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Tuesday, 01 December 2009 01:04 |
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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
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Monday, 30 November 2009 23:46 |
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De Morgan's transformation
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Tuesday, 24 November 2009 02:18 |
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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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