A question on Farey's sequences.
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From: Ludovicus on 23 May 2010 20:30 Thanks Gerry, That's just that I wanted to know. A formula for determining the rank of a fraction or the fraction knowing the rank, without calculating the former fractions. Otherwise it would be impossible if the order is, say, 10^6. Ludovicus
From: Rory on 24 May 2010 14:27 Ludovicus, you may find some information on the positions of fractions in Farey (sub)sequences of several types here: http://arxiv.org/abs/math/0411026 (remark 7.10(ii)(a) and proposition 7.3(i)), http://www.integers-ejcnt.org/vol8.html -> A24 (remark 2(ii)(b)) Rory
From: spudnik on 26 May 2010 15:59
or, in any numbertheory book that treats it, I'd say. thusNso: there's only one possible cure for that kind of thing; sit back & read Shakespeare, aloud; switch-off with the KJV Holy Bible (translated by WS & co. .-)... unless, you hate Shakespeare more than the British Petroleum oligarchy. thusNso: that is not an "image of a photon," but an "artist's impression" of some heuristic statement by a theoretician (deBroglie e.g., as much status as any of us can have, hereinat). the wave & particle are merely mathematical duals, not that the object in question is both at the same time, or neccesarily both at different times. > http://superstruny.aspweb.cz/images/fyzika/foton.gif thusNso: Death to the lightconeheads; long-live Minkowsksi! thusNso: "real-valued time" is why, we have quaternions; it's the "scalar" in Hamilton's lingo of vectors. now, you mentioned tensors, and that is apropos, because it is used for stress & strain, which are clearly irrereversible; perhaps, that is one of the first math-physics examples of it. thusNso: I haven't read _Disquisitiones_ in Latin, either, but there are good translations & it is highly recommended by the LaRouchies ... they should put it on their website, like they have *Les OEuvres du Fermatttt*, but you can look at some cool tutorials, in the meantime, at wlym.com. thusNso: I never read a word about Palin's hubbie's Seccesh "movement" in the Liberal Media (Owned by consWervatives) and that is sort-of the issue in AZ. I'm all for kids whose parents managed to sneak across the border & give birth, but I was taken aback by the "sense of entitlement" that the older kids have, about college (the DREAM Act; I stated to a group of them, that crossing the border is essentially a Mexican "rite of passage," and it is certainly not very dangerous as a proper hike, if you check the FAQs and maps & so forth from the Mexican goment (and those advocacy/ haven groups in the USA). well, it's either that or college *in* Mexico, or you'll probably be made to join a gang. La Raza d'Atzlan are openly racist, not just by their title; at least, that's the impression that I got, attending one of their meetings at UCLA, two or three years ago -- it's in their God-am constitution. of course, teh real problem is "free trade," and this is already here to roost; the little spill in the Gulf is being used by British Petroleum -- which is also the #1 driller in the Alaska North Slope, that Ted Palin works for -- to creata an "outsourcing" mandate to solve the problem, because we can't do it with our post-industrial cargo cult. well, screw it; read LaRouche, if you want to know the history with Lincoln and his "Spot Resolutions;" Cinco de Mayo should be a pan-american holiday! thusNso: Dear AG candidate Kelly; no change from Jerry Brown's '69 "platform," eh? it is intolerably stupid, insofar as we do need "fossilized fuels TM (sik)," to not get our share from our own "reserves." really, though, it is merely biomass, and the techniques have progressed since '69. Dubya's bro's ban offshore of Florida (and Louisiana) seemed like a tactical maneuver to support the oilcos' scarcity programme in our state. (why O why O why do folks believe, that the oilcos did not support the Kyoto Protoccol, which was just another cap'n'trade "free trade" nostrum, that Dubya'd have undoubtdely signed, if he had been told?) British Petroleum, the balls-out advocate of cap'n'trade, "Beyond Petroleum," is also the biggest company in the Alaska North Slope -- doesn't any body wonder, why no-one asked Palin about her BP-employed hubbie, and his Seccesionist ideals? one must take into consideration, with all of the hype about it, that oil comes out of the ground underwater in "seeps," under pressure. so, how much would come out, if BP et al ad vomitorium were not pumping like crazy? Waxman's current cap'n'trade bill just mandatorizes the huge, voluntary cap'n'trade since 2003 -- tens of billions in hedging per annum. what the Liberal Media (Ownwd by consWervative) don't talk about, is that he brought the first cap'n'trade bill in '91, under HW (who worked with Gore on the Kyoto cap'n'trade). what it amounts to, as Waxman basically admitted to, when he was at UCLA, is "let the arbitrageurs raise the price of energy, as much as they can in the 'free market' -- free beer, freedom!" a small, adjustable carbon tax would achieve the same ends -- as I even read "in passing" in a guest editorial in the WSUrinal, as well as from an "expert" in a UCLA seminar, but who said that it was (some how) "politically impossible" -- without being the Last Bailout of Wall Street (and the City of London). --mister Kelly, please, take me off of your list, Brian H. --Light: A History! http://wlym.com |