enjoy special privileges." The waiter understood the principle of not losing out on a meal for a small gain; he couldn't let two cups of coffee cost him a set meal.
"Can the VIP card discount be weighted towards the discount for Package B?" Shen Qi asked again.
The waiter didn't understand. "What weighted average?"
Shen Qi explained, "The VIP card's all-day discount value and the lunch discount value of Set Meal B will be used to calculate a final value, which is the actual amount we need to pay when we pay. What I mean is, is the actual amount we pay a weighted average? It's better to ask clearly to avoid disputes."
Shen Qi explained the weighted average value, which the waiter didn't quite grasp, but he understood the general idea. He said, "If you've already enjoyed the set meal discount, you can't enjoy the VIP discount either way; it's the one with the higher discount."
Shen Qi shook his head. "That's not scientific. What's the point of me getting VIP card if I can only enjoy discounts on purified water? A water card? The reason I didn't simply use the 60% multiplied by 80% calculation, but instead considered a weighted algorithm, is based on scientific principles."
"A 60% discount multiplied by 80% is indeed unfair to you, and a 48% discount might cause your store to lose money, but considering the weighting factor, everything is reasonable. Don't argue with me, the National Bureau of Statistics calculates it this way too," Shen Qi said.
"I... I'll ask the manager, please wait a moment." The waiter, who only had a vocational school education, retreated; he couldn't afford to offend him.
A while later, Package B was delivered to Shen Qi and Ou Ye's booth, without coffee.
"This is the weighted set meal, please enjoy." The waiter maintained a polite attitude; he had learned a new concept today: the weighted algorithm.
"So your manager knows math?" Shen Qi asked the waiter.
"The store manager is a college graduate, quite cultured," the waiter said, then left to attend to other customers.
"The spaghetti is yours, the rest of the food is mine. Eat up, use your fork." Shen Qi placed the spaghetti in front of Ou Ye. He finished his steak first to replenish his energy before continuing the fight.
Ou Ye doesn't eat much; one serving of pasta is enough for her.
The two students from the Mathematics Department of Yenching University ate their lunch, occasionally discussing mathematical problems, their eyes never leaving their computers.
By 2 p. m., Shen Qi had finally finished writing the "appeal draft." He showed it to Ou Ye and asked, "What do you think?"
After studying it for a long time, Ou Ye concluded. "Sprout."