Chapter 386: Hiss!
Chapter 386
Professor Fresnel explained the idea very thoroughly.
To put it simply, the concepts of the generalized directional derivative and generalized gradient of the Lipsehitz function are first given on the Riemannian manifold.
Then, the properties and algorithms of generalized gradients are derived by using the properties of the Riemannian manifold locally with the Euclidean space open-set differential homeomorphism, tangent mapping and cotangent emission.
At the same time, it is proved that the necessary condition for obtaining the small value of the letter defined on the Riemann blast shape is that the generalized gradient contains zero elements. These properties are used to give the Fritz John-type optimality conditions for mathematical programming problems on Riemannian manifolds.
The framework built by Professor Fresnel is not perfect at present, because the subsequent drawing of the specific context still has to be determined according to the specific situation of the research at that time. But this imperfect framework alone is beyond Cheng Nuo's current reach.
After a peek at the leopard, Cheng Nuo had to admire Professor Fresnel's attainments in the field of geometry, which was more than one grade above himself.
"There's still a long way to go!" Cheng Nuo sighed lightly.
The general framework is already there, and Cheng Nuo is not the main researcher, so there is not much work that falls on him.
This time, he participated in the research of this national key mathematics project with the purpose of learning.
After receiving the assignment from Professor Fresnel, Cheng Nuo and Hull exited the cubicle together.
Outside the cubicle, Hull exhaled lightly and patted Cheng Nuo's shoulder, "Cheng, in the next two months, I'm afraid we will be busy!"
He has been an assistant to Professor Fresnel for almost two years, and has been involved in several "big projects" like this one.
The days of that time can only be described as busy in the dark, even if a group of them were working for Professor Fresnel.
The tasks given to them by Professor Fresnel were certainly the ones that were less difficult and less complex. But, that was in Professor Fresnel's view.
For their group of assistants, Professor Fresnel thinks that simple tasks are no less difficult than writing a SCI paper in Zone 1.
Of course, during that time, under various pressures, they did grow much faster than usual.
Now that the same situation has fallen on him again, Hull is both heartbroken and happy at the thought of staying up late in the office for the next two months.
Fortunately, at least this time he was accompanied by Cheng Nuo, and the pain in his heart could be reduced a little.
It's just that, looking at the expression on Cheng Nuo's face next to him, why didn't he look worried?
Cheng Nuo grinned, "Hull, don't worry, with Professor Fresnel and I, I won't let you live a hard life for two whole months!"
Naturally, Professor Fresnel's level of mathematics goes without saying.
Cheng Nuo believes that even without him and Hull, Professor Fresnel alone can solve the project in two months.
Now the horses leading the carriage have changed from one to three, and although the other two horses are very thin, as long as they do not lag behind, it will naturally not take two months so long.
And Cheng Nuo, only others drag him back, how can he hold others back?
"Come on!" Cheng Nuo patted Hull, who didn't understand the meaning of his words, and walked back to the desk with a smile.
Cheng Nuo moved his fingers and started the day's work.
The research process of the project has been tentatively divided into three phases.
In the first stage, his task was simply to build a few concepts.
Cheng Nuo, who has already experienced countless topics, is already familiar with this, and he crackles on the computer:
[Let (M,g) be the m-Riemannian manifold, and at each point x∈M the cut of the null asks TxM given a quantity product g(u,v)=< u，v> ,?u,v∈TxM; v||x=< v，v> Represents the norm of the vector v∈TxM at the point x. This defines an equivalence norm in the tangent space......]
【...... Thus, for each point x, the Riemannian metric g induces an isomorphism between TxM and T(n,x)M: v*=gx(v,n)(v*,u)=gx(v,u),?u∈TxM.]
[The norm that defines the vector on the cut-off space T*xM is ||.] v*||=||v||=gx(v,v), so that there is the Cothian inequality < v*，u> ≤||v*||||u||，?u∈TxM.】
The operation was as fierce as a tiger, and Cheng Nuo's fingers almost flew out of the phantom on the keyboard.
Cheng Nuo, who has a clear mind, almost never encountered any stuckness. Formulas appear on the computer screen as if they should be smooth.
The task progress bar has been rising steadily.
3%，8%，15%，23%......
On the other hand, our Hull classmate was looking at the task list in his hand, frowning and thinking.
At this stage, his task is to study the transformation relationship between some properties of the Lipschitz function and the Fritz John-type optimality condition, which is about the same difficulty as the task obtained by Cheng Nuo.
But at this time, he was in a state of sadness, and a pen kept writing and drawing on the paper.
f(y)-f(x)|≤L|φ(y)-φ(x)|
f(x，v)=lim... lim...
No, it's not like that, it's not like that!
Hull crossed it out with all his might.
What about that? Hey, it doesn't seem right!
Ahhh
Hull rubbed his short blonde hair vigorously, and his blue eyes were full of lovelessness.
Riemann manifolds are Hull's forte, but the Lipschitz function clearly falls into the realm of function theory, and he doesn't know much about it. Therefore, starting this project is much more headache than the previous big projects.
Looking at the crossed-out announcement on the paper, Hull just wanted to shout:
Oh my God, who's going to save me!
Hull, who was in a state of melancholy, looked around the office, and finally landed on Cheng Nuo, who was not far away.
Over there, Cheng Nuo was happily slapping the keyboard, looking extremely excited.
Hull's eyes lit up.
............
"Cheng!" Cheng Nuo, who was happily typing on the keyboard, suddenly saw a head suddenly appear next to him, and he was so frightened that he almost threw the computer out.
He glanced at Hull, who was squatting beside him, covered his forehead and said, "Hull, if you don't go to work, what are you doing here?"
It's okay not to say this, but as soon as he mentioned this, Hull showed an extremely helpless expression, "I also want to work hard, but I can't figure out some of the tasks assigned to me by the teacher, so I came to you." ”
"Then what do you mean?" asked Cheng Nuohu.
"How about we swap missions?" Hull suggested.
Cheng Nuo shook his head, refusing, "No." ”
"Why?" Hull was puzzled.
Cheng Nuo smiled and said, "Because of my task, I have already completed a third of it." ”
"What, a third?!" Helton's eyes widened.
He looked directly into Cheng Nuo's gaze, "Cheng, you won't be joking, right?"
"Oh, don't you believe it?" Cheng Nuo moved to the side, revealing the computer screen.
Hull looked at the computer screen, then landed on the pile of formulas that filled two pages.
Hiss——!