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Comments:
<0> yes, it's called 'integration'
<1> I'm taking calculus right now
<1> and I know what a derivative is
<0> http://wikipedia.org/wiki/Integral
<1> and apparently an integral is related to a derivative
<1> okay, thanks
<0> integrals are related to derivatives through the fundamental theorem of calculus.
<2> which states?
<1> so I have to find an antiderivative of f(x)
<0> if f: [a, b] -> R is a real-valued function on the closed interval [a, b] that is continuous at c, and we set F(x) = int(a..x, f(t) dt), then F is differentiable at c, and F'(c) = f(c).
<0> (an integrable real-valued function, of course)
<1> so essentially the antiderivative of f(x) is used to calculate the area between {a,b} on the x-axis?
<0> careful - f will have many antiderivatives.
<3> have people been trolling this chan again?
<0> the fundamental theorem (above) ***erts a remarkable connection between integrals (defined in terms of limits of sums) and derivatives, which on the surface have no obvious relationship to one another at all.
<0> mnvl - not really.
<1> okay then, you have to find an antiderivative of f such that F' = f?
<1> is that better?
<0> [Shiba] - the theorem implies that if f is continuous (everywhere) on [a, b], then the function F(x) = int(a..x, f(t) dt) is differentiable on [a, b], and F'(x) = f(x). Now, if g is another function satisfying g' = f (such a function is called an antiderivative of f), then it must differ from F by a constant, g(x) = F(x) + C. But F(a) = 0, so g(a) = F(a) + C = C, which means g(x) = F(x) + g(a). This in turn means that g(b) = F(b) + g(a), or F(b) = ...
<0> ... int(a..b, f(t) dt) = g(b) - g(a).
<4> "you have to find an antiderivative of f such that F' = f?"
<4> that almost makes no sense
<4> by definition, if F is an antiderivative of f, then F'=f
<1> okay thats a bit clearer
<1> thanks
<5> hello
<5> i was wondering if anyone could share some insight.
<5> i am trying to output multiple plots from octave into a single postscript file
<5> how do i append the additional files rather than overwrighting?
<6> what the hell is integrable systems?
<7> Hi if I rotate a _point with Matrix multiplication with vector: <90,0,180>( as in <x,y,z>: as in <pitch,yaw,roll>) How can I get _point back to it's original location?
<8> Afat: use the inverse matrix
<8> or you proabbly want to use quaternions for rotation stuff
<7> Okay that sounds great. Cuase it's for a program. I tried iverting the vector(as in <x*-1,y*-1,z*-1) but that isn't really working...
<7> So, _llll_, Is it going to rotate back to the point with InV_Matrix? :p
<3> by definition, afat
<7> by definition? -- what does that mean again?
<9> I don't understand pitch, yaw, roll.
<7> pitch-rotation around x-asix, yaw around y-axis, roll around z-axis.
<7> By the way no one saw kenshin-reminiscene?
<7> :p
<8> if you want to use a rotation matrix you want to ahve the point in coordinates rather than giving the angles
<8> but iirc quaternions are better for your pitch/roll/yaw stuff
<7> I do have the Point in Cartisean. The Problem is.. The code is very complicated and changing from matrix to Quat would get me back a few days.(all is hanging around it)
<7> The _Point is in Cart, I convert the 1X3Matrix(20,80,180) to a 4X4Matrix and Multiply that with the Point. Will the inverse of Martix4X4 rotate the _point back to it's previous Location?
<8> you mean 3x3 i guess. if Mv=v', then the invers matrix N does Nv'=v
<3> by definition i meant
<10> all you really need is a rotation matrix and the inverse of that rotation matrix
<3> if you multiply a vector by a matrix and then by the inverse matrix you will definitely get back the original point
<3> that's the definition of inverse matrix
<7> Awesome people, Thanks To all of you! You saved me hours of (radical)programming.
<8> hmm, you should really get an "intro to linear algebra" book if you are programming this stuff
<7> Yeah, I kinda read some, But I can't keep reading forever. (But I'm an Ape...I will do the Inverse of that)
<2> _llll_: did you tell him that for rotations quaternions are better than fast matrix multiplication?
<7> Okay here you go: I will use both Interchangebly, Depending on the Distance of The Interpolations.
<11> how large is 1 acre?
<12> xahlee: What units do you want it in?
<2> cgs i presume
<11> Dacicus: square meters or square km
<12> http://www.onlineconversion.com/ <-- I think that can help for all your conversion needs
<12> 4 046.856 422 4 sq m
<11> http://en.wikipedia.org/wiki/Acre
<11> was going to visit the Hearst castle yesterday,
<11> but arrived too late
<2> what is hearst castle?
<11> Manyfold: http://en.wikipedia.org/wiki/Hearst_castle
<3> xanadu
<2> After a room in the estate was bombed in the 1970s during her crime spree with the Symbionese Liberation Army, <- bomb the system :)
<13> xahlee : it is worth a visit
<13> though the entrance fee is a bit expensive iirc
<11> kmh: mm.... yoeu've been there?
<13> xahlee : a few years back /driving from SF to LA)
<11> kmh: nice....
<13> it is one of the main attraction on that road
<13> haha
<13> not sure whether hearst castle in particularly interesting for mathematicians though
<11> kmh: right :) ...
<13> but most of the coastline there is kinda scenic (and somewhat famous)
<11> kmh: where are you located?
<13> in germany
<2> he is a hun :)
<3> i want to visit weierstr***' grave in berlin
<3> germany full of interesting mathematicians' graves
<2> what's so interesting about weierstr*** grave?
<13> mnvl : indeed, i currently live close to goettingen btw
<2> except those that left after 1933 that is
<3> weierstr*** is my hero
<13> Manyfold : well in some regard 33-45 killed german math
<3> right kmh
<2> i find non-standard analysis better
<3> and made american math you could argue
<3> well Manyfold without standard analysis there would be no standard analysis
<13> there's a nice quote by hilbert, asked by a nazi official about the impact of race laws to the math institut
<3> and weierstr*** is the father of standard analysis
<13> hilbert simply replied : there's no institute anymore
<3> cool
<3> but kmh i kind of agree
<4> well, at least all of those german mathematicians came to the US
<3> it's my ambition to write a text book on analysis that avoids all the parts that simply arose through historical accident
<3> like the use of natural numbers
<4> that's pretty much the only reason the US has fared as well as it has scientifically and mathematically
<4> you want to avoid positive integers?
<4> that's ambitious.
<4> nay, that's ambition itself
<3> well positive integers might arise :)
<3> but not in the definition of convergence
<3> or similar
<3> does anyone remember the latex syntax for defining newcommands with default arguments?
<3> nm
<13> HiLander: actually not only german scientist, but scientist from all over europe wherever the nazis showed (i.e. france,austria,hungary,poland, etc)
<4> yeah
<14> i'm back :p
<15> i was worried
<14> So when the suffix tree is defined as a dfa, the transition function g(x, a) = y (x=substr,a=char in alphabet(sigma)), where y=xa
<14> What is 'y'? And what does y=xa mean?
<16> jbalint: 'y' is the resultant state
<14> but as far as the suffix tree is concerned, what would be the next state?
<16> I don't know what you mean by "suffix tree"
<14> it could be the next explicit parent node, or any number of child nodes
<2> looks like compiler design
<14> rah: Here is an explanation. They are using the same terminology as Ukkonen(1995) which is on citeseer http://www.csse.monash.edu.au/~lloyd/tildeAlgDS/Tree/Suffix/
<2> are we talking about an accepting finite state auromaton?
<14> Manyfold: implicitly yes, but in the context of interpreting the suffix tree as the automaton
<2> u am reading the text so give me some time
<14> Ok, thanks you.
<16> jbalint: if x is a state and also a word, y would be a state and also a word, in which case y is the word x, concatenated with a
<14> The formal definitions are explain in the (b) Faster section
<16> it seems that the notation is using words as states in the dfa
<14> rah: Ah... they have a mapping function x->x(bar) from word/substr to the state
<14> But the concatenation makes sense. 'y=xa' just looked confusing to me :)
<16> jbalint: then if that function is f(x), the result is not y = xa, but y = f(x)a
<14> What is the upside-down T on there called?
<14> rah: Yes, it's g(x,a)=y where y=xa, so it makes sense.
<16> that doesn't make sense
<16> if x is a state, but not a word, that doesn't make sense
<14> So what does 'where y=xa' mean?
<16> actually, it would be f(y) = f(x)a
<16> if x is a state and there's a function f(x) which maps from the state to a word, then only f(y) = f(x)a
<14> Well, I am ***uming (which seems to be left out(?) of that page) that in the statement it's x(bar), the state.
<2> what is a dfa?
<14> deterministic finite automaton
<16> Manyfold: a set of states, an alphabet of symbols, and a function that maps states and symbols to states
<14> http://citeseer.ist.psu.edu/ukkonen95line.html Here's the original paper.
<2> ah
<16> err.. and a designated start state
<17> Random start states are better !
<18> Anyone have any ideas about how to get sound data into a format in which it can be mathematically analyzed? If I even knew what this process is called I could google it.
<16> tjack: sampling
<16> tjack: "sound data"
<16> tjack: the issue is: what do you mean by "mathematically analysed"?
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