Question 1: What is power? There is an inverse relationship between the size of an individual and its ranking, R(x)=ax (-b power). Among them, x is the scale (such as population, performance, turnover...), R(x) is its ranking (the first one has the largest scale), a is the coefficient, and b is the power. When both sides take logarithms (log), the formula becomes log(R(x)) = log(a) - bBlog(x). If log(R(x)) is the X-axis and log(x) is the Y-axis, the distribution graph will be a straight line with a negative slope. The smaller the absolute value of the slope, the smaller the scale difference.

The phenomenon of the power law was discovered more than 100 years ago. Many empirical studies have found that factors such as urban population, website size, frequency of (English) vocabulary, gross national product... all show a power law phenomenon ( isoc/..._2 ). Among them, the most famous is Zipf's Law, whose power is -1 (linkage.rockefeller.edu/wli/zipf/).

The power law is also an important "self-organization" phenomenon in complex systems (plex systems). There are six characteristics of complex systems: no overall growth control rules, scattered individual interactions, hierarchical structure, dynamic evolution process, constant emergence of novel phenomena, and imbalanced state. A complex system composed of individual nonlinear (equation) interactions may present simple formal rules (self-organizing phenomenon) on the overall level. The power law is one of these very common phenomena.

Research on "Urban System": (1) In 1933, German geographer Walter Christaller proposed the "central place theory", (2) In 1949, Zipf proposed the "Grade Size Law" "(rank-size rule). (3) In 1996, Krugman conducted an empirical analysis using American cities and found that the 130 cities formed in the United States in the past one hundred years (1890-1990) showed a power relationship with a slope close to -1.

Question 2: What inspiration can the law of Hades bring to marketing planning? Use 80% of your energy to market 20% of your customers; it is very important for marketing planning; marketing must first understand the core users, who are the most The valuable 20% of the target audience, in fact, all the basis for positioning in marketing comes from this. The key to successful marketing lies in the rational use of funds, channels, platforms, human resources and other resources to deliver products to target customers to generate purchases. Wherever you focus your resources, the final results will be shown. Therefore, the law of Hades can basically be regarded as one of the basic laws of marketing.

Question 3: Will XP take full advantage of the hardware performance than 98, so that the game can run more smoothly? As a system that has been in service for more than ten years, it has ushered in its destiny. Now, netizens all over the world can't help but stand in awe of this system that has tenaciously existed in Microsoft for more than ten years. Only by constantly exploring, trying, and innovating can the system operation be made more humane. In this regard, XP cannot compete with 7 and 8.1.

Question 4: What is the difference between exponential and power law? exponential

adj. exponential

n. exponential

power law

Power law; power law

Question 5: Ask about the meaning of an English notation. In fact, it is just a word-like thing. I don’t know what it means. It is similar to the power of a number. ROUTE66 is the name of a famous highway in the United States. It later became the trademark of one of the most commonly used GPS navigation software on smartphones.

This should refer to the latter. As for the "1" in the upper right corner, if you look at the end of the article or the footer, it should be something like a comment.

This sentence roughly means

It may eventually become the mainstay of the so-called data super highway, or it may become like the United States by widening and adding new channels. The highway has the same existence as Route 66 in history.

I just translated it casually, don’t go into details. .

The arc should compare something (a network?) to an American highway extending in all directions, connecting "data" everywhere, just like Route 66 does to an American highway.

Hope this helps.

Question 6: Ask a question about Taylor's formula in advanced mathematics. The (A-B) type of Taylor's formula expansion principle: the principle of lowest power

Expand A and B until the coefficients are not equal to the lowest power of x.

Question 7: What is the difference between exponential and power law? exponential

adj. exponential

n. exponential

power law

Power law; power law