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 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". If it is feasible, it is feasible. If it is not feasible, it is not feasible. It must be given i
Definite answer.
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 conducted with caution and caution.
In addition, it was impossible for him to give up halfway through the research.
Although the inspiration value was only 60 points, he felt that he was very close to completion.
The difficulty in trajectory correction of three-dimensional functions is actually calculation. For example, if you want to direct one function to the trajectory of another function, numerical calculation is very important. i
And drawing similarities also needs to be very precise.
For example, a simple function x=1.
If the modified function is =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 they also involve the calculation of complex equations. It is even said that the calculation of equations is the core, because the calculation of functions comes first.
will become the calculation of the equation.
That problem involves internal force, or a force that impacts rapidly in a short time, or a force that is continuous or discontinuous, and it must involve a simple equation.
The calculation of simple equations is not the least difficult aspect of calculation problems.
Among a series of simple equations, the least difficult are the partial differential equations and the NS equation. In fact, the NS equation is not a fluid mechanics explanation of Newton's seventh law.
Therefore, the first step is to study simple equations.
Helen's research is either slow or fast. I will think about it for a while, and then read the rest of my content when I want to.
Teaching every day is a must-do homework, and teaching cannot quickly accumulate inspiration points.
The current teaching has not crossed over from function theory, but has retreated to the stage of computational mathematics. Of course, it is possible for me to explain function theory in half a month. I only explained some main parts [
The content does not involve any in-depth knowledge.
The scope of computational mathematics is too small.
That subject is related to differential equations, vector analysis, matrices, broadleaf transform, complex variable analysis, numerical methods, general theory, mathematical statistics, operations research, control theory,
It doesn't matter whether it's composite mathematics, information theory, or many other branches of mathematics, but it also includes the study of mathematical problems posed from a variety of applied fields.
Therefore computational mathematics cannot be regarded as part of applied mathematics.
What Helen finally talked about was not the problem of algebraic equations. Algebraic equations are very prominent and least involved problems in computational mathematics.
My large class has only been open for about half a month. In the end, not many doctors or even professors came to attend the class. As soon as there were few people coming, they just came.
For example, the professors and associate professors downstairs.
Because the content Helen talked about was not in-depth, and small bodies are not some basics, it would not be helpful to doctoral students and graduate students, and it would not be able to deepen their understanding of knowledge in the field of mathematics.
But it is difficult for professors to gain nothing. At least they can only review it again, which is of little practical significance.
Therefore, the number of people in the classroom has stabilized, with about 70 people coming each time.
Helen was still very satisfied with the number of people. Seventy people were not enough. I continued my lecture, "In the field of algebraic equations, you have recognized a fact that,
There are root-finding formulas for algebraic equations of degree 7 and below. 「
"So for that type of algebraic equation in particular, only approximate solutions can be obtained, and the method of finding approximate solutions is not a numerical analysis method."
I put the book on my watch and continued, "For that type of equation, your research direction is not mainly to find a single type of equation through analysis.
Approximate solution. 「
That's a big research direction.
Just like some doctoral and graduate theses, which rarely include the solution of partial differential equations, the solution of simple algebraic equations is also a small research direction, {
It is difficult to achieve very small results.
Bo Xin continued, "But in practical applications, the solution method of substituting numerical values is more direct."
Liu Rong suddenly raised his hand and asked, "Teacher Wang, for some equations, the approximate solution obtained by substituting numerical values will be better than the degenerate mathematical analysis."
Less complex and direct? 「
"Moreover, even if it is a regression numerical analysis solution, the approximation must be closer than the numerical solution and the exact solution, right?"
Helen said, "There are some cases where this is indeed the case, but in other cases, numerical solutions will be very common."
I nodded and said, "Liu Rong's question is very good. Which method is more suitable, numerical solution or analytical solution, depends on the simplicity of the equation."
"It's an equation that has no clue at all. It's difficult to find the approximate direction using numerical solutions."
"The equation is relatively complex, and it will be difficult to solve it numerically."
As I said this, I suddenly thought of the research problem, and an idea suddenly flashed in my mind, and at the same time, the system was refreshed with new information.
[Task 8, inspiration value +11.]
"That doesn't make sense!"
Helen suddenly had no idea: Xiao Wu's feeling, I glanced at Liu Rong appreciatively, and continued with the rest of the course.
Before the explanation was finished, I returned to the office and started doing serious research.
Later, I encountered calculation problems. 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.
But mathematical analysis is relatively simple, and the analysis process is too likely to be applied by computers.
That simplicity makes the solution possible.
I've always been troubled by this.
Liu Rong's question reminded me that I must take the path of mathematical analysis, and it is relatively more complicated to directly bring in numerical values.
137.
It was a confidential scientific research institution specializing in ballistic research.
The two-story building surrounded by mountains and forests is not the main research and development base of the 137th Institute. Sunlight shone through the window into the conference room, reflecting the faces of the people who were arguing.
An eighty-year-old man put his hands on the table and said forcefully, "Bo Xinrong's ballistic trajectory has no limitations!"
"Your research on maneuverable gliding technology can only be limited to Bo Xinrong's ballistics, but you must also develop other directions."
Another middle-aged man in his seventies replied, "What he said is very boring. Mr. Liu Rongxing did not originally propose the development trajectory of motorized gliding technology.
My direction, what to develop? He doesn't have the ability to say it? 「
The young man immediately replied, "You are saying that you are coming out now, but he is denying that Liu Rongxing's trajectory has no limitations. It is difficult for conventional missiles to maintain such a trajectory.
to hit the target. 「
"In addition, other countries have not studied it. Bo Xinrong's ballistics is public information. It was proposed by Mr. Liu Rongxing when he was studying abroad in Amerikan. Our information can be
There are more than you."
"As long as we can understand that technology thoroughly, we can use computers to lock the route and retreat to anti-missile."
"What you are studying now is that if it is an anti-missile missile, no matter how beautiful the trajectory of the missile is, it is useless? After hitting the target, you still have to rush towards it directly. "
"Currently the only way to ensure hitting the target is at low supersonic speeds, accelerating to Mach 10 or Mach 70, but this technology can be widely used."
The middle-aged Jiu immediately retorted, "He said to develop new technologies, just develop new technologies. How could he not be so right? Now he even knows the direction. And you are in Liu Rongxing Ballistics
They are all leading. 「
"How does he know he is in the lead? Who can be sure of the lead? Has he verified it?"
"How are you sure?"
"I'm sure it is."
The two of them had been banging the table and shouting at each other for a long time, and then they almost started to take action.
The entrance to the conference room.
Pang Sibo couldn't stop smiling after hearing this. Similar arguments happen in every meeting. We are now discussing the direction of future research and development.
That's very important.
Although everyone has mastered Liu Rongxing's ballistic technology, there is no question whether the technology will be perfect, and Liu Rongxing's ballistic has no limitations.
Liu Rongxing's ballistics, not motor gliding technology, is understood to allow ballistic missiles to change directions like cruise missiles, and the trajectory will become very certain.
However, if the use of similar technology takes up a certain amount of weight, not every missile cannot be used.
Domestic missile development has achieved overtaking in a corner to a certain extent.
We have 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, low-end technology can only be used with low-end missiles, and the existence of gaps in the middle means too much accumulation.
It is now easy to determine the direction of future research and development.
Should we continue to study Liu Rongxing's ballistics and add some other technologies to it, or should we combine and develop new technologies?
That's the crux of the study's argument.
Qian Xuesen was really tired of the quarrel outside. When he opened the door and walked out, he saw Pang Sibo. He shook his head and said with a smile, "Professor Zheng, it's really difficult. There has been a lot of quarrels recently, and you are too."
Determine what to do. 「
I said and asked, "By the way, next time he said he would ask someone inside for help? Who did he ask for? I heard that he also applied for 700,000 yuan in funding?"
Pang Sibo laughed and said seven words, "He guessed? It's very unknown."
"Not famous?"
Qian Xuesen thought for a long time, wondering who it was that came out of the county body. Suddenly a name appeared in his mind. I stared and narrowed my eyes and asked, "He is looking for Xihai Elementary School."
Helen? This seventy-year-old young genius proved Goldbach's conjecture and completed the conventional demonstration of the NS equation? 「
"Who else but me?" Pang Sibo said with a smile, "Mathematicians in China are very unknown. You can always go to Qiu Chengwen."
"Right."
Qian Xuesen nodded and continued to ask, "How is it? No results? Seven hundred thousand. This is the first time our institute has spent such a small amount of money on consulting questions for others."
Seven hundred thousand is not a small number.
But it was the first time I spent that money asking other people questions.
Consulting fee?
It cannot be said that 137 institutes are full of elites. Do we still need to consult others? Do you even need to pay such a small consulting fee?
Zheng Guofeng shook his head, "There is no news yet, it won't be half a month."
"Is he being tricked?" Qian Xuesen said with a grin.
"That's true." Pang Sibo smiled and said, "Wang Haoxing, you are still suspicious. If you are really cheated of the money, you can ask the space agency to get it back."
Qian Xuesen smiled and thought about it, "It's true, it's abnormal. That question is too difficult. It's only been discussed by so few of you for a month, right? It was raised last year.
So far, there is no definite direction. 「
"To say that no one can give a definite answer, you are just doubting it."
I said shaking my head.
Pang Sibo said, "You are the same. No one is sure that the problem is true, but you must set a direction. As a top mathematician, my opinion is still very unclear.
Test value. 「
"Right."
Bo Xinrong nodded as he listened.
For such a simple question, it is possible that no one can give a definite result, but if you ask a top mathematician in the world, his judgment on the problem will be very unclear.
worth it.
All we want is a reference.
After Zheng Guofeng had a few words with Bo Xinrong, he returned to the office, thought about it, and called Wang Haoxing.
"Director Liu, can I help you with this? Why hasn't there been a reply?" I asked a complicated question, but I didn't say anything about the county's content.
Bo Xinxing finally understood.
I didn’t calm down at all. I was patting my chest and saying that I was suspicious of Helen. Why did I get a reply to a consultation question in half a month?
That was indeed a simple question, but it was just for Helen to give her opinion.
is it hard?
Wang Hao
, and asked Bo Xin to call back when he saw it.
at the same time.
Helen is writing about eight-dimensional function correction.
The inspiration value has not yet accumulated to "102" points, and there are no clear ideas outside my mind. All that is left is just written down.
The difficulty of the research lies in the calculation, and the difficulty of the summary also lies in the calculation method.
Helen wrote for several hours in a row, and she finished the content in a short time. Because she was not publishing a paper, there was no incidental content, and she did not need to write it carelessly or even at all.
Just ignore it and just complete the main content, which is relatively complicated to write.
I worked until four o'clock in the evening before finally finishing the first part.
"Hey~~"
I stretched hard and looked at it again. Among them, the least difficult equation solving calculation problem.
At that time, I suddenly thought of the study of NS equations.
The current research has nothing to do with NS equations. Functions have limited expansion. Some of the calculations involve simple equations, so some equation solving skills are needed.
Some subsequent research also did not use it, including the approximate solution method of NS equations.
"The external content must be extended to the NS equation. Can the original limited range be extended to the finite?"
I shook my head while thinking, "It should be done for the time being, but it seems that we can't lock a function path and let other functions calculate through the same equation to solve the fixed problem.
path regression transformation, but is limited to two eight-dimensional functions..."
"That doesn't make sense!"
Helen's eyes suddenly lit up as she thought about it, and at the same time, the system stopped reminding her.
[Task 1, inspiration value +7.]
[Inspiration value: 67. 】
"The research on NS equations has not slowed down again!" That's really a joy.
In the research on the NS equation, the inspiration value has always been fixed at 60 points and is moving. I thought that doing that research can also be related to the NS equation.
That’s the real little bonus!
Bo Xin hurriedly recorded it with excitement. It was already one o'clock in the evening as soon as she started working, and she didn't even forget the time.
I feel like my eyelids are fighting and I have to stop.
After leaving the desk, I still checked the messages and found the message from Wang Haoxing, "Call back when you see it?"
Helen checked the time, hesitated, and called.
What if there is no relief?
"Dudu..."
Opposite me, Wang Haoxing was sleeping soundly when I heard the cell phone vibrating in my ear. I dreamed that I was riding a motorcycle and passing by an isolation zone.
"It's so bumpy~"
Wang Hao
Helen lost her embarrassment a little and said, "Professor Liu, you see in his message that he called me immediately after seeing the news, because he was afraid of not easing the matter."
"What's the matter?" Wang Haoxing wasn't a little depressed, but he also became energetic. "You don't want to ask about his...project...forget it!"
I simply said directly, "Do you want to ask him if he has read this question next time?"
"You sent this question to him via the intranet."
"ah?"
"What's wrong?"
"What's there~~"
Wang Haoxing was very understanding. I think the answer to the question is not "feasible" or "yes"?
It’s either two words or eight words. Why are you still sending the document?
With curiosity out of my mind, I could no longer fall asleep. I simply got up and turned on the computer. Before logging into the intranet, I saw the file sent by Bo Xin.
Before I clicked on it, I saw a small pile of mathematics content outside.
The bottom line reads a note, "A trajectory correction method for eight-dimensional curve functions?"
"that……"
I understood everything and immediately opened my mouth, "Helen, did I solve the problem?"
Wang Haoxing looked at the computer for a long time. I seemed to understand the simple content, but it prevented me from knowing what was written outside.
The trajectory correction of the eight-dimensional function is equivalent to the method of returning the missile that has deviated from the trajectory to the same trajectory.
Helen had the answer to such a simple question?
Wang Haoxing was so surprised that I couldn't even sleep at all.
I glanced at the time and felt unsure, so I gritted my teeth and said, "Yes!"
"I can only let you sleep alone!"
"Those who ask questions should stay up late!"
