2009年11月26日 星期四

Log Is Everywhere

今日聽seminar時忽發奇想,不如在這裏玩一個遊戲(要大家參與的)。數學上有很多重要的函數,其中一個就是logarithm(這裏不管是還是都可以)。這個函數涉及的範疇科目包括數學、物理、化學、計算機科學、各種工程學、天文學、金融等等。我想大家可以在這裏接力每人列三個logarithm出現的地方,看看可以去到幾長。

我先開始吧:

1)

2) 一種不穩定的物質進行radioactive decay。若它在k秒內質量由1變成,則該物質的half-year為

3) 絕大部分在現實使用將數字排序(sorting)的算法(algorithm),其運算時間為

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規則:每人只可以列最多三個,但少一些是可以的(就是說你只想到一個,就列一個吧)。

6 則留言:

Pop 提到...

化學:
pH = -log [H+]

Pop 提到...

物理:
dB = 10*log(I/Io)

something 提到...

黎克特制~

tobywhcheng 提到...

Hyperbolic Geometry:
metric of the half plane

Applied maths:
Logarithmic spiral

Thermodynamics or information theory:
Entropy and Stirling's approximation

Optics:
Optical thickness and skin depth

Astronomy:
Magnitude of stars
(and hence in general,
Stevens' power law)
Palermo Technical Impact Hazard Scale, or Torino Scale

Cartography:
Mercator projection

Accounting or Auditing:
Benford's law

Music:
frequency of pitches

basically whenever you have an exponential, you are associated with a log

P.S.
There's a matrix inversion method described in Numerical Recipe. The computational cost of which scales as N^{log_2 7}, compare to LU in N^3

Pop 提到...

play game, u need to read the rule first :)

提到...

Prime Number Theorem
number of primes < x ~ x/ln(x)

Fractals
In calculating the fractal dimension by "box dimension"

Thermodynamics/Statistical Mechanics
Boltzmann entropy, von Neumann entropy
(application:Clausius-Clapeyron equation, Chemical Reaction Rate, ...)