Omnipotent Data

Chapter 386

Professor Fresnel explained the ideas thoroughly.

To put it simply, the concepts of generalized directional derivative and generalized gradient of the lipsehitz function are first given on the Riemannian manifold.

Then, using the properties of the open-set differential homeomorphism of the Riemannian manifold and the Euclidean space, as well as the tangent map and the cotangent projection, the properties and operation rules of the generalized gradient are derived.

At the same time, it is proved that the necessary condition for the function defined on the Riemann plague to obtain the minimum value is that the generalized gradient contains zero elements. And using these properties, the fritzjohn-type optimality conditions of mathematical programming on Riemannian manifolds are given.

The framework established by Professor Fresnel is currently not perfect, because the subsequent drawing of the specific context still needs to be determined according to the specific situation of the research at that time. But this imperfect framework alone is beyond the reach of Cheng Nuo.

Taking a glimpse of the leopard, Cheng Nuo had to admire Professor Fresnel's accomplishments in the field of geometry, which was more than a grade beyond himself.

"There is still a long way to go!" Cheng Nuo sighed lightly.

The general framework is there, and Cheng Nuo is not a major researcher, so the work that falls on him is not much.

This time, with the purpose of learning, he participated in the research of this national key mathematics project.

After receiving the task from Professor Fresnel, Cheng Nuo exited the cubicle with Hull.

Outside the cubicle, Hull sighed and patted Cheng Nuo on the shoulder, "Cheng, in the next two months, we might be busy!"

He has served as Professor Fresnel's assistant for almost two years, and has participated in several times like this "big project".

The days during that period can only be described as being very busy, even if a group of them beat Professor Fresnel.

Although the tasks assigned to them by Professor Fresnel are certainly those with less difficulty and lower complexity coefficient. But that is in the view of Professor Fresnel.

For their group of assistants, Professor Fresnel thinks that a simple task is no less difficult than writing a district-one sci paper in their eyes.

Of course, during that time, under various pressures, they did grow faster than usual.

Now that the same situation fell on him again, Hull felt painful and happy when he thought of staying up late in the office for the next two months.

Fortunately, at least Cheng Nuo was with him this time, and the pain in his heart could be slightly reduced.

It's just that, looking at the expression on Cheng Nuo's face next to him, why didn't he show the slightest worry?

Cheng Nuo grinned, "Hull, don't worry, Professor Fresnel and I are here, and you won't be able to live through two months of hardship!"

Needless to say, Professor Fresnel's mathematics level.

Cheng Nuo believed that even without him and Hull, Professor Fresnel alone would be able to solve the problem in two months.

Now the horses holding the carriage have changed from one to three. Although the other two horses are very thin, they naturally don’t need two months as long as they don’t drag their legs.

As for Cheng Nuo, only others are holding him back. How can he hold back others?

"Come on!" Cheng Nuo patted Hull, who didn't understand what he meant, and walked back to the desk with a smile.

Cheng Nuo moved his fingers to start a day's work.

The research process of the project is temporarily set into three stages.

In the first stage, his task was simply to construct a few concepts.

Cheng Nuo, who has already experienced countless tasks, is already familiar with this. He crackled on the computer:

[Suppose (m, g) is an m-dimensional Riemannian manifold, at each point x ∈ m tangent, txm is given a quantity product g(u, v)=amp;lt;u, vamp;gt;, ?u, v∈txm; where vx=amp;lt;v, vamp;gt; represents the norm of vector v∈txm at point x. This defines an equivalent norm in the tangent space...]

[... Therefore, for each point x, the Riemann metric g induces an isometric isomorphism between txm and t(n, x)m: v*=gx(v,n)(v*,u)= gx(v,u),?u∈txm.】

[Define the norm of the vector on the cotangent space t*xm as v*=v=gx(v, v), so there are the Cossi inequality amp;lt;v*, uamp;gt; ≤v*u, ?u ∈txm.】

After the operation was fierce, Cheng Nuo's fingers almost flew out of the keyboard.

Cheng Nuo, with clear thinking, hardly encountered any lag. The formulas appear on the computer screen as if they should be smoothly.

The task progress bar has also been rising.

3%, 8%, 15%, 23%...

On the other side, our classmate Hull, looking at the task list in his hand, frowned and thought hard.

At this stage, his task is to study the transformation relationship between some properties of the lipshitz function and the fritzjohn-type optimality condition. The difficulty is similar to the task obtained by Cheng Nuo.

But at this moment, he was in a state of frowning, and he kept writing and drawing on the paper with a pen.

f(y)-f(x)≤lφ(y)-φ(x)

f(x,v)=lim...lim...

No, not so, not so!

Hull crossed it hard.

What about this? Hiss, it doesn't seem right!

Ahhhhh! How to do it!

Hull rubbed his short blonde hair vigorously, and his blue eyes were filled with unlovable look.

Riemannian manifolds are Hull's strengths, but the lipshitz function obviously belongs to the category of function theory, and he doesn't know much. Therefore, starting this project is more troublesome than the previous large projects.

Looking at the crossed-out announcement on the paper, Hull just wanted to shout:

Oh my god, who will save me!

Classmate Hull, who was in melancholy, wandered around in the office, and finally fell on Cheng Nuo not far away.

Over there, Cheng Nuo was happily popping the keyboard, looking extremely excited.

Hull's eyes suddenly brightened.

…………

"Cheng!" Cheng Nuo, who was happily typing on the keyboard, suddenly saw a head suddenly appeared beside him, so scared that he almost didn't throw the computer directly.

He glanced at Hull, who was squatting beside him, clutching his forehead and said, "Student Hull, if you don't go to work, why are you running to me?"

It’s okay not to mention this. When mentioning this, Hull showed a very helpless expression, "I want to work hard too, but the task assigned to me by the teacher, I don’t understand in some places~www.mtlnovel. com~ So I came to find you."

"Then what do you mean?" Cheng Nuohu asked.

"How about we exchange tasks?" Hull suggested.

Cheng Nuo shook his head as a refusal, "No."

"Why?" Hull puzzled.

Cheng Nuo smiled and said, "Because of my task, one third of it has been completed."

"What, a third?!" Helton's eyes widened.

He stared at Cheng Nuo, "Cheng, are you kidding me?"

"Hey, don't you believe it?" Cheng Nuo moved aside, revealing the computer screen.

Hull looked on the computer screen, and then landed on the pile of formulas that filled up two pages.

hiss!

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