“I recall just enough group theory from university that I sometimes think of PCs as being like a coset of 2 elements – the +1 version and the -1 version, which thus are an unoriented element.”
“To Moshe, as you say, there have been studies of time dependent string backgrounds, orbifods of flat spacetime, coset constructions, linear dilatons etc.”
“My understanding is that a few examples have been explored, such as linear dilatons, coset constructions etc. but that either there was still a static metric (Einstein or string frame) or there were unresolved issues of instabilities.”
“Using a combination of mathematical tricks and careful programming, we were able to solve a complete coset of H, either optimally, or with sequences of twenty moves or less, on a single desktop PC, at the rates shown in the table at left.”
“Each coset would take a "good PC 20 to 30 seconds to sort", said Prof Davidson, meaning it would take a huge amount of time to compute with a standard desktop PC.”
“At an optimistic 20 seconds per coset, this would have taken a reasonable PC the best part of seven months to solve, and the team started to look around for a supercomputer to carry out the processing for them.”
“This coset is used by our leaders to imply this without faith because they use law there own law not gods law.”
“The main idea is to use Theorem 1 to trap most of X inside a coset progression, at which point one can use Fourier-analytic additive combinatorial tools to show that the distribution is "smooth" in some non-trivial direction r, which can then be used to approximate the discrete distribution by a continuous one.”
“This is essentially a sharp characterisation of such sets, except for the fact that one would like a more explicit description of these coset nilprogressions.”
“Euclidean geometry, the relation between figures that can be superposed by rigid motions modular arithmetic, the property of integers having the same remainder on division by a given modulus ring theory, the property of elements of a ring lying in the same coset of a given ideal matrix theory, the property of matrices relating to the same abstract algebra, an equivalence relation which respects algebraic operations”
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