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Comments:
<0> linear is like y" +y'=f(x)
<0> if you had 0 on the RHS then the solutions would form a vector space, (im sure there's anicer way to say all this)
<1> _llll_: ok, so for linear equtions a non-zero RHS just means an offset vector, right?
<0> yeah
<1> _llll_: we were (informally) taught in a circuit theory lecture that (in tensor notation) for y'=Ay+b one can look for equilibrium points (y'=0), which yields y_\inf:=y=-A^{-1}b, and "shift" the solution space using y^*:=y-y_\inf<=>y=y^*+y_inf=y^*-A^{-1}b, y^*'=y^* (because the added constant tensor doesn't change it)
<1> so now we have y*'=Ay*+A(-A^{-1}b)+b=Ay*
<1> but we're drifting slightly away...I wonder whether it helps to find ALL solutions for the homogenous solution and then reduce the order, instead of finding one and then reducing the order (which seems to be way more straightforward)
<0> you canl find all the heomogoensous solutosna and add a particular solution
<0> ie if all the homog. solutions are Ae^(at) +Be^(bt), and z(x) is a particular solution to the full equation, then the general solution is Ae^(at)+Be^(bt)+z(x)
<1> _llll_: my current problem is that I want to avoid to write the whole thingie as first-order ODE system and use the Wronski determinant to find a particular solution
<1> the problem is how to find z for n-th order differential equation for z >= 2
<1> sorry, n >= 2
<1> do I have to reduce the order with one of the homogenous solutions?
<0> hmm, not sure. but anything that works is good... i guess doing that should work
<1> yeah, but I'm just curious whether there is a less tedious strategy, because using one solution when you have a whole space doesn't sound too intelligent
<1> but probably that would require to use the variation of constant/wronski strategy
<1> ok, applying order reduction according to d'Alembert makes only sense for homogenous equations, the RHS disappears anyway
<1> Manyfold: how can I find a particular solution of a linear homogenous ordinary differential equation using an arbitrary solution, when I already have the homogenous solution space?
<1> reducing the order sounds braindead, because I already have all homogenous solutions
<2> Manny: i just woke up
<1> Manyfold: sorry
<1> http://en.wikipedia.org/wiki/Green%27s_function sounds good
<0> btw "Green function" should be the preferred name (compare "ChecbyChev Polynomials", etc)
<1> if anybody (speaking German) is interested, I understood now how to do it: http://fed.matheplanet.com/mpr.php?stringid=1260534
<1> basically it IS the Wronski stuff
<1> thanks for your help
<1> also, everybody interested in maths and listening to me now should make sure that he understands the fundamental concept of binomes because it is VERY handy for linear ODE :)
<3> can two circunferences (placed in the space) be tangent and at the same time be "not perpendicular" (i.e.: the plane which contains one circunference isn't perpendicular to the another which contains the other)?
<4> sure. you can get 2 tangent circles in one plane e.g.
<3> lieven: ok, sorry, exclude that case
<4> even then, you can get them with the planes in any angle
<3> lieven: ok thanks that's what I wanted to know, but I'm not sure why...
<5> how do I get n days after a given date?
<5> what's 100 days after july 4th 2006 ?
<6> 30 days has september, april, june and november...
<5> just tell me
<4> or if its for programming, many languages have a library to convert between dates and the julian day number
<7> So, is the second part of Cale's lecture on enumerative combinatorics today?
<5> no i want to do it on my brain quicly
<5> give me math algorithm for it
<5> http://www.timeanddate.com/date/dateadd.html
<5> hah!
<0> Dacicus: YES
<0> oops, caps-lock
<7> Okay, cool.
<7> Well, actually, I'll probably miss it due to church.
<7> But I can log it.
<7> bbl
<1> all your ugly terms are belong to us!
<8> hello. anyone there?
<8> i am doing linear regression with zero intercept. but the R-squared is always one. can anyone tell me why? thanx
<9> @keal
<10> you need a Zh function in Haskell
<2> Zh?
<2> %(x-1)^3 //SIMPLIFY
<2> % (x-1)^3 //Simplify
<10> Manyfold: (-1 + x)^3
<2> % (x-1)^3 //Expand
<10> Manyfold: -1 + 3*x - 3*x^2 + x^3
<9> If a = (a_1, ..., a_n) is in R^n and e > 0, then there exists a C^oo function f: R^n -> R that is positive on (a_1 - e, a_1 + e) x ... x (a_n - e, a_n + e) and 0 elsewhere. Show that if A is an open subset of R^n and C is a compact subset of A, then there is a non-negative C^oo function f: A -> R^n such that f(x) > 0 for x in C and f = 0 outside of some closed set contained in A.
<11> hello people
<11> I have a problem of computational geometry I can not resolve
<11> I have completely no idea how to approach it, even taking into account several known algorithms for computational geometry
<11> it's pretty simple: given 2n points, group them into 2 subsets whose convex hull is minimum in length
<11> if anyone has some idea, please help: I gave up
<11> forgot to mention: 2 balanced subsets (n points each)
<12> f00: the interior of the two convex hulls will be disjoint.
<11> int-e: thanks, let me work on it
<11> I can get a point I'm sure is on a convex hull (e.g., the leftmost), but the only way I can take advantage of the disjunction is knowing a *segment* belonging to one CH. Which I can't
<12> f00: if two convex sets in the plane are disjoint then there's a straight line separating the two sets. (oh. I hope your problem is 2D?)
<11> I will work again on the idea of cutting two segments from the complete convex hull and compose the two by adding segments to inner points
<11> of course it's 2d :)
<11> ok, so you're confirming my idea. I did not go far with it however
<11> well, actually I spoke about convex hulls
<11> the definition of my problem doesn't state anything about convexity
<11> AFAIK, it is possible to have two subset fields whose perimeter is minimal and not convex
<11> okay, I could not prove that the minimal perimeter of those sets is necessarily convex, given the constraint of each set being n points large, but i'll ***ume this
<13> http://www.anil.pl/wiki/index.php/For_Anil
<14> Chandra!
<13> hi Safrole
<15> I have a crypto question -- is this the right place?
<15> Wow... satan himself.
<16> greetings minions
<17> hey
<17> who can make a difficuld capthas image reader?
<9> @arrr
<10> Arrr!
<17> hey
<17> can anybody
<17> help me
<17> pls
<18> rrrrrr12: no, because nobody here knows what you need help with
<17> well
<17> i need a image scanner
<17> it needs to read 3 careacters out of those kind of images check this site pls --->>> http://www.freewebs.com/baracodes/
<19> rrrrrr12: this is hardly the right channel to ask in
<17> thought so
<18> hmm... doesn't seem like math to me
<17> lol
<18> though I'd be highly interested in the piece-wise functions needed to draw these
<17> excelblue i'm so sorry but that thingy that i want needs to be done with math things :)
<20> um
<17> so who can make a image scanner?
<20> dude
<17> dont call me dude
<18> rrrrrr12: it's not really possible at this point
<20> those look like captchas
<17> oh
<20> designed to keep automatons from processing forms automatically
<17> they are
<20> right
<20> you don't automate them
<17> yeah
<20> duh.
<20> that's the whole bloody point
<17> but
<20> so whatever grandiose ideas of spam you have in mind
<18> the point of such images are designed to be encoded to such a level that only a human can break them
<17> i dont need it
<20> no buts!
<17> for spam
<20> bull****.
<18> what do you need it for?
<20> you come in here waving arms asking about stuff totally irrelevant to math
<12> you don't need it.
<12> period :)
<17> madpickle stfu ***hole
<17> i need it for a onlinegame
<20> uh-oh
<20> you angered the cat
<20> lol
<20> nice one =)
<18> thanks Catfive
<12> (Maybe he should ask the site administrator, I'm sure if his motives are pure they can work something out. Duh.)
<18> heh... maybe the 12 at the end of his name is his age
<20> he'd have more luck trying to use a speech processing engine for the disability option
<20> or IQ
<2> well i find this question relevant for autonomous robots
<18> agreed
<12> yes, but if they employ captchas they probably don't want any of these.
<20> yes
<20> and those look quite complex
<2> that's one of the number one problems occuring azt the robo-cup
<20> and use only two colors
<2> anyone here been there?
<20> with no discernible patterns for edge detection except line slanting
<20> i'm no expert on screen scraping or anything, but that's quite a challenge.
<21> FaKeShAdOw, >:|
<22> ... wait!
<22> raidz0r, i'll brb.
<19> so how do i write "is included in" in irc :P..for set notation and whatnot
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