By the time he returned to Aries City, he had already had a number of titles.

National middle school men's long jump champion, middle school men's jump national record holder, athlete level, national first prize player ranked first in biology competition, member of the national training team, and student of Mizuki University...... These titles were won by Ranger in the last two months, and he entered a burst period.

Lan Jinhui and He Yuyi expressed their satisfaction and happiness, He Yuyi said, Ajie, the house in the compound of the Sports Committee is for you, and the house can only be lived in and not sold, so you can keep it for marriage. Of course, Applejack, you're still a long way away from getting married, not to mention that you don't know if you're going to be in Aries City in the future. All in all, the house key of the sports committee compound gives you a key, and you go over from time to time to clean and maintain the cleanliness of your property.

Lan Jie took the key and said thank you to his parents.

Handing over the keys to the house is an important family ritual.

Although Lan Jie is not yet a minor in law, he already has the ability to act, judge and think as an adult in the minds of his parents.

Turnkey means that from this point on, Ranger has a high degree of independence and freedom.

Growing up, Langer's creditor was his sister, and his benefactor was his aunt.

Aunt Lan Yunhui has been sponsoring Lan Jie, and Lan Yunhui gave Lan Jie 10,000 yuan, saying that you should keep this money for college.

With a house and savings, Lan Jie reached the pinnacle of his life overnight.

Lan Ying, who was an exchange student in Toronto, had a video call with Lan Jie after learning about Lan Jie's latest results.

"Applejack, you actually won the first prize in the biology competition, and you still won the first overall score. ”

"I played mediocre and relied on my opponents to give me chances. ”

"You owe me 30,000 yuan, you don't have to pay it back. ”

"Sister, our debts have been cleared?"

"It's clear. ”

"Sister, you also spend a lot of money in North America, why don't I pay you back 12,000 symbolically?"

"Rangier, don't be so fake. ”

"Okay, okay, thank you, sister, huh, sister, are you outside? You guys are in the snow there, you seem to be wearing a swimsuit?"

"Hey, Annie, help me with my phone, I'm going to show my brother live. Lan Ying said in English.

In the next second, in the snowy environment, Lan Ying jumped into a river that did not freeze.

"Wow, sister, you're swimming in winter! The snow in Canada is so big! I've never seen such a big snow!"

Lan Ying in the winter swim shouted in the river: "This is much cooler than ****!"

"Wow, is this the life of your college students?" Lan Jie was eye-opening, and sure enough, college students could play.

Ranger has achieved some success, and his family has rewarded and encouraged him in various ways.

After a few days of rest in Aries City, Lan Jie set out on his journey again, and he traveled to the capital with the Sheep Racing Team, where he stayed in the dormitory of Mizuki University.

This year's CPhO national finals and national sports training were all hosted by Mizuki University. Ranger is already a Mizuki man, he fights at home, and he feels like he has a BUFF bonus.

Ding Ding Ding!

The competition begins.

Three theoretical questions, each worth 10 points, and the answering time is five hours.

In the first question, try to find the equivalent resistance between any two nodes of a planar square infinite resistance network. It is known that the resistance of each small segment in the network is r, and it is extended to other types of infinite resistance networks, such as planar rectangular networks, planar regular triangular networks, planar regular hexagonal networks, three-dimensional stereo networks, etc., and try to find the equivalent resistance between any two nodes of these infinite resistance networks.

'The first question, it's so difficult!'

Lan Jie couldn't help but sigh, after all, the national decision is a national decision, and the first theoretical question of the national competition is not sure how many players will be stumped?

The first question should blow up most of the contestants.

But not me, Applejack!

For a planar square infinite resistance network with a resistance of r in each segment, it is easy to find the equivalent resistance between two adjacent sections.

However, the equivalent resistance between any two non-adjacent nodes is difficult to calculate.

So it is necessary to use a two-dimensional plane Fourier expansion to derive an analytic solution of the equivalent resistance between any two nodes of a planar square infinite resistance network!'

Ranger drew an electrical diagram in which he established εη coordinates on the network plane so that the coordinates of any two nodes A and B were A(0,0),B(m,n), and the coordinates of all the other nodes could be expressed as (k,l). where m, n, k, l are integers, let the current I(k,l) be the current flowing into the node (k,l), considering that the current I flows from point A, and the current I flows out from point B after stabilization, then there are:

I（k，l）=1/r[V（k，l）-V（k-1，l）]+1/r[V（k，l）-V（k+1，l）]+ 1/r [V（k，l）-V（k，l-1）]+ 1/r [V（k，l）-V（k，l+1）]

Simplified to: V(k,l)-£V(k,l)=r/4I(k,l)

The homogeneous equation V(k,l)-£V(k,l)=0 is obtained

Then find the special solution of the non-homogeneous equation!

Find the function F(x,y) and expand it into a two-dimensional Fourier series over the interval [-π,π;-π,π]!

After complex mathematical calculations, Renger found Rmn=r/4π^2∫-ππ∫-ππ1-cos(mx+ny)/2-cosx-cosydxdy.

This is the analytic solution of the equivalent resistance between any two nodes of a planar square infinite network!

Continue to calculate and find the equivalent resistance between any two nodes of the planar rectangular network, the planar regular triangular network, the planar regular hexagonal network, and the three-dimensional network!

Only 20 percent of the problem is physics, and the rest is all mathematics. ’

This is Lan Jie's evaluation of the first question, and he immediately tackles the next two.

The last two questions are very physical, and Lan Jie completed all the theoretical questions half an hour early.

Ding Ding Ding!

Submit the papers!

The players have a half-day break and will have a test match tomorrow morning.

Li Zihan is also a national finalist of the sheep competition team, and he came to the capital for the first time, and of course it was the first time to come to Mizuki University.

Accompanied by Lan Jie, Li Zihan visited Mizuki University with great interest.

"Lan Jie, you're quite familiar with Mizuki University, right?"

"At the beginning of October, I was here for a few days, and I don't know each other very well, but it's okay. ”

"As far as I know, the competition training class of Yan University is very powerful, and the previous CPhO national finals were hosted by Yan University, and the training base of the national team has always been located in Yan University. Why in recent years, Yanda and Shuimu have taken turns to hold the CPhO national finals and take turns to undertake the task of training the national team?"

"The information I understand is that a few years ago, Mizuki said that Yanda had a monopoly on the holding of competitions and training for the national team, which was not suitable, and should be brought by Mizuki and Yanda. Then the Physics Association agreed to Mizuki's suggestion, and then Yanda and Mizuki took turns. ”

"Lan Jie, as far as I know, the venue of the national competition and the training base of the national team have always been the same as Shuimu High School, didn't Yan Da put forward any suggestions and opinions?"

"Shuimu High School is a middle school, and the business of the middle school has nothing to do with Yanda. ”

"That's right, but Mizuki High School is in Mizuki Garden, well, this is Mizuki High School. ”

The two walked around and walked to the door of Shuimu High School, Li Zihan said: "I always feel that Shuimu is stronger than Yanda, and I really want to come to Shuimu." ”