Although he could solve the problems on the paper cards, he did not finish his words and just said that he would give it a try first.
If he uses conventional methods, he can definitely 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.
Xu Chuan's attention returned 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’s just now, and there are still a few months until IMO is held.
"Has it been solved yet?"
At least in this complete question, Xu Chuan could not find any place to use mathematical analysis and complex analysis.
"Teacher Zhang, please see if this answer is correct. Why do I feel like there is something wrong?"
If the answer is correct, then the process will most likely be correct.
After confirming that there were no problems with his answer steps, Xu Chuan stood up and handed the manuscript paper in his hand to Zhang Weiping who was standing aside.
He only thought that this new mathematical problem-solving method had attracted Zhang Weiping's attention. After all, for any mathematician, a brand-new problem-solving method is the focus of attention.
(116.72)(39.56)(14.1225)!
Three sets of numbers, a very strange answer, at least he has never seen anything like it.
It took Xu Chuan a while to calculate the answer.
Half an hour later, he finally breathed a sigh of relief, raised his head and stared at Xu Chuan like a monster.
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.
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 more than half of the page.
Looking at the three sets of numbers on the manuscript paper, Zhang Weiping's breathing suddenly became heavy.
Zhang Weiping couldn't help but swallowed his saliva, reached out and took the manuscript paper and looked at it.
Just like during the previous provincial training camp, he used a new method to solve physics problems and immediately caught Xu Cheng's attention.
It is precisely for this reason that he attaches so much importance to this new problem-solving method.
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.
As mentioned before, the properties of the Dirichlet function are quite special. It is a function defined in the range of real numbers, with a discontinuous value range, and it is an even function.
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∫)
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.
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.
Zhang Weiping was in a daze and looked at his phone. About fifteen minutes had passed.
More importantly, this current problem-solving method is not simply knowledge in the field of mathematics.
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).
A high school student has better math skills than most math professors?
Or is this method of solving the problem really that simple? Or maybe he didn't solve it and wrote the wrong solution process and answer?
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, and then solve it.
But it is obvious that the above three sets of values do not conform to the law of Dirichlet function at all.
Without a correct derivation process, it is impossible to just write a few answers to match the set of answers.
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.
For the vast majority of high school students, even those who can compete in IMO, the three years of high school are basically the stage of laying the foundation.
Can an encrypted message be deciphered in fifteen minutes?
This speed is faster than most of the mathematics professors in the Information Security Department.
But he calculated the answer again. What is the situation?
Staring at the solution, 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.
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.
Without integrating the knowledge in your mind, it is impossible to innovate.
However, as the Dirichlet function is a measurable function that is discontinuous everywhere, mathematical analysis and complex analysis are not applicable to all situations.
After thinking for a while, Xu Chuan picked up the pen and paper in his hand and started to calculate.
He didn't look at the proof process first, but looked directly at the answer at the bottom.
However, the calculated answer made him feel very confused.
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.
He really can't understand the student in front of him now.
is it possible?
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.
(116.72)(39.56)(14.1225)!
The answer is absolutely correct!
What's more, this kind of innovation is even more rare.
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.
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.