Archive for February, 2012

How strong is your password?

In the online life, security is always a concern. The following link will show the amount of time a PC needs to find your password. The password cracking programs use sort of random generators but are clever enough to check for complete words. So never use a word which exists in the dictionary. As usual, the following factors are important for a safe password: 1) combination of lower and upper case, 2) better to be 16 character long, 3) use numbers and special characters.



cghftkd         32 sec   (8 characters, only lower case)

cghf6tkd       3 hour   (9 char, lower case and number)

cghf+6tkd    2days     (10 char, lower case, number, and special character)

cGhf+6tkd_qrz     5 Million years    (13 char, lower/uppaer, number, special char)

cGhf+6&Vtkd_qPrz   193 Billion years  (16 char, upper/lower, number, special char)

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Energy of earthquakes

The expression Richter magnitude scale refers to a  ways to assign a single number to quantify the energy contained in an earthquake. In this system invented by Charles Richter in 1935, one magnitude more is roughly equal to a factor 32 more energy. That means an earthquake of magnitude 6.0 has 32 times more energy than an earthquake of magnitude 5.0. The below plot shows the amount of released energy in earthquakes with different magnitudes.

In the above image, the energy is expressed in Joule [left axis] and equivalent to ton TNT [right axis]. The black horizontal line shows the estimated energy of the first nuclear bomb dropped on Hiroshima. It roughly weights as a six Richter earthquake. Note that a large fraction of the energy of earthquakes is absorbed in the deep layers of the earth.

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Consider a one dimensional time-independent Schrödinger equation for some arbitrary potential V(x). Prove that if a solution Ψ(x) has the property that Ψ(x) →0 as x→±∞, then the solution must be nondegenerate and therefore real, apart from a possible overall phase factor.


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