# Curious Thoughts in Math & Science Math Online Tom Circle

1. Statistical Mechanics: \$latex e^ {- Ht} \$

Quantum Mechanics: \$latex e^{iHt}\$

2. Ramanujian:

\$latex 1 +2 + 3 + …+ n = -frac {1}{12} \$

Tau Special Function:

\$latex boxed {displaystyle sum_{n=1}^{infty}tau (n) x^{n} = x {(1-x)(1-x^{2})(1-x^{3})… }^{24}}\$

3. Boolean Algebra: George Boole (1847 in 《The Mathematical Analysis of Logic》) used Symbolic variables (not numbers) for Logic, inspired by Galois (1832 in Groups & Finite Fields), Hamilton’s quaternion algebra (1843),

AND” \$latex boxed {x.y}&fg=00bb00&s=3\$

NOT” \$latex boxed {1-x}&fg=00bb00&s=3\$

XOR” \$latex boxed {x+y-2x.y}&fg=00bb00&s=3\$

Extra constraints ” \$latex boxed {x^{2}=x}&fg=00bb00&s=3\$

4. Solomon Golomb, Sol: “Linear Feedback Shift Register” (LFSR) – shift left the first register, fill in the back register with XOR of certain “Taps” (eg.chosen the 1st, 6th, 7th registers)

Maximal Length = The shift register of size n will repeat every \$latex 2^{n}-1\$ steps (exclude all ‘0’ sequence).

Which arrangement…

View original post 60 more words ## Author: tomcircle

Math amateur

Posted on Categories math

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