Zhan Guyue and others had breakfast and continued walking. Looking from a distance, there is a mountain.
A few people were herding sheep on the mountain, a lot of sheep. There are several small peaks, and a few bundles of fresh grass are placed on the highest peaks. There is very little grass on the hillside.
Those few people were watching from the side. Probably a sheep herder.
Zhan Guyue said: "What are they looking at?"
Dong Chu said: "Which group of sheep can reach the top of the mountain first? They will watch the sheep that reaches the top of the mountain first, and then lower their heads and write down it."
Zhan Guyue said: "They didn't lower their heads, they just stood."
Dong Chu said: "Well, if it were me watching the sheep climb the mountain, I would write down which sheep climbed to the top of the mountain first."
Zhan Guyue said: "Isn't herding sheep just watching the sheep eat grass? What's the use of looking at the top of the mountain?"
Dong Chu said: "Maybe it's because there is a lot of grass on the top of the mountain."
Zhan Guyue said: "Does he know which sheep went up first?"
Dong Chu said, "Don't you remember? Every sheep looks the same."
Zhan Guyue said: "I can tell the difference between the sheep I raise."
Liu Mozhi said: "There are many, almost a hundred, let me see."
Dong Chu said: "This is a farm. There is no need to record who goes up first."
Liu Mozhi said: "If it were me, I would write down which end reached the top of the mountain first. After all, I like analyzing data."
Dong Chu said: "They don't analyze this data. What's the use of analyzing it?"
Liu Mozhi said: "It works. Next time, let other sheep go to the top of the mountain to graze first. This will make it more balanced."
Sheep were just grazing on the mountain opposite. Everyone thought that there was a lot of discussion here and they were just looking for something to talk about.
Until now, Mr. Jiang has not notified the specific location and time of the seminar, which is too urgent. But Mr. Jiang and the teacher are both busy people, and the dragon is hard to find because it is nowhere to be found. It turned out that when I came out to look for him, I couldn't get in touch with him for a long time. I guess something happened, so I'll wait here. This time the teacher also paid more attention to the meeting and sent him over. I really want to ask Mr. Jiang and his colleagues for advice.
There were two young men talking next to them.
Mao Mo and Angui looked a little excited. "Let me tell you about the situation here." Angui listened excitedly, but then he looked hesitant.
"You take it too much for granted." Angui said anxiously. "I want to tell you my opinion." The two of them talked in a crackling manner, with a fast pace and a quick talk and a quick temper. "One more thing. You don't see the behavior of the people in this town. It's very strange," he said pointedly. "Yes, didn't you see?" Angui had a look of contempt on his face.
They asked the two young people: "What are you discussing? Are you also studying mathematics?"
"Didn't you think of anything when you saw this?" Angui asked them.
"No."
"The first thing that comes to mind is optimization." Angui said. "There are several common methods for optimization. 1. Gradient descent method: The gradient descent method is the earliest and simplest optimization method. In general, its solution is not guaranteed to be the global optimal solution, and the speed of the gradient descent method is not necessarily The fastest. The optimization idea of the gradient descent method is to use the negative gradient direction of the current position as the search direction. Because this direction is the fastest descent direction of the current position, it is also called the steepest descent method. The closer the steepest descent method is to the target value , the smaller the step size, the slower the progress. 2. Newton's method: Newton's method is a method of approximately solving equations in the real number domain and the complex number domain. The method uses the first few terms of the Taylor series of the function f(x) to find The root of the equation f(x) = 0. The biggest feature of Newton's method is its fast convergence speed. 3. Conjugate gradient method: The conjugate gradient method is a method between the steepest descent method and Newton's method. It only needs to use the first-order derivative information, but overcomes the shortcomings of slow convergence of the steepest descent method and avoids the shortcomings of Newton's method that requires storage. Its advantages are that it requires a small amount of storage, has step convergence, high stability, and does not require storage. No external parameters are required. 4. Heuristic optimization method: Heuristic method refers to a method of discovery based on empirical rules that people take when solving problems. There are many types of heuristic optimization methods, including classic simulated annealing methods, genetic algorithms , ant colony algorithm, particle swarm algorithm, etc. 5. Lagrange multiplier method: As an optimization algorithm, the Lagrange multiplier method is mainly used to solve constrained optimization problems. Its basic idea is to introduce Lagrange multiplier method. The Granger multiplier will contain
The constrained optimization problem of variables and k constraints is transformed into a problem containing (
+k) unconstrained optimization problem with variables. The mathematical meaning behind Lagrange multipliers is that they are the coefficients of each vector in a linear combination of the gradients of the constraint equations. "
"Then which way does this flock of sheep get to the top of the mountain?" Zhan Guyue said.
"Heuristic optimization method." Angui said.
For example, the ant colony algorithm. Ants find the shortest path, mainly relying on pheromones and the environment. Suppose there are two roads leading from the ant nest to food. At the beginning, the number of ants on the two roads is about the same: when the ants reach the end, they will return immediately, and the ants on the shorter road will The round trip time is short and the repetition frequency is fast. The number of ants traveling back and forth per unit time is large, and more pheromones are left behind. This will attract more ants and leave more pheromones. The opposite is true for long paths, so more and more ants gather on the shortest path. This is an optimization method. You can find the shortest path, the maximum value, and the minimum value.
Liu Mozhi said: "Are these sheep numbered?"
Zhan Guyue said: "Maybe it looks different? The shepherd is more familiar with it."
Dong Chu said: "I still believe that I can recognize people. For example, security guards can recognize people entering and leaving an office building. But it is too difficult to recognize a sheep's face."
Zhan Guyue said: "Maybe the sheep have numbers on them."
Dong Chu said: "It's possible. We are standing too far away and can't see clearly. We can take a closer look."
They walked along the path on the hillside.
The hillside is not too high. After a while, he walked closer to the sheep. It seems that there is indeed a sign with numbers on it.
There are some trees next to it, as well as some telephone poles and signal base stations.
After walking for a while, we reached the top of the mountain. Look into the distance. There are also some ginkgo trees and magnolia trees with broad leaves and thick shade. The river meanders. There are bungalows and low buildings beside the woods. Under the light mist, it is calm and beautiful.
Liu Mozhi said: "Let's continue going down the mountain along the path."
Zhan Guyue said: "Okay. Walk towards the woods."
There is an open space near a bungalow. This should be a farmer.
On one side is a plow moving back and forth, and on the other side is a millstone rotating in a circle. As the plow moves, the millstone rotates. It seems to be a linkage device.
Several people stood nearby, watching the position of the plow machine and millstone.
An old man is very strong, with a light blue-gray sun hat on his head, dark olive green clothes, overalls, a blue belt around his waist, and a pair of old pattern cloth shoes on his feet.
A young man is tall and broad-shouldered, with long arms and legs, and black curly hair. The two eyebrows are thick and black. A pair of red phoenix eyes and a flat nose. Fair skin and a smile.
Dong Chu said: "These are people doing farm work. One is plowing the field, and the other is pushing the millstone."
"It seems that they are studying the positional relationship between the plow machine and the millstone, and maybe they are trying to derive some formula." Zhan Guyue said.
"Yes, the formula, we came here and said we were going to hold a meeting, but so far we have nothing to show for it." Liu Mozhi said.
"They are studying formulas, right?" Dong Chu said.
Liu Mozhi said: "The relationship between a straight line and a circle? What formula is this?"
"Straight lines map to circles, and circles map to straight lines." Dong Chu said. "It's like the domain of time and the domain of complex numbers."
Z transform can transform discrete time series into expressions in the complex frequency domain. The Laplace transform can transform a continuous time signal into an expression in the complex domain.
The Laplace transform is an integral transformation commonly used in engineering mathematics. It is also known as the Laplace transform. It is a linear transformation that can convert a function with a real parameter t (t ≥ 0) into a function with a complex parameter s.
The Laplace transform converts the time domain signal into a complex domain signal, and conversely, the inverse Laplace transform converts the complex domain signal into a time domain signal.
In some cases, it is not easy for a real variable function to perform some operations in the real number domain. However, if the real variable function is subjected to Laplace transformation and various operations are performed in the complex number domain, the operation results are then transformed into Laplace transforms. Inverse transformation to obtain the corresponding result in the real number domain,
In classical control theory, the analysis and synthesis of control systems are based on the Laplace transform. One of the main advantages is that transfer functions can be used instead of constant coefficient differential equations to describe the characteristics of the system. This allows an intuitive and simple graphical method to determine the entire characteristics of the control system and analyze the motion process of the control system.
The Z-transform of discrete-time signals is an important tool for analyzing linear time-invariant discrete-time system problems. It converts the time-domain mathematical model of linear shift (time)-invariant discrete systems, the difference equation, into an algebraic equation in the Z domain, making the discrete system Analysis is also simplified.
"They are not farmers. I see that the young man has fair skin and has not been exposed to the sun often." Zhan Guyue said.
"What are you doing?" Zhan Gu asked over.
The young man said, "In this open space, we are plowing the ground and grinding flour at the same time."
"Are these two sides connected?" Zhan Guyue said.
"Yes, together, the tractor pulls the plow, and by the way, it also pulls the flour grinder."
"Does it need to be so laborious?" Zhan Guyue said.
"I'm just having fun, but it saves me some time grinding the dough."
It also sounds reasonable. But I haven't seen anyone do this. Several people were looking at the wheat field nearby. There are wheat, corn, rapeseed, pepper, etc. in the fields nearby, and various grains and vegetables are hung outside the house, which is the style of farmers in the fields.
As I was walking, I saw three people under the tree.
Qi Ao said straightforwardly, Mr. Xun plowed the rice and listened attentively. There was a look of surprise on his face. Several people are intoxicated in the joy of thinking.
"I also observed the behavior of people in the town." He said concisely and concisely. There was a look of fear on Young Master Xun's face, and a look of hesitation on Li Daodao's face.
"Hello, are you also invited to the meeting?" Dong Chu went up to say hello.
"Yes, we study computers. Chess, Xun Shao, and plowing rice."
Dong Chu said, "What are you discussing?"
"The unfinished business in the institute has nothing to do now anyway, so let's continue working. It's about computer software."
"We are Zhan Guyue, Dong Chu, and Liu Mozhi. I think it is necessary to meet with everyone and discuss our current situation. Mr. Jiang cannot be contacted. Mr. Tang is also missing. I don't know if there is any danger. ." Zhan Guyue said.
Qi Ou said: "What does this circle represent? Feuerbach's circle? The midpoint of the three sides of the triangle, the three heights of the vertical feet and the three Euler points [the midpoints of the three line segments obtained by connecting the vertices of the triangle and the vertical center] 9 The points make a circle.”
Xun Shao said: "We also searched the millstone and found no triangular marks."
If it is a Feuerbach circle, you can also think of Simson's line. A perpendicular line is drawn from a point P on the circumcircle of the triangle to the three sides of the triangle. The three perpendicular legs must be located on a straight line. This straight line is called Simson Line.
For a three-point hypocycloid, take the center of the Feuerbach circle as the center and a radius three times the radius of the Feuerbach circle. The two circles are concentric circles.
It seems they are looking for problems related to circles.
He thought again of the two groups of people he met earlier. The people who are currently known to be here for the meeting include Tang Ling and Yu Cheng who are majoring in mathematics, Mao Mo and An Gui who are studying algorithms, and Qi Ao, Xun Shao and Li Daoda who are majoring in computer science. If you have something to discuss, you can go to the conference room where Mr. Tang held the meeting last year.
