Great Country Academician

"I'll try." Xu Chuan replied.

Even though he could solve the problems on the paper cards, he didn't talk too much, he just said that he would try it first.

If you use conventional methods, he can definitely make it.

But from Zhang Weiping's words just now, Xu Chuan knew that what he cared about should be the method used when solving the problem at night.

Now to solve the problem by yourself, you should also start from this method.

And this idea of ​​converting the Dirichlet function into an integral has just been researched by him, and it has not been published yet. I don't know if it can be applied to this kind of mathematical law problem.

Returning his attention to the card in his hand, Xu Chuan carefully re-read the topic on the card, and then fell into deep thought.

On the side, Zhang Weiping watched nervously and expectantly.

He wanted to go up to observe, but he was worried that it would interfere with Xu Chuan's solution.

The three questions that Guoji students did tonight were indeed disassembled from paper cards.

It is also because of this that he attaches so much importance to this new problem-solving method.

The simpler the method and steps of solving the problem, 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 hadn't linked it to the information warfare after IMO yet.

It is only now, and there are still a few months before the IMO is held.

He only thought that this new mathematical problem-solving method caught Zhang Weiping's attention. After all, for any mathematician, a brand-new problem-solving method is the focus of attention.

Just like during the provincial training camp before, 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 began to calculate.

Solution: Starting from the Laplace transform, get L(f(t)/t)(s)=∫sL(f(t))(9)pd

Thus, the Dirichlet integral can be obtained ∫sL(f(t)

Calculated by double finite integration, the order of integration gives (I=∫s∫)

certificate:

The key to solving the Dirichlet function by the simplification method is to convert it into a Dirichlet integral, and this step is obtained through mathematical analysis or complex analysis.

But the Dirichlet function is a measurable function that is discontinuous everywhere, so mathematical analysis and complex analysis are not applicable to all situations.

At least in this complete question, Xu Chuan could not find a place to use mathematical analysis and complex analysis.

After thinking about it for a while, he decided to distort the Dirichlet function law through Laplace transform and double finite integral.

Although this method is feasible, it is not a small trouble.

The most troublesome part is the base conversion included in the title. When calculating the value, it needs to convert the decimal system commonly used in mathematics into binary, which is very troublesome.

Fortunately, he had learned binary for a period of time before, so that he could smoothly convert the Dirichlet function into the Dirichlet integral without interrupting the calculation.

After transforming the function into an integral, the next thought will be much smoother. Use the complex variable function and the integral to transform, and then solve it.

After spending a little time, Xu Chuan calculated the answer.

However, the calculated answer made him feel very puzzled.

(116.72) (39.56) (14.1225)!

Three sets of numbers, very strange answers, at least he has never seen such ones.

As I said before, the nature of the Dirichlet function is quite special. It is a function defined in the range of real numbers and has a discontinuous range, and it is an even function.

Normally, its answer value will be evenly and symmetrically distributed on the two segments of the Y axis, that is, any x in the domain of the function f(x) has f(x)=f(-x).

But it is obvious that the above three sets of values ​​do not conform to the law of the Dirichlet function at all.

But he figured out the answer again. What's the situation?

Staring at the solution, Xu Chuan was a little puzzled. For a moment, he even wondered if he made a mistake in the process of solving to get such a set of numbers.

After earnestly re-verifying his solution process, he finally determined that there was nothing wrong with his verification process, and the problem was the problem.

"Mr. Zhang, please see if this answer is correct. Why do I feel a little wrong?"

After confirming that there was no problem with his answer steps, Xu Chuan got up and handed the manuscript paper to Zhang Weiping who was standing aside.

"Have you figured it out?"

Zhang Weiping was in a daze. He glanced at his phone. About fifteen minutes had passed.

An encrypted message can be deciphered in fifteen minutes?

This speed is faster than most of the mathematics professors in the information security department.

is it possible?

A high school student with better math skills than most math professors?

Or is this solution really that simple? Or, he didn't solve it, and wrote a wrong solution process and answer?

Zhang Weiping couldn't help swallowing, reached out to take the manuscript paper and read it.

He didn't look at the proof process first, but directly looked at the bottom answer.

(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 the correct pushing process, it is impossible to just write a few answers to this 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 took up most of the page.

Half an hour later, he finally breathed a sigh of relief, raised his head and stared at Xu Chuan with shining eyes, like looking at a monster.

He really couldn't understand the student in front of him now.

For the vast majority of high school students, even those who can enter the IMO competition, the three years of high school are basically the stage of laying the foundation.

Even a genius can accumulate enough college knowledge in high school, but 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.

It is impossible to innovate without integrating the knowledge in your mind.

More importantly, the current method of solving problems is not simply knowledge in the field of mathematics.

Use Laplace transform and double finite integral to transform Dirichlet function into Dirichlet integral, then use complex variable function to calculate integral, and then solve.

This kind of problem-solving thinking, although the proof process is a pure mathematical language, but the thinking is a combination of calculation formulas in the calculation of the critical and linearly independent special solutions of the damped free vibration equation in the physical field

Compared with innovation in the field of pure mathematics, this kind of innovation is more difficult.

After all, there is generally only one area of ​​knowledge that a person is proficient in, and there are very few geniuses who can master mathematics and physics.

Even if there is, it is usually only after entering a university or even a graduate student that this talent is revealed.

In high school, he didn't even dare to think about it.