Awakening Elementary School System in University
Chapter 33 - 31: Spending More Time Together Is Effective

Chapter 33: Chapter 31: Spending More Time Together Is Effective

Yunqing had stopped replying, which Chen Lin found a little strange. ’She believed me that easily? That doesn’t seem like her.’

But he didn’t dwell on it. There was no point in getting hung up on it.

Just then, he arrived at the glass doors of the library.

He swiped his card to enter, and a refreshing blast of cold air hit him, instantly waking him up.

With final exam week still a month away, the library was far from the point where it would be packed to the gills, a time when you’d have to show up before dawn on a weekend just to grab a seat.

Chen Lin easily found an empty single-person study room on the third floor and closed the door.

He opened his laptop, originally planning to browse a popular review site for a few critiques of Long Season. He wanted to see if there were any angles he hadn’t considered that could spark some ideas.

However, the moment he clicked into the review section and saw the highly-upvoted titles on the front page, that notion vanished into thin air.

The Tragedy of a Small-Town Beauty

Years Later, and We’re Still Just Shy of Chinese TV’s "Birth of a Villainess"

Long Season: The True, Enduring Depression Is a Woman’s Quiet, Mysterious Life

...

Chen Lin, expressionless, moved his mouse and clicked the "X" in the top-right corner of his browser.

’I’d better just buckle down and write it myself.’

He created a new Word document, put on his headphones, and opened the already-cached show. He didn’t press play, simply letting the familiar opening credits freeze on the screen.

Recalling his feelings from his first and second viewings, his fingers flew across the keyboard as he began to fill the blank document:

"Long Season has been hailed as one of the best recent film and television works to combine commercial appeal with artistic value. The show is less a suspense thriller and more a period drama. With a single main plot unfolding across three timelines, it masterfully portrays the chaotic and struggling lives of ordinary people during the era of mass layoffs..."

"...What is most commendable about the show is the way it’s interspersed with comedic gags worthy of the golden age of sketch comedy. These laughs aren’t built on a foundation of cheap, vulgar jokes, but are slice-of-life vignettes that hide the hardships of everyday people. It’s a sophisticated form of comedy rooted in real life, with tragedy at its core..."

"...The core story of the show is an exploration of fate..."

"...The countless major and minor characters in the drama, experiencing joy and sorrow and reaping what they sow under the tides of the era—it is these many different faces that together form this complex tapestry of the world."

...

After fluidly typing out over a thousand words, Chen Lin stopped. He read through it once, nodded in satisfaction, and pressed Ctrl+S.

His thoughts were flowing smoothly, and his progress was right on schedule. He’d written the bulk of it in one morning. The remaining small portion and the conclusion could easily be finished next week during a free afternoon.

He glanced at the time in the bottom-right corner of his computer screen—12:51.

’Hmm, it’s about time to reward myself for a hard morning’s work.’

He shut down his laptop, packed his bag, and left the library.

The cafeteria and the study classroom weren’t on the same route. In the past, to save time, he would have probably just grabbed a sandwich or a rice ball from a convenience store along the way.

But hadn’t he just earned a nice chunk of change at the bar yesterday? Plus, he hadn’t eaten breakfast and his stomach was completely empty. Chen Lin decided he had to splurge a little for lunch today.

On weekends, the service windows on the first and second floors of the cafeteria were closed. Only the food stalls on the third floor and the hot pot, barbecue, and milk tea shops on the fourth floor were still open.

Chen Lin’s idea of "splurging" was just ordering a lunch box with two meat dishes and one vegetable dish from the "Aunt Wang’s Stir-Fry" stall on the third floor. Then, he ran over to the nearby "Ziyan Hundred Flavors Chicken" window and bought a 25-yuan portion of beef, tendon, and tripe.

The two items together cost less than 50 yuan in total.

Chen Lin was genuinely starving. He took his lunch box to a window seat and, without even taking a sip of water, picked up his chopsticks and started wolfing down his food.

After inhaling his meal, he’d cleaned out the two lunch boxes and the small plastic bowl, leaving not even a single grain of rice behind.

He leaned back in his chair, let out a satisfied burp, and felt like he had come back to life.

He had originally planned to head straight to the study classroom after eating, but a glance at his phone showed it was only 1:19 PM, so he stayed put and scrolled through his phone for a bit.

After a little while, Chen Lin checked the time again. There were still over twenty minutes until his two o’clock meeting with Shen Yan. It was still a bit too early to head over.

So, he decided to go up to the fourth floor, buy a drink, and wander over slowly.

He pulled out his phone, opened his chat with Shen Yan, and after a moment’s thought, typed out a line.

Chen Lin: [I’m about to head from the cafeteria to the study classroom. Want me to bring you a milk tea or fruit tea? What would you like?]

Less than ten seconds after he sent the message, Shen Yan’s reply came.

Shen Yan: [Ah, no, that’s okay. You can just get one for yourself.]

The corner of Chen Lin’s mouth curled up as he continued typing.

Chen Lin: [Don’t be polite. Just think of it as a value-added service for my top client.]

This time, the other side went silent for over ten seconds.

Just as Chen Lin thought she wouldn’t reply, a new message popped up.

Shen Yan: [Then I’ll just have the same as you.]

...

Ten minutes later, Chen Lin walked into the study classroom carrying two popular green grape drinks.

He pushed open the door to find Shen Yan was already there.

She was sitting in her chair, head down, looking at her laptop. Hearing the door open, she immediately looked up.

When she saw the two drinks in Chen Lin’s hands, she stood up, clearly a little embarrassed. She walked quickly to the door, took her cup from him, and said softly, "Thank you."

Chen Lin placed his own cup on a desk and casually glanced her over, a flicker of surprise in his eyes.

The Shen Yan today seemed a little different from her usual nerdy, stay-at-home science major persona.

She was wearing a simple white short-sleeved T-shirt with a pair of simple black hot pants. The most obvious change was her hair. Although it was still worn down over her shoulders, it was clearly well-groomed, falling smoothly over her shoulders. There was no trace of the slight messiness it used to have from being left uncombed for too long.

Her whole appearance was fresh and pleasant.

Chen Lin’s heart stirred, and he couldn’t help but tease her, "Not bad, Shen Tongxue. You look a lot prettier than usual today."

Shen Yan’s face instantly flushed red. Like a cat whose tail had been stepped on, she spun around in a fluster and hurried back to her seat, even forgetting to put the straw in her drink. "W-we should just talk about the questions for today!" she said quickly.

As she spoke, she placed the drink beside her, quickly opened a folder she had already prepared on her laptop, and turned the screen toward Chen Lin.

Chen Lin smiled and leaned in.

He listened as Shen Yan, while navigating her computer, explained in her unique, cool yet serious tone, "This time, I mainly want you to explain two topics in partial differential equations: elliptic equation theory and diffusion equations. I’ve prepared corresponding problems for you, following the same format as last time. Can we start now?"

Looking at the neatly organized folders and documents on the screen, Chen Lin was secretly pleased.

’Looks like spending more time together is paying off. Shen Yan remembers my preferences perfectly.’

He pulled over a chair and sat down next to her. The faint, fresh scent of shampoo seemed to drift from the ends of her hair.

"Alright, let’s go through them by solving the problems, same as before," Chen Lin said, a hint of a smile in his voice that even he didn’t notice, his gaze focused on the computer screen.

[Problem 1: Let Ω ⊂ ℝⁿ be a bounded open set. Consider the boundary value problem

−Δu + u = f in Ω,

u = 0 on ∂Ω,

where f ∈ L²(Ω).

(1) Write down the definition of the weak solution for this problem (give the Sobolev space, bilinear form, and linear functional).

(2) Use the Lax–Milgram theorem to prove the existence and uniqueness of the weak solution.

(3) Provide the a priori estimate for the solution: ∥u∥_{H¹} ≤ C∥f∥_{L²}, and explain the dependency of the constant C.]

As he wrote on a piece of scratch paper, Chen Lin explained to Shen Yan, "For the first part, we first set the working space as the Sobolev space V := H₀¹(Ω), with the norm defined as ∥v∥_{H¹} := (∥v∥_{L²}² + ∥∇v∥_{L²}²)^{1/2}."

"Then, we define the bilinear form a(u, v) := ∫_Ω(∇u·∇v + u v) dx, for u, v ∈ V."

"Define the linear functional ℓ(v) := ∫_Ω f v dx, for v ∈ V.

If u ∈ V satisfies a(u, v) = ℓ(v) for all v ∈ V, then u is called the weak solution to the original boundary value problem."

"Next, let’s look at the second question..."

Just like their last session, Chen Lin continuously wrote down the steps on his scratch paper, pausing occasionally to give Shen Yan a detailed explanation of a key point.

Shen Yan listened attentively most of the time, occasionally raising a question. Chen Lin would answer it, wait for her to understand, and then move on to the next problem.

Over two hours passed quickly, and the sun outside began to slowly set in the west.

"...Continuing the iteration, we find that the Hölder regularity of u improves, increasing by two orders of differentiation each time, forming a closed loop. By induction, we get u ∈ C^{k,α}(Ω̄) for all k ≥ 2. Next, we take the limit: u belonging to all Hölder spaces implies u ∈ C^∞(Ω̄). Therefore, starting from an H¹ weak solution, we obtain L^∞ control via the maximum principle, and then by a bootstrap argument, we progressively improve the regularity to finally obtain a smooth solution."

Having finished explaining another problem, Chen Lin paused. He took a sip of his still mostly full green grape drink, waiting for Shen Yan to fully grasp the concept before he moved on to the last problem of the day.

Suddenly, a crisp, clear voice that was especially familiar to Chen Lin rang out from the classroom doorway. "I knew you two would be here! Hey, Junior Chen Lin, come help your big sister with dinner."

Chen Lin: ?