Chapter 191 Wang Hao completed his research, Liu Rongxing: I cant sleep, and you cant sleep either!
Regarding 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 he said "feasible" is a vague conclusion is because he is not 100% sure, but the probability of certainty is more than 90%.
If you want to be completely sure, you have to come up with a plan.
Wang Hao is not in a hurry to give an answer. Mathematics is very rigorous. There is no such thing as "probably feasible". What is feasible is feasible, and what is not feasible is not feasible. A definite answer must be given.
He also hopes to do a more perfect job rather than give ambiguous answers, especially when the question may involve the trajectory of ballistic missiles.
This kind of research must be carried out with caution and caution.
In addition, it was impossible for him to give up halfway through the research.
Although the inspiration value was still only 60 points, he felt that he was very close to completion.
The difficulty in trajectory correction of three-dimensional functions is actually calculation. How to orient one function to the trajectory of another function is very important. Numerical calculations are very important, and the similarity needs to be very precise.
For example, a simple function x=1.
If the modified function is x=2, the difference is too large, and the approximated function x value must be limited to the value '1'.
Precise calculations related to functions are very important, and at the same time involve the calculation of complex equations. It is even said that equation calculation is the core, because the calculation of functions will eventually become the calculation of equations.
This problem involves external forces, or forces that impact rapidly in a short period of time, or forces that are continuous, 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 one is the partial differential equation, the NS equation. In fact, the NS equation is the fluid mechanics explanation of Newton's second law.
So the problem ultimately comes to the study of complex equations.
Wang Hao's research is not in a hurry. He will think about it for a while, and if he can't think of anything, he will look at other content.
Teaching every day is a must-do homework, and teaching can slowly accumulate inspiration points.
The current teaching has moved beyond function theory and entered the stage of computational mathematics. Of course, it is impossible for him to explain function theory 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 great.
This subject is related to differential equations, vector analysis, matrices, Fourier transforms, complex variable analysis, numerical methods, probability theory, mathematical statistics, operations research, control theory, combinatorial mathematics, information theory and many other branches of mathematics. It is also
Includes the study of mathematical problems posed from a variety of application areas.
Therefore computational mathematics can be regarded as a part of applied mathematics.
The first thing Wang Hao talked about was the problem of algebraic equations. Algebraic equations are very prominent and the most involved 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 Wang Hao talks about is not in-depth, it is basically some basics. It can be helpful for doctoral students and graduate students to deepen their understanding of knowledge in the field of mathematics, but it is difficult for professors to gain anything. At most, they can only re-learn
Reviewing it again does not have much practical significance.
So the number of people in the class has stabilized, with about twenty people coming each time.
Wang Hao was still very satisfied with the number of people. Twenty people were 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 the fifth degree and above.
.”
"Therefore, only approximate solutions can generally 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, "For this type of complex equations, our research direction is mainly to find approximate solutions to individual types of equations 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 large 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, "Teacher Wang, for some equations, would it be much simpler and more direct to obtain approximate solutions by substituting numerical values than through mathematical analysis?"
"Moreover, even if numerical analysis is used to solve the problem, the approximation is not necessarily closer than the numerical solution and the exact solution, right?"
Wang Haodao, "In some cases, this is indeed the case, 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 an equation that has no clue at all, it will be difficult to find the approximate direction using numerical solutions."
"The equation is relatively simple, and it will be easy to solve it by inserting numerical values into it."
As he was talking, he suddenly thought of the research problem, and an idea suddenly flashed in his mind, and at the same time, the system was refreshed with new information.
[Task three, inspiration value 11.]
"It makes sense!"
Wang Hao suddenly felt a sudden realization. He glanced at Helen appreciatively and continued with the rest of the course.
After the explanation was completed, he returned to the office and began to do research seriously.
I encountered computational problems in my previous research. Because I am very good at mathematical analysis, I felt that I had reached a dead end and kept doing research in the direction of mathematical analysis.
However, mathematical analysis is relatively too complex, and the analysis process is unlikely to be applied by computers.
This complexity makes the problem impossible to solve.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! He has been troubled by this.
Helen's question reminded him that it was not necessary to follow the path of mathematical analysis. It was relatively simpler to directly bring in the numerical values.
…
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. The sunlight shines into the conference room from the window, reflecting the faces of the people who are arguing.
A young man in his thirties put his hands on the table and said forcefully, "Qian Xuesen's ballistics also has limitations!"
"Our research on maneuverable gliding technology cannot be limited to Qian Xuesen's ballistic trajectory, but must also develop in other directions."
Another middle-aged man in his forties replied, "What you say is very interesting. The trajectory of motorized gliding technology was originally proposed by Mr. Qian Xuesen. What other directions can be developed? Do you have the ability to tell me?
?”
The young man immediately replied, "I can't tell you now, but do you admit that Qian Xuesen's ballistic trajectory has limitations? It is difficult for conventional missiles to maintain that trajectory until it hits the target."
"In addition, there are also studies in other countries. Qian Xuesen's ballistics is public information. It was proposed by Mr. Qian Xuesen when he was studying abroad in Amerikan. Their information may be no less than ours."
"As long as they can understand this technology thoroughly, they can use computers to lock the route for anti-missile purposes."
"What we are studying now is how to avoid being anti-missile. No matter how beautiful the trajectory of the missile is, what's the use? Before hitting the target, we still have to rush directly towards it."
"Now the only way to ensure hitting the target is hypersonic speed, which can accelerate to Mach 10 or Mach 20, but that technology cannot be widely used."
The middle-aged man immediately retorted, "You said to develop new technology, just develop new technology. How can it be that simple? Now we don't even know the direction. And we are already leading in Qian Xuesen's ballistic trajectory."
"How do you know you are in the lead? Who can determine the lead? Have you verified it?"
"Why am I not sure?"
"You can't be sure."
"..."
The two people slapped the table and shouted at each other, almost starting to use their hands.
The door of the conference room.
Zheng Guofeng couldn't help but smile bitterly after hearing this. Similar arguments occurred in every meeting. They were now discussing the direction of future research and development.
this is very important.
Although Qian Xuesen ballistics technology has been mastered, no technology can be perfect, and Qian Xuesen ballistics also has its limitations.
Qian Xuesen's ballistics refers to maneuvering gliding technology, which can be understood as allowing ballistic missiles to change directions 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.
Domestic missile development has achieved overtaking in a corner to a certain extent.
They developed directly from conventional ballistic missiles to maneuvering gliding technology, directly skipping the stage of re-entering maneuvering gliding ballistic missiles.
Although overtaking in corners has been achieved, high-end technology can only be used on high-end missiles, and the existence of gaps 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 study's argument.
Pang Sibo really couldn't stand the quarrel inside. He opened the door and saw Zheng Guofeng when he walked out. He shook his head and smiled, "Professor Zheng, it's really difficult. There have been constant quarrels recently. I'm not sure what to do."
He said and asked, "By the way, didn't you say you asked someone outside for help last time? Who did you ask for? I heard that you also applied for 500,000 yuan in funding?"
Zheng Guofeng laughed and said five words, "Guess? Very famous."
"Famous?"
Pang Sibo thought about it 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're not looking for Wang Hao from Xihai University, are you? The one who is in his twenties?"
A young genius who is 20 years old and has proved Goldbach's conjecture and completed the conventional demonstration of the NS equation?"
"Who else could be there besides 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 our office has spent so much money on consulting other people."
Half a million is not much.
However, this is the first time I have spent the money by asking other people questions.
Consulting fee?
It can be said that 137 institutes are full of elites, so do they still need to consult others? Do they even need to pay such a large consulting fee?
Zheng Guofeng shook his head, "There is no news yet, it's been half a month."
"Are you being tricked?" 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 problem is too difficult. So many of us have been discussing it for a month, right? It was raised last year, and there is no definite direction until now."
"If anyone can give a definite answer, I don't believe it."
He said and shook his head.
Zheng Guofeng said, "I don't believe it either. No one can be sure about this issue, but we must set a direction, and the opinions of top mathematicians are still of great reference value."
"Right."
Pang Sibo nodded as he listened.
For such a complex problem, it is impossible for anyone to give a definite result, but if you ask a top mathematician in the world, his judgment on the problem will definitely be of great reference value.
All they want is a reference.
After Zheng Guofeng had a few words with Pang Sibo, he returned to the office, thought about it, and called Liu Rongxing.
"Director Liu, can you help me push it? Why hasn't there been a reply yet?" He asked simply without saying the specific content.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! Liu Rongxing still understands.
He was also a little anxious. At that time, he patted his chest and said that he believed in Wang Hao. Why did he not get a reply to a consultation question for half a month?
This is indeed a complicated issue, but I just want Wang Hao to give me an opinion.
is it hard?
Liu Rongxing picked up the phone and called him. After thinking about it, it would not be 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, asking Wang Hao to call him back after seeing it.
at the same time.
Wang Hao is writing content related to three-dimensional function correction.
The inspiration value has accumulated '102' points, I have clear ideas in my mind, and the rest is just writing it out.
The difficulty of this research lies in the calculation, and the difficulty in summarizing is also in the calculation method.
Wang Hao wrote for several hours and almost finished the content. Because he was not publishing a paper, there were some incidental content that did not need to be written carefully. He could even ignore it and just finish the main content. It was relatively easy to write.
Be simpler.
He worked until eight o'clock in the evening before finally completing the final content.
"Hey~~~"
He stretched hard and took another look at the most difficult equation-solving calculation problem.
At this time, he suddenly thought of the study of NS equations.
Current research is also closely related to NS equations. Functions are infinitely expandable. Some calculations involve complex equations, which requires some equation solving skills.
Some previous studies have also been used, including methods for approximate solution of NS equations.
"If the content inside is expanded to the NS equation, can the original limited range be extended to infinity?"
He thought and shook his head, "It shouldn't be possible for the time being, but it seems that a function path can be locked and other functions can be calculated through the same equation to transform the fixed path, instead of being limited to two three-dimensional functions..."
"It makes sense!"
Wang Hao's eyes suddenly lit up as he thought about it, and at the same time, the system also issued a reminder.
[Task 1, inspiration value 7.]
[Inspiration value: 67.]
"!!"
"The research on NS equations has made progress again!" This is really an unexpected surprise.
In the research on the NS equation, the inspiration value has been fixed at 60 points. I didn’t expect that this research can still be related to the NS equation.
This is the real big gain!
Wang Hao quickly recorded it with excitement. It was already one o'clock in the evening as soon as he started working, and he even forgot about the time.
He felt like his eyelids were fighting, so he had to stop.
Before leaving the desk, he still 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?
"Dudu..."
Opposite him, Liu Rongxing was sleeping soundly when he heard the cell phone vibrating in his ear. He dreamed that he was riding a motorcycle and passed by an isolation zone.
“It’s so bumpy~~”
Liu Rongxing was awakened by the shock. He rubbed his eyes with his hands, picked up his phone and took a look at it. He pressed the answer button depressedly, "Professor Wang, are you in Americen?"
Wang Hao felt a little embarrassed and said, "Professor Liu, I saw that you left a message saying that you would call back immediately after seeing the news, because you were afraid of something urgent."
"What's the emergency?" Liu Rongxing was a little depressed, but he also became energetic, "I just want to ask you about...the project...forget it!"
He simply said directly, "I want to ask you, did you read the question last time?"
"That question, I sent it to you via the intranet."
"ah?"
"What's wrong?"
"Nothing~~"
Liu Rongxing was very puzzled. He thought the answer to the question was 'feasible' or 'not feasible'?
It’s either two words or three words, why are you still sending the document?
With curiosity in his heart, he could no longer fall asleep. He simply got up and turned on his computer. After logging into the intranet, he saw the file sent by Wang Hao.
After he clicked on it, he saw a lot of complicated mathematical content inside.
The top line reads a note, "A trajectory correction method for three-dimensional curve functions?"
"this……"
He understood it carefully and suddenly opened his mouth, "Wang Hao, has he solved the problem?"
Liu Rongxing looked at the computer for a long time. He couldn't understand the complicated content, but it didn't stop him from knowing what was written inside.
The trajectory correction of the three-dimensional function is equivalent to the method of returning the missile that has deviated from the trajectory to the normal trajectory.
Such a complicated problem was solved by Wang Hao?
Liu Rongxing was so surprised that he didn't even feel sleepy at all.
He glanced at the time and hesitated, then gritted his teeth and said, "No!"