From University Lecturer to Chief Academician

In response to the three-dimensional function trajectory correction problem sent by Liu Rongxing, Wang Hao already had a "vague" conclusion in his mind.

The conclusion is two words - 'feasible'.

The reason why "feasible" is a vague conclusion is because he is not 100% sure, but the probability of being sure is more than 90%.

If you want to be completely sure, you must come up with a plan.

Wang Hao is not in a hurry to give an answer. Mathematics is very rigorous. There is no "probably feasible".

He also hopes to be more perfect, instead of giving ambiguous answers, especially if the question may involve the trajectory of ballistic missiles.

This kind of research must be cautious, more cautious.

In addition, halfway through the research, it is impossible for him to give up halfway.

Although the inspiration value is only 60 points, he feels that it is very close to completion.

The trajectory correction of the three-dimensional function, in fact, is difficult in the calculation. How to orient one function to the trajectory of another function is very important, and the similarity needs to be very fine.

For example, a simple function x=1.

If the modified function is x=2, the difference is too large, and the value of the approximated function x must be limited to the value '1'.

Fine calculations related to functions are very important, and at the same time involve the calculation of complex equations, and even the calculation of equations is the core, because the calculation of functions will eventually become the calculation of equations.

This problem involves external force, or the force of short-term rapid impact, or continuous force, and it must involve complex equations.

The calculation of complex equations is the biggest difficulty in calculation problems.

Among a series of complex equations, the most difficult ones are partial differential equations and NS equations. In fact, NS equations are the fluid mechanics interpretation of Newton's second law.

So the problem is finally to the study of complex equations.

Wang Hao's research is not in a hurry, he will think for a while by himself, and look at other content if he can't think of it.

Daily teaching is a must-do homework, and teaching can slowly accumulate inspiration points.

The current teaching has stepped over the theory of functions and entered the stage of computational mathematics. Of course, it is impossible for him to explain the theory of functions in half a month. He only explained some main content and did not continue to involve advanced knowledge.

The scope of computational mathematics is too large.

This subject is related to many branches of mathematics such as differential equations, vector analysis, matrix, Fourier transform, complex variable analysis, numerical methods, probability theory, mathematical statistics, operations research, control theory, combinatorics, information theory, etc. Includes the study of mathematical problems posed from a variety of application areas.

So computational mathematics can be seen as a part of applied mathematics.

Wang Hao first talked about algebraic equations. Algebraic equations are very prominent and involve the most problems in computational mathematics.

His small class has been open for about half a month. At first, many doctors and even professors came to attend the class, but gradually some people stopped coming.

For example, the professors and associate professors upstairs.

Because the content of Wang Hao's lectures is not in-depth, it is basically some basics. It can be helpful for doctoral students and graduate students to deepen their understanding of the field of mathematics, but it is difficult for professors to gain anything. Review it again, it doesn't have much practical significance.

So the number of people in the class has stabilized, and there are about 20 people who come each time.

Wang Hao is still very satisfied with the number of people. Twenty people are enough. He continued his lecture rhythm, "In the field of algebraic equations, we generally recognize the fact that there is no root-finding formula for algebraic equations of degree five and above. .”

"Therefore, only approximate solutions can be obtained for this type of algebraic equations, and the method of obtaining approximate solutions is the method of numerical analysis."

He put down the book in his hand and continued, "Aiming at this type of complex equation, our research direction is mainly to find an approximate solution to a single type of equation through analysis."

This is a small research direction.

Just like the thesis of some doctoral students and graduate students, including the solution of many partial differential equations, the solution of complex algebraic equations is also a big research direction, but it is difficult to produce great results.

Wang Hao continued, "But in practical applications, the solution method of substituting numerical values ​​is more direct."

Helen suddenly raised her hand and asked, "Mr. Wang, for some equations, is it easier and more direct to obtain approximate solutions by substituting numerical values ​​than performing mathematical analysis?"

"Also, even if numerical analysis is used to solve the problem, the degree of approximation is not necessarily closer than the numerical solution and the exact solution, right?"

Wang Haodao, "In some cases, this is true, but in other cases, the numerical solution will be very complicated."

He nodded and said, "Helen's question is very good. Which method is more suitable, numerical solution or analytical solution, depends on the complexity of the equation."

"If it is a completely clueless equation, it is difficult to find an approximate direction by numerical solution."

"The equation is relatively simple, and it will be easy to solve it numerically."

As he spoke, he suddenly thought of the research question, and suddenly a flash of inspiration flashed in his mind, and at the same time, the system refreshed new information.

[Task 3, inspiration value +11. 】

"It makes sense!"

Wang Hao suddenly felt a sense of enlightenment. He glanced at Helen appreciatively, and continued with the rest of the lecture.

After the explanation was finished, he returned to the office and began to do research seriously.

The previous research encountered calculation problems, because I am very good at mathematical analysis, I feel that I have reached a dead end, and I have been doing research in the direction of mathematical analysis.

But mathematical analysis is relatively too complicated, and the analysis process is unlikely to be applied by computer.

This complexity makes the problem impossible to solve.

He has been troubled by it.

Helen's question reminded him that it is not necessary to take the path of mathematical analysis, it is relatively easier to directly bring in the numerical value.

...

137.

This is a confidential scientific research institution specializing in ballistic research.

The two-story building surrounded by mountains and forests is the main research and development base of Institute 137. Sunlight shines into the meeting room from the window, reflecting the faces of the crowd in dispute.

A young man in his thirties propped his hands on the table and said vigorously, "Qian Xuesen's trajectory also has limitations!"

"Our research on maneuvering gliding technology should not be limited to Qian Xuesen's trajectory, but should also be developed in other directions."

Another middle-aged man in his forties replied, "It's very interesting what you said. The trajectory of motor gliding technology was originally proposed by Mr. Qian Xuesen. What is the development of other directions? Do you have the ability to say it?" ?”

The young man immediately replied, "I can't say it now, but you admit that Qian Xuesen's trajectory has limitations. It is difficult for conventional missiles to maintain that trajectory until it hits the target."

"In addition, there are studies in other countries. Qian Xuesen's ballistics is public information. It was proposed by Mr. Qian Xuesen when he was studying in American. Their information may not be less than ours."

"As long as they can fully understand this technology, they can use computers to lock the route for anti-missile."

"What we are studying now is how not to be anti-missile. What's the use of a missile with a beautiful trajectory? Before hitting the target, we still have to rush directly to it."

"Now the only way to ensure that the target is hit is hypersonic speed, accelerating to Mach 10 or Mach 20, but that kind of technology cannot be widely used."

The middle-aged man immediately retorted, "If you say that you want to develop new technology, you should develop new technology. How can it be so simple? Now you don't even know the direction. And we are already ahead in Qian Xuesen's trajectory."

"How do you know it's the lead? Who can determine the lead? Have you verified it?"

"Why am I not sure."

"You can't be sure."

"..."

The two of them slapped the table and yelled at each other, and they almost started fighting.

The door of the conference room.

Zheng Guofeng couldn't stop smiling wryly. Similar arguments happen in every meeting. They are now discussing the direction of future research and development.

this is very important.

Although he has mastered the technique of Qian Xuesen's ballistics, no technique is perfect, and Qian Xuesen's ballistics also has its limitations.

Qian Xuesen's ballistic is the maneuvering gliding technology, which can be understood as making ballistic missiles change direction like cruise missiles, and the trajectory will become very uncertain.

However, the use of similar technologies will definitely take up a certain amount of weight, and not every missile can be used.

The development of domestic missiles has achieved curve overtaking to a certain extent.

They have developed directly from conventional ballistic missiles to maneuver gliding technology, directly crossing the stage of re-entry maneuver glider ballistic missiles.

Although overtaking in curves has been achieved, high-end technology can only be used on high-end missiles, and the existence of faults in the middle means less accumulation.

It is very difficult to determine the direction of future research and development now.

Should we continue to study Qian Xuesen's ballistics and add some other technologies to it, or should we combine and develop new technologies?

This is the crux of the research debate.

Pang Sibo couldn't stand the quarrel inside. He opened the door and came out and saw Zheng Guofeng. He shook his head and smiled, "Professor Zheng, it's really difficult. I've been arguing all the time recently, and I'm not sure what to do."

He asked, "By the way, didn't you say to ask someone outside to help you take a look last time? Who did you ask? I heard that you also applied for a grant of 500,000 yuan?"

Zheng Guofeng smiled and said five words, "Guess? Very famous."

"Famous?"

Pang Sibo thought for a long time, but couldn't figure out who it was. Suddenly, a name appeared in his mind. He widened his eyes and asked, "You won't be looking for Wang Hao from Xihai University, right? The one in his twenties The young genius who proved Goldbach's conjecture and completed the routine demonstration of the NS equation?"

"Who else but him?" Zheng Guofeng said with a smile, "The domestic mathematicians are very famous. I can't go to Qiu Chengwen."

"Right."

Pang Sibo nodded and continued to ask, "How is it? Is there any result? Five hundred thousand, this is the first time we have spent so much money for other people's consultation."

Five hundred thousand is not much.

However, it is the first time to spend this money by consulting other people.

Consulting fee?

It can be said that the 137 institutes have produced elites in large numbers, so do you still need to consult other people? Do you even need to pay such a large amount of consulting fees?

Zheng Guofeng shook his head, "There is no news yet, it has been half a month."

"You can't be tricked, can you?" Pang Sibo said with a grin.

"That's not true." Zheng Guofeng said with a smile, "I still believe in Liu Rongxing. If he is really cheated of this money, I will ask the space agency to get it back."

Pang Sibo smiled and thought about it, "But it's normal. This question is too difficult. We have been discussing it for a month, right? It was brought up last year, and there is no definite direction until now."

"If there is someone who can give a definite answer, I don't believe it anyway."

He said shaking his head.

Zheng Guofeng said, "I don't believe it either. No one can determine this issue, but we must set a direction, and the opinions of top mathematicians are still very valuable."

"Right."

Pang Sibo listened and nodded.

For such a complicated problem, it is impossible for someone to give a definite result, but to ask a world-class mathematician, the other party's judgment on the problem must be of great reference value.

All they want is a reference.

After Zheng Guofeng talked with Pang Sibo for a few words, he returned to the office and thought about it, before calling Liu Rongxing.

"Director Liu, can you remind me, why hasn't there been a reply?" He asked simply, without specific content.

Liu Rongxing still understood.

He was also a little anxious. At that time, he patted his chest and said that he believed in Wang Hao. Why didn't he reply to a consultation question for half a month?

This is indeed a complicated question, but it is just for Wang Hao to give an opinion.

is it hard?

Liu Rongxing picked up the phone and called, but after thinking about it, it was not good to say it directly, so he simply put down the phone and sent a message to ask about the project of the system engineering department, so that Wang Hao would call back when he saw it.

at the same time.

Wang Hao is writing the content related to three-dimensional function correction.

The inspiration value has accumulated '102' points, and I have a clear idea in my mind, and the rest is just to write it out.

The difficulty of this research lies in the calculation, and the difficulty of summarizing is also in the calculation method.

Wang Hao wrote for several hours, and almost finished writing the content, because he is not publishing a thesis, there are some incidental content, which does not need to be written carefully, and can even be ignored directly. It is good to complete the main content, and it is relatively easy to write. Keep it simple.

He worked until eight o'clock in the evening before finally finishing the final content.

"Hey~~~"

He stretched his waist vigorously, and looked at it again. Among them, the most difficult problem was to solve the calculation problem of the equation.

At this time, he suddenly thought of the study of the NS equation.

The current research is also closely related to the NS equation. The function is infinitely expandable, and some of the calculations involve complex equations, which require some equation-solving skills.

Some previous studies are also useful, including the approximate solution of the NS equation.

"If the content inside is extended to the NS equation, can the original limited range be extended to infinity?"

He shook his head thinking about it, "It shouldn't be possible for the time being, but it seems that one function path can be locked, and other functions can be calculated by the same equation to transform against the fixed path, not limited to two three-dimensional functions..."

"It makes sense!"

Wang Hao's eyes lit up as he thought about it, and the system also had a reminder.

[Task 1, inspiration value +7. 】

[Inspiration value: 67. 】

"!!"

"The research on the NS equation has made progress again!" This is really a surprise.

In the study of the NS equation, the inspiration value has been fixed at 60 points. I did not expect to be able to connect to the NS equation after doing this research.

This is the real big gain!

Wang Hao hurriedly recorded it with excitement. It was one o'clock in the evening as soon as he started working, and he even forgot the time.

He felt that his eyelids were fighting, so he had to stop.

Before leaving the desk, he checked the message and found the message from Liu Rongxing, "Call back when you see it?"

Wang Hao looked at the time, hesitated, and called.

What if there is an emergency?

"Toot..."

On the opposite side, Liu Rongxing was sleeping soundly, when he heard the mobile phone vibrating next to his ear, and he dreamed that he was riding a motorcycle and passing a separation zone.

"It's so bumpy~~"

Liu Rongxing was awakened by the shock. He rubbed his eyes with his hands, picked up the phone to look at it, and pressed the answer button depressedly, "Professor Wang, are you in Americon?"

Wang Hao was a little embarrassed, and said, "Professor Liu, I see that you left a message saying that you will call back immediately after seeing the news, because you are afraid of something urgent."

"What's the rush?" Liu Rongxing was somewhat depressed, but he became more energetic, "I just want to ask you...the project...forget it!"

He simply said, "I want to ask you, did you read the question last time?"

"That question, I sent it to you through the intranet."

"ah?"

"What's wrong?"

"Nothing~~"

Liu Rongxing was very puzzled when he heard that, he felt that the answer to the question was 'feasible' or 'not feasible'?

Either two words or three words, why did you send the document?

When he was curious, he could no longer fall asleep, so he simply got up and turned on the computer. After logging into the intranet, he saw the file sent by Wang Hao.

After he opened it, he saw a lot of complicated mathematics inside.

The top line reads a note, "A trajectory correction method for a three-dimensional curve function?"

"this……"

He understood carefully, then opened his mouth wide, "Wang Hao, did he solve the problem?"

Liu Rongxing stared at the computer for a long time. He couldn't understand the complicated content, but it didn't prevent him from knowing what was written in it.

The trajectory correction of the three-dimensional function is equivalent to the method of returning the missile that deviates from the trajectory to the normal trajectory.

Wang Hao solved such a complicated problem?

Liu Rongxing was so surprised that he didn't even feel sleepy at all.

He glanced at the time, hesitated a little, then gritted his teeth, "No way!"

"I can't just keep me awake!"

"The person who asks the question should stay up all night!"

"..."