God's Crown
Chapter 90 Bottleneck
After Gou Liqun hummed, he didn't continue talking.What An Yan said is indeed correct, it is indeed very difficult to rely on the two of them to achieve the result, but if other people are added to the result, the result will not be so difficult.After all, there are many people and power is great, and other people don't understand calculation as well as they do, but there are still so many people.Even if the result doesn't come out, there should still be a breakthrough.In addition, school itself is about to start, and those who are on vacation are about to come back.
An Yan thought that maybe he would be able to return to the University of Zurich in the near future, but these things are still uncertain.There is no guarantee to anyone that they will be able to make a breakthrough within this year.Graphene itself is a worldwide problem. With these people, if they can make a breakthrough, they can be regarded as their luck is good enough. A blind cat meets a dead mouse.
Of course, luck itself is also a kind of strength.
After packing up their things, An Yan and Gou Liqun went back to the dormitory alone, and went back to the hotel to rest.
For the next few days, An Yan and Gou Liqun continued to make graphene models.But unfortunately, none of them were able to make it. It seems that there are still some things that need the help of more people.
An Yan looked at his mathematical model and thought for a while, but he didn't know which step was wrong. The only thing he can be sure of now is that he must have made a mistake in some step.And there was a mistake when introducing the mathematical formula. The previous idea is not used at all now.As if something was different, I pondered for several days.An Yan still didn't find out what was wrong, and Gou Liqun also showed An Yan the mathematical model.
It's a little odd that neither of them has figured out exactly what went wrong.Both of them looked at the mathematical model and found that the calculated data were the same, and not quite the same as the theory.That is to say, this data is wrong, it is not the theoretical data, and it is even much worse than the theoretical data.
In fact, An Yan was a little embarrassed, because he was going to do this, but now he realized that many places seemed to be different from what he had imagined, and there were still many places that were too difficult and beyond control range, it's just that he's dropped it so many times.For example, the twin prime number conjecture, or the flow field.He really can't give up on graphene research now, even if he dies to the end, he still has to make graphene.
No matter how long it takes, even if he can't graduate after a year, he still has to make graphene batteries.Since the professor asked him to take over the graphene research group, he trusted him to be competent for the graphene research group. If he didn't make something, he would be sorry for the professor's trust.
In addition, Professor Li brought him the money from the big dog, so even if he couldn't embarrass Professor Li, he had to make this thing.
"Brother Qun, we've reached a bottleneck now, we need to make a total calculation." An Yan put down the pen in his hand, and turned to look at Gou Liqun who was still studying the graphene model.At this moment, Gou Liqun was thinking about the graphene model and calculating.Hearing An Yan's voice, he raised his head, looked at him and said, "Tell me, how should we sum up? I think, if we really want to count up, I'm afraid we really have to wait until they return to school. It's not until they return to school It's getting late, um, probably tomorrow or the day after tomorrow, I can go back to school. At that time, let them discuss this matter together, and finally we will count it up?"
"Hmm..." An Yan frowned, resting her chin with her hands, and thought for a while, "I'm thinking about it, maybe before they come back, I will be able to find out where we do it. wrong."
Gou Liqun didn't speak, just nodded slightly.He has a terrible headache now, and he doesn't know what to say about it.Under the current situation, they must study first, and when the group of researchers come back, everyone will study together.But before that, they may leave this thing behind and not study it, so they definitely need to continue to study it.
It's just that he definitely can't research it now. As for An Yan, it seems that he hasn't researched it much.This problem is a bit serious, after Gou Liqun thought for a while.When he raised his head again and looked at An Yan, he found that An Yan had already counted on the blackboard with his hands.
He pondered and said, "An Yan, why don't we ask the professor first? Then come and see what's wrong?"
"The professor still has some research on graphene. However, as for whether the professor can know about our current situation, I... I don't know." Gou Liqun said that his voice became softer afterward.
Professor Li has indeed done some research on graphene, but the research is not that deep.Perhaps the problems they are encountering now cannot be solved by Professor Li.
An Yan was stunned for a moment. When he heard that Gou Liqun was looking for a professor, he suddenly thought that he could also look for a professor.He remembered that at the physics conference, not only had Professor Li's email address, but he even had to go to Professor Constantine's email address.If we talk about the current understanding of graphene, I am afraid that Professor Constantine is at the top level in the world.
To ask Professor Constantine, naturally you need to send the model you have made to Professor Constantine.There is nothing wrong with An Yan, after all, this is not a project of his alone, so naturally such matters need to be consulted with Gou Liqun.If Gou Liqun disagreed, then this matter must not be done.
An Yan still understands this principle, he can still distinguish clearly what can be done and what cannot be done.
"Brother Qun, I have an idea, would you like to listen to it?" An Yan organized his words, "This method may not work, but I think we can try it."
"Tell me." Gou Liqun became interested. They have been troubled by this problem for several days. If there is a way to solve this problem, it will be a very good thing.His eyes were fixed on An Yan, motionless.
"It's just that I have Professor Constantine's email address, if you think it's okay, we can email Professor Constantine, maybe he can point out to us what's wrong. It's just that if we want to unravel this The problem is that the current mathematical model needs to be sent together. When the time comes..." An Yan looked at Gou Liqun, afraid that he would be angry, "What do you think?"
His face was full of caution, as if he was afraid that he would offend Gou Liqun somewhere.
"Konstantin?" Gou Liqun was taken aback for a moment, "You mean the professor who made graphene?"
"If it's him, maybe we can really see what's wrong with our mathematical model, but..." Gou Liqun was still a little puzzled, "Do you think it's feasible?" His meaning is very clear, if they work hard It is not worth it if the hard-working mathematical model is used by others.
After all, this mathematical model took them more than a month of effort, if it is just used by others.He will definitely collapse, even though this mathematical model is immature now, and even a bit too confusing and wrong.But this is their hard work, how can they just let others use it.
"Are you worried...will it be used by Professor Constantine?" An Yan said with some doubts, "Actually, I don't think so. Professor Constantine is a world-renowned professor and a Nobel Prize winner after all. In terms of our mathematical model, to be honest, I think Professor Constantine should not like it."
After staring at the mathematical model for a while, An Yan shook his head and said, "To be honest, if it weren't for the fact that I made this model, I might not like this mathematical model either. It's really too bad." An Yan covered her face and said, "The front is fine, but when it comes to core computing, it is completely wrong, and there is nothing to argue about. That's why I said that if this data were given to me, I might not look."
"That's right." Gou Liqun said with some embarrassment, "Then let's show this mathematical model to Professor Constantine?"
If An Yan didn't say what he just said, Gou Liqun probably wouldn't have sent this to Professor Constantine.Although this thing may not have any value at all in the eyes of others, in Gou Liqun's view, it is quite valuable.After all, this is something he made, so how could it be worthless.
Even if others think this thing is worthless, he will regard it as a priceless treasure.
But after An Yan said that, it was different.After all, An Yan contributed more than him, since An Yan believed that Professor Constantine would not steal their achievements.So naturally he has no more opinions, and now they can't find a better way.I originally wanted to ask Professor Li for help, but unfortunately, Professor Li is not at Peking University now.It seems that there is something, and I went to another place for a meeting.
"However, even if I send it to Professor Constantine by e-mail, I'm not sure he can really reply to us in time." An Yan said after a moment of silence, "I'm not sure about this matter, but I think Asking Professor Constantine for help is indeed the best way so far. Even if Professor Constantine doesn't know how to solve our confusion, he should be able to provide some ideas."
"Brother Qun, what do you think?"
"Okay, since you have already made up your mind, I won't say anything more. So far, we really don't have many methods, and this is also a feasible method. Just do as you said." Gou Liqun spread his hands , took a deep breath, shook his head and said, "Okay, now that this matter is settled, let's go eat first."
The two had been chatting in the laboratory for a long time, and it was almost completely dark. When they left the laboratory, An Yan glanced at the time.It was almost nine o'clock, and their bellies were growling with hunger.
Touching his shriveled stomach, An Yan sighed, turned to look at Gou Liqun next to him and asked, "By the way, Brother Qun, in the next few days I will send our mathematical model to Kang Professor Standing. Maybe I don’t have much time to come to the classroom, so I will trouble you. However, I will also think about this issue by myself in the hotel, and I will refer to the existing literature..."
"Don't worry, I'm not a fool, how could I not know what to do." Gou Liqun patted his chest and said to An Yan as if reassuring, "You can settle this matter in the hotel with peace of mind. At that time, if Professor Li comes back, I will also ask the professor."
"That's good." It's also good to ask a few more people. Maybe after gathering the ideas of these professors together, they will have a clearer idea of how to do future research.
…………
Back at the hotel, An Yan turned on his laptop, and typed the mathematical model and questions on the computer.Because there are too many words, and the data is somewhat difficult to sort out.It was already a week later when An Yan sent it to Professor Constantine and Professor Benson.
This week, in addition to editing documents, An Yan also searched for the latest literature on the Internet.The latest information about graphene seems to be a breakthrough made by myself.The rest of the people used their own experimental data as a theoretical basis after their own breakthroughs, and obtained some theoretical results.
It’s okay to take a look at it. If something has not been tested, it will be very miserable if it is taken seriously.
Not being able to find the literature he wanted, he was quite a bit discouraged.There are so many documents, but none of them are about the next data and experiments after the breakthrough of graphene.
Rubbing the center of his brows with a headache, he drank a cup of coffee while carefully reading the documents.Not long after he sent emails to Professor Constantine and Professor Benson, he didn't think the professors would reply to him so quickly.So when he was reading documents, he was quite leisurely.
I don't know what's going on with Brother Qun, I haven't been to the laboratory for a week.However, Brother Qun is much better than the people in the laboratory of the University of Zurich before.
That group of people seemed to be clocking in for work, but the laboratory at Beijing University was different.Although Brother Qun said that he was too tired and needed time to rest.But when it's actually done, it doesn't hold back at all.Even like An Yan, it will be an endless situation when you study it.It's almost the kind of person who struggles with the experiment to the end, and the person in charge always has such an attitude.I believe that the entire Beijing University experimental team will not be too far behind, An Yan is particularly assured that Gou Liqun will lead the entire team well.
After looking at the literature for a while, I didn't find the literature I wanted.He changed his mind, since there is no graphene data, he can look at the progress of mathematical data.This itself is a combination of mathematics and physics. If there is progress in mathematics, will it bring some changes to his research?This is also impossible to say.
He has been doing a graphene experiment for almost a year.A lot of things are already very familiar.
Therefore, when reading documents, he does not need to compare them with the graphene materials. He just goes through them once in his mind, and it is almost the same.
After reading a circle of materials about mathematics on arXiv, An Yan thought that there were no new documents published recently.Sure enough, these things still need to be studied by oneself, and others seem a little unreliable.
After thinking about it, I got off the computer.Pick up the ratio in your hand and start to calculate the graphene data. There is a difference between the theoretical data and the real data, but the error is generally not too large.How to ensure that the experiment I made is within the allowable range of error is a particularly big problem.
I really want to make the subject of graphene as soon as possible!
Gou Dahu did not specify the time when he will complete the graphene project.Just let him make graphene as soon as possible before the experimental team in the United States makes it.The American research group was caught off guard.You know, whoever makes this thing first has the patent.Although both parties may reach the same goal in different ways, the method of doing it is similar.
But if you do it one step earlier, you will be able to collect patent fees.And if it is done one step later, it can only pay the patent fee.
It also means that the United States is expected to collapse unless it withdraws from the patent system.But it is impossible for the United States to withdraw from the patent system. So far, the United States is the country with the largest patent income in the world.It is also a country with the most lucrative patent income, if they do not charge patent fees, or do not pay patent fees.Other countries can naturally continue to use the patents in the hands of the United States and refuse to pay patent fees.
At that time, the losses of the United States will be huge.
Unless the fourth industrial revolution is fully developed, the patents on the American side are useless, and they did not become the first echelon during the fourth industrial revolution.At that time, the United States probably wouldn't care about patents or not.
It's just that at that time, other patent countries may start arguing with the United States because the United States does not abide by the patent rights.
Thinking about it differently, An Yan felt that the patent this time was really necessary.Graphene itself is part of the materials of the fourth industrial revolution, and the places where graphene can be applied are very broad.Almost all high-tech products are related to a certain extent. If the patent of graphene is obtained by the United States, it is estimated that Huaguo will be in trouble for many years.
It's just that it's useless for him to think so much now, he might as well think about what he should do next.
Constantine and Professor Benson may not find out about his past emails this month, or even next month.Well-known professors, especially top professors, are very busy. For example, students' projects, their own projects, etc. are added together, and they are simply too busy.
Even the time to read emails is almost pitiful, and when looking at emails, the chances of finding emails sent by yourself from more than ten or even dozens of emails are even more pitiful.
An Yan didn't hope that the two professors could reply to him. Of course, he had to study this kind of thing by himself!
An Yan thought that maybe he would be able to return to the University of Zurich in the near future, but these things are still uncertain.There is no guarantee to anyone that they will be able to make a breakthrough within this year.Graphene itself is a worldwide problem. With these people, if they can make a breakthrough, they can be regarded as their luck is good enough. A blind cat meets a dead mouse.
Of course, luck itself is also a kind of strength.
After packing up their things, An Yan and Gou Liqun went back to the dormitory alone, and went back to the hotel to rest.
For the next few days, An Yan and Gou Liqun continued to make graphene models.But unfortunately, none of them were able to make it. It seems that there are still some things that need the help of more people.
An Yan looked at his mathematical model and thought for a while, but he didn't know which step was wrong. The only thing he can be sure of now is that he must have made a mistake in some step.And there was a mistake when introducing the mathematical formula. The previous idea is not used at all now.As if something was different, I pondered for several days.An Yan still didn't find out what was wrong, and Gou Liqun also showed An Yan the mathematical model.
It's a little odd that neither of them has figured out exactly what went wrong.Both of them looked at the mathematical model and found that the calculated data were the same, and not quite the same as the theory.That is to say, this data is wrong, it is not the theoretical data, and it is even much worse than the theoretical data.
In fact, An Yan was a little embarrassed, because he was going to do this, but now he realized that many places seemed to be different from what he had imagined, and there were still many places that were too difficult and beyond control range, it's just that he's dropped it so many times.For example, the twin prime number conjecture, or the flow field.He really can't give up on graphene research now, even if he dies to the end, he still has to make graphene.
No matter how long it takes, even if he can't graduate after a year, he still has to make graphene batteries.Since the professor asked him to take over the graphene research group, he trusted him to be competent for the graphene research group. If he didn't make something, he would be sorry for the professor's trust.
In addition, Professor Li brought him the money from the big dog, so even if he couldn't embarrass Professor Li, he had to make this thing.
"Brother Qun, we've reached a bottleneck now, we need to make a total calculation." An Yan put down the pen in his hand, and turned to look at Gou Liqun who was still studying the graphene model.At this moment, Gou Liqun was thinking about the graphene model and calculating.Hearing An Yan's voice, he raised his head, looked at him and said, "Tell me, how should we sum up? I think, if we really want to count up, I'm afraid we really have to wait until they return to school. It's not until they return to school It's getting late, um, probably tomorrow or the day after tomorrow, I can go back to school. At that time, let them discuss this matter together, and finally we will count it up?"
"Hmm..." An Yan frowned, resting her chin with her hands, and thought for a while, "I'm thinking about it, maybe before they come back, I will be able to find out where we do it. wrong."
Gou Liqun didn't speak, just nodded slightly.He has a terrible headache now, and he doesn't know what to say about it.Under the current situation, they must study first, and when the group of researchers come back, everyone will study together.But before that, they may leave this thing behind and not study it, so they definitely need to continue to study it.
It's just that he definitely can't research it now. As for An Yan, it seems that he hasn't researched it much.This problem is a bit serious, after Gou Liqun thought for a while.When he raised his head again and looked at An Yan, he found that An Yan had already counted on the blackboard with his hands.
He pondered and said, "An Yan, why don't we ask the professor first? Then come and see what's wrong?"
"The professor still has some research on graphene. However, as for whether the professor can know about our current situation, I... I don't know." Gou Liqun said that his voice became softer afterward.
Professor Li has indeed done some research on graphene, but the research is not that deep.Perhaps the problems they are encountering now cannot be solved by Professor Li.
An Yan was stunned for a moment. When he heard that Gou Liqun was looking for a professor, he suddenly thought that he could also look for a professor.He remembered that at the physics conference, not only had Professor Li's email address, but he even had to go to Professor Constantine's email address.If we talk about the current understanding of graphene, I am afraid that Professor Constantine is at the top level in the world.
To ask Professor Constantine, naturally you need to send the model you have made to Professor Constantine.There is nothing wrong with An Yan, after all, this is not a project of his alone, so naturally such matters need to be consulted with Gou Liqun.If Gou Liqun disagreed, then this matter must not be done.
An Yan still understands this principle, he can still distinguish clearly what can be done and what cannot be done.
"Brother Qun, I have an idea, would you like to listen to it?" An Yan organized his words, "This method may not work, but I think we can try it."
"Tell me." Gou Liqun became interested. They have been troubled by this problem for several days. If there is a way to solve this problem, it will be a very good thing.His eyes were fixed on An Yan, motionless.
"It's just that I have Professor Constantine's email address, if you think it's okay, we can email Professor Constantine, maybe he can point out to us what's wrong. It's just that if we want to unravel this The problem is that the current mathematical model needs to be sent together. When the time comes..." An Yan looked at Gou Liqun, afraid that he would be angry, "What do you think?"
His face was full of caution, as if he was afraid that he would offend Gou Liqun somewhere.
"Konstantin?" Gou Liqun was taken aback for a moment, "You mean the professor who made graphene?"
"If it's him, maybe we can really see what's wrong with our mathematical model, but..." Gou Liqun was still a little puzzled, "Do you think it's feasible?" His meaning is very clear, if they work hard It is not worth it if the hard-working mathematical model is used by others.
After all, this mathematical model took them more than a month of effort, if it is just used by others.He will definitely collapse, even though this mathematical model is immature now, and even a bit too confusing and wrong.But this is their hard work, how can they just let others use it.
"Are you worried...will it be used by Professor Constantine?" An Yan said with some doubts, "Actually, I don't think so. Professor Constantine is a world-renowned professor and a Nobel Prize winner after all. In terms of our mathematical model, to be honest, I think Professor Constantine should not like it."
After staring at the mathematical model for a while, An Yan shook his head and said, "To be honest, if it weren't for the fact that I made this model, I might not like this mathematical model either. It's really too bad." An Yan covered her face and said, "The front is fine, but when it comes to core computing, it is completely wrong, and there is nothing to argue about. That's why I said that if this data were given to me, I might not look."
"That's right." Gou Liqun said with some embarrassment, "Then let's show this mathematical model to Professor Constantine?"
If An Yan didn't say what he just said, Gou Liqun probably wouldn't have sent this to Professor Constantine.Although this thing may not have any value at all in the eyes of others, in Gou Liqun's view, it is quite valuable.After all, this is something he made, so how could it be worthless.
Even if others think this thing is worthless, he will regard it as a priceless treasure.
But after An Yan said that, it was different.After all, An Yan contributed more than him, since An Yan believed that Professor Constantine would not steal their achievements.So naturally he has no more opinions, and now they can't find a better way.I originally wanted to ask Professor Li for help, but unfortunately, Professor Li is not at Peking University now.It seems that there is something, and I went to another place for a meeting.
"However, even if I send it to Professor Constantine by e-mail, I'm not sure he can really reply to us in time." An Yan said after a moment of silence, "I'm not sure about this matter, but I think Asking Professor Constantine for help is indeed the best way so far. Even if Professor Constantine doesn't know how to solve our confusion, he should be able to provide some ideas."
"Brother Qun, what do you think?"
"Okay, since you have already made up your mind, I won't say anything more. So far, we really don't have many methods, and this is also a feasible method. Just do as you said." Gou Liqun spread his hands , took a deep breath, shook his head and said, "Okay, now that this matter is settled, let's go eat first."
The two had been chatting in the laboratory for a long time, and it was almost completely dark. When they left the laboratory, An Yan glanced at the time.It was almost nine o'clock, and their bellies were growling with hunger.
Touching his shriveled stomach, An Yan sighed, turned to look at Gou Liqun next to him and asked, "By the way, Brother Qun, in the next few days I will send our mathematical model to Kang Professor Standing. Maybe I don’t have much time to come to the classroom, so I will trouble you. However, I will also think about this issue by myself in the hotel, and I will refer to the existing literature..."
"Don't worry, I'm not a fool, how could I not know what to do." Gou Liqun patted his chest and said to An Yan as if reassuring, "You can settle this matter in the hotel with peace of mind. At that time, if Professor Li comes back, I will also ask the professor."
"That's good." It's also good to ask a few more people. Maybe after gathering the ideas of these professors together, they will have a clearer idea of how to do future research.
…………
Back at the hotel, An Yan turned on his laptop, and typed the mathematical model and questions on the computer.Because there are too many words, and the data is somewhat difficult to sort out.It was already a week later when An Yan sent it to Professor Constantine and Professor Benson.
This week, in addition to editing documents, An Yan also searched for the latest literature on the Internet.The latest information about graphene seems to be a breakthrough made by myself.The rest of the people used their own experimental data as a theoretical basis after their own breakthroughs, and obtained some theoretical results.
It’s okay to take a look at it. If something has not been tested, it will be very miserable if it is taken seriously.
Not being able to find the literature he wanted, he was quite a bit discouraged.There are so many documents, but none of them are about the next data and experiments after the breakthrough of graphene.
Rubbing the center of his brows with a headache, he drank a cup of coffee while carefully reading the documents.Not long after he sent emails to Professor Constantine and Professor Benson, he didn't think the professors would reply to him so quickly.So when he was reading documents, he was quite leisurely.
I don't know what's going on with Brother Qun, I haven't been to the laboratory for a week.However, Brother Qun is much better than the people in the laboratory of the University of Zurich before.
That group of people seemed to be clocking in for work, but the laboratory at Beijing University was different.Although Brother Qun said that he was too tired and needed time to rest.But when it's actually done, it doesn't hold back at all.Even like An Yan, it will be an endless situation when you study it.It's almost the kind of person who struggles with the experiment to the end, and the person in charge always has such an attitude.I believe that the entire Beijing University experimental team will not be too far behind, An Yan is particularly assured that Gou Liqun will lead the entire team well.
After looking at the literature for a while, I didn't find the literature I wanted.He changed his mind, since there is no graphene data, he can look at the progress of mathematical data.This itself is a combination of mathematics and physics. If there is progress in mathematics, will it bring some changes to his research?This is also impossible to say.
He has been doing a graphene experiment for almost a year.A lot of things are already very familiar.
Therefore, when reading documents, he does not need to compare them with the graphene materials. He just goes through them once in his mind, and it is almost the same.
After reading a circle of materials about mathematics on arXiv, An Yan thought that there were no new documents published recently.Sure enough, these things still need to be studied by oneself, and others seem a little unreliable.
After thinking about it, I got off the computer.Pick up the ratio in your hand and start to calculate the graphene data. There is a difference between the theoretical data and the real data, but the error is generally not too large.How to ensure that the experiment I made is within the allowable range of error is a particularly big problem.
I really want to make the subject of graphene as soon as possible!
Gou Dahu did not specify the time when he will complete the graphene project.Just let him make graphene as soon as possible before the experimental team in the United States makes it.The American research group was caught off guard.You know, whoever makes this thing first has the patent.Although both parties may reach the same goal in different ways, the method of doing it is similar.
But if you do it one step earlier, you will be able to collect patent fees.And if it is done one step later, it can only pay the patent fee.
It also means that the United States is expected to collapse unless it withdraws from the patent system.But it is impossible for the United States to withdraw from the patent system. So far, the United States is the country with the largest patent income in the world.It is also a country with the most lucrative patent income, if they do not charge patent fees, or do not pay patent fees.Other countries can naturally continue to use the patents in the hands of the United States and refuse to pay patent fees.
At that time, the losses of the United States will be huge.
Unless the fourth industrial revolution is fully developed, the patents on the American side are useless, and they did not become the first echelon during the fourth industrial revolution.At that time, the United States probably wouldn't care about patents or not.
It's just that at that time, other patent countries may start arguing with the United States because the United States does not abide by the patent rights.
Thinking about it differently, An Yan felt that the patent this time was really necessary.Graphene itself is part of the materials of the fourth industrial revolution, and the places where graphene can be applied are very broad.Almost all high-tech products are related to a certain extent. If the patent of graphene is obtained by the United States, it is estimated that Huaguo will be in trouble for many years.
It's just that it's useless for him to think so much now, he might as well think about what he should do next.
Constantine and Professor Benson may not find out about his past emails this month, or even next month.Well-known professors, especially top professors, are very busy. For example, students' projects, their own projects, etc. are added together, and they are simply too busy.
Even the time to read emails is almost pitiful, and when looking at emails, the chances of finding emails sent by yourself from more than ten or even dozens of emails are even more pitiful.
An Yan didn't hope that the two professors could reply to him. Of course, he had to study this kind of thing by himself!
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