Chapter 42 Strange Questions and Strange Answers
"I'll try." Xu Chuan replied.
Although he could solve the problems on the paper cards, he did not finish the words and just said that he would give it a try first.
If he used conventional methods, he would definitely be able to do it.
But from Zhang Weiping's words just now, Xu Chuan knew that he should be concerned about the method used when solving problems at night.
Now when solving problems by yourself, you should start from this method.
This idea of converting the Dirichlet function into integrals was only recently developed by him and has not been published yet. I wonder if it can be applied to this kind of mathematical regularity problem.
Turning his attention back to the card in his hand, Xu Chuan carefully read the title on the card again, and then fell into deep thought.
On the side, Zhang Weiping looked nervously and expectantly.
He wanted to go forward and observe, but he was worried that it would interfere with Xu Chuan's problem-solving.
The three questions that Guoji students did tonight were indeed disassembled from paper cards.
It is precisely because of this that he attaches so much importance to this new problem-solving method.
The simpler the problem-solving methods and steps are, the easier it is to write the corresponding mathematical model, which is extremely important for mathematical modeling of information warfare.
Xu Chuan didn't think too much about it. Although this was his goal, he had not yet connected this matter to the information war after IMO.
It’s just now, and there are still a few months until IMO is held.
He only thought that this new mathematical problem-solving method attracted Zhang Weiping's attention. After all, for any mathematician, a brand-new problem-solving method is the focus of attention.
Just like during the previous provincial training camp, he used a new method to solve physics problems and immediately caught Xu Cheng's attention.
After thinking for a while, Xu Chuan picked up the pen and paper in his hand and started to calculate.
Solution: Starting from the Laplace transform, we get L(f(t)/t)(s)=∫sL(f(t))(9)pd
From this, we can get ∫sL(f(t)
by integrating Dirichlet
Calculated through double finite integrals, the integral sequence is (I=∫s∫)
Certificate:
The key to solving the Dirichlet function by the simplification method is to convert it into a Dirichlet integral. This step is performed through mathematical analysis or complex analysis.
However, as the Dirichlet function is a measurable function that is discontinuous everywhere, mathematical analysis and complex analysis are not applicable to all situations.
At least in this complete question, Xu Chuan could not find any place to use mathematical analysis and complex analysis.
After thinking for a while, he decided to twist the Dirichlet function law through Laplace transformation and double finite integral.
Although this method is feasible, it is also troublesome.
The most troublesome part is the base conversion included in the question. When calculating numerical values, it is necessary to convert the decimal system commonly used in mathematics into binary, which is very troublesome.
Fortunately, he had studied binary for a period of time before, so he could smoothly convert the Dirichlet function into the Dirichlet integral without interrupting the calculation.
After converting the function into an integral, the next step of thinking becomes much smoother. Just use the complex variable function and the integral to transform it, and then solve it.
It took Xu Chuan a while to calculate the answer.
However, the calculated answer made him feel very confused.
(116.72) (39.56) (14.1225)!
Three sets of numbers, a very strange answer, at least he has never seen anything like it.
As mentioned before, the properties of the Dirichlet function are quite special. It is a function defined in the range of real numbers and has a discontinuous value range, and it is an even function.
Normally, its answer value will be evenly and symmetrically distributed in the two segments of the Y-axis, that is, any x within the domain of function f(x) will have f(x)=f(-x).
But it is obvious that the above three sets of values do not conform to the laws of Dirichlet function at all. But he figured out the answer again. What is the situation?
Staring at the answer, Xu Chuan was a little confused. For a moment, he even wondered if he had made a mistake in the solution process to get such a set of numbers.
After carefully re-verifying his solution process, he finally determined that there was nothing wrong with his solution process, but the problem was the problem.
"Teacher Zhang, please see if this answer is correct. Why do I feel there is something wrong?"
After confirming that his answer steps were correct, Xu Chuan stood up and handed the manuscript paper in his hand to Zhang Weiping who was standing aside.
"Have you solved it?"
Zhang Weiping was in a daze and looked at his phone. About fifteen minutes had passed.
Can an encrypted message be deciphered in fifteen minutes?
This speed is faster than most of the mathematics professors in the Information Security Department.
Is this possible?
A high school student with better math skills than most math professors?
Or is this method of solving problems really that simple? Or maybe he didn't solve it and wrote the wrong solution process and answer?
Zhang Weiping couldn't help but swallowed his saliva, stretched out his hand to take the manuscript paper and read it.
He didn't look at the proof process first, but looked directly at the answer at the bottom.
(116.72) (39.56) (14.1225)!
The answer is absolutely correct!
Looking at the three sets of numbers on the manuscript paper, Zhang Weiping's breathing suddenly became heavy.
If the answer is correct, then the process will most likely be correct.
Without a correct derivation process, it is impossible to just write a few answers to match the set of answers.
If the process is correct, then this kind of problem-solving ideas and methods.
Thoughts flashed through his mind, and Zhang Weiping quickly turned his attention to the verification process that occupied most of the page.
Half an hour later, he finally breathed a sigh of relief, raised his head and stared at Xu Chuan like a monster.
He really couldn't understand the student in front of him now.
For most high school students, even those who can compete in IMO, the three years of high school are basically the stage of laying the foundation.
Even if a genius can accumulate enough university knowledge in high school, accumulating knowledge and applying this knowledge like a fish in water are two completely different concepts.
What's more, this kind of innovation is even more rare.
Without integrating the knowledge in your mind, it is impossible to innovate.
More importantly, this current problem-solving method is not simply knowledge in the field of mathematics.
Use Laplace transform and double finite integral to convert the Dirichlet function into Dirichlet integral, then use the complex variable function to calculate the integral, and then solve it.
Although the proof process of this problem-solving idea is purely mathematical language, the idea is a fusion of calculation formulas for calculating critical and linearly independent special solutions of damped free vibration equations in the field of physics
Compared with innovation in the field of pure mathematics, this kind of innovation is more difficult.
After all, a person is generally proficient in only one area of knowledge, and there are very few geniuses who can master mathematics and physics.
Even if there is, such talent is usually revealed only after entering university or even graduate school.
In high school, he couldn't even think about it.
(End of chapter)