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Self-Similar Reverse-Sum Sequences
Tuesday, 01 December 2009 01:04

For any positive integers N and B let RB(N) denote the integer given by reversing the digits of N in the base B.  For example, R10(2316) = 6132.  When the base B is understood, we can abbreviate the notation, and simply denote the digit reversal operation by a “prime” symbol, so the reversal of x is denoted by x’. (This operation is somewhat similar to logical negation, since two consecutive applications is the identity.) It's interesting that for some initial integers x0 and bases B, the reverse-sum recurrence

 
De Morgan's transformation
Monday, 30 November 2009 23:46

De Morgan's transformation

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CP Violation
Tuesday, 24 November 2009 02:18

As the Universe expands and cools and the process of creation and annihilation of matter/anti-matter pairs slows down. Soon matter and anti-matter has time to undergo other nuclear processes, such as nuclear decay. Many exotic particles, massive bosons or mesons, can undergo decay into smaller particles. If the Universe is out of equilibrium, then the decay process, fixed by the emergent laws of Nature, can become out of balance if there exists some asymmetry in the rules of particle interactions. This would result in the production of extra matter particles, rather than equal numbers of matter and anti-matter.

 
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