Col_Buendia
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llantwit said:Nice image.
Ha!! like you'd know anything about cleaning... filthy little get!
The "Emo" kid threat to Cardiff!
- Thread starter Col_Buendia
- Start date
Ha!! like you'd know anything about cleaning... filthy little get!
Col_Buendia
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kate44 said:
Kate44, yesterday.
lewislewis
Lumumba Cymru
Brilliant thread.
Sweaty Betty
Hemo rising!
kate44 said:
Floquet theory is a branch of the theory of ordinary differential equations relating to the class of solutions to linear differential equations of the form,
The main theorem of Floquet theory, Floquet's theorem, gives a canonical form for each fundamental matrix solution of this common linear system. It gives a coordinate change y = Q ? 1(t)x with Q(t + 2T) = Q(t) that transforms the periodic system to a traditional linear system with constant, real coefficients.
In solid-state physics, the analogous result (generalized to three dimensions) is known as Bloch's theorem.
Note that the solutions of the linear differential equation form a vector space. A Matrix ?(t) is called fundamental matrix solution if all columns are linearly independent solutions. It is called a principal fundamental matrix at t0 if ?(t0) is the identity. Because of existence and uniqueness of the solutions there is a principal fundamental matrix ?(t0) = ?(t)? ? 1(t0) for each t0. The solution of the linear differential equation with the initial condition x(0) = x0 is x(t) = ?(t)? ? 1(0)x0 where ?(t) is any fundamental matrix solution.
[edit]Floquet's theorem
If ?(t) is a fundamental matrix solution of the periodic system , with A(t) a periodic function with period T then, for all ,
?(t + T) = ?(t)? ? 1(0)?(T).
In addition, for each matrix B (possibly complex) such that:
eTB = ? ? 1(0)?(T),
there is a periodic (period T) matrix function such that
?(t) = P(t)etB for all .
Also, there is a real matrix R and a real periodic (period 2T) matrix function such that
?(t) = Q(t)etR for all .
[edit]Consequences and applications
This mapping ?(t) = Q(t)etR gives rise to a time-dependent change of coordinates (y = Q ? 1(t)x), under which our original system becomes a linear system with real constant coefficients . Since Q(t) is continuous and periodic it must be bounded. Thus the stability of the zero solution for y(t) and x(t) is determined by the eigenvalues of R.
The representation ?(t) = P(t)etB is called a Floquet normal form for the fundamental matrix ?(t).
The eigenvalues of eTB are called the characteristic multipliers of the system. They are also the eigenvalues of the (linear) Poincaré maps . A Floquet exponent (sometimes called a characteristic exponent), is a complex ? such that e?T is a characteristic multiplier of the system. Notice that Floquet exponents are not unique, since. The real parts of the Floquet exponents are called Lyapunov exponents. The zero solution is asymptotically stable if all Lyapunov exponents are negative, Lyapunov stable if the Lyapunov exponents are nonpositive and unstable otherwise.
Floquet Theory is very important to the study of dynamical systems
Floquet theory shows stability in Hill's equation (introduced by George William Hill) approximating the motion of the moon as a harmonic oscillator in a periodic gravitational field.
[edit]References
Chicone, Carmen. Ordinary Differential Equations with Applications. Springer-Verlag, New York 1999
Gaston Floquet, "Sur les équations différentielles linéaires à coefficients périodiques," Ann. École Norm. Sup. 12, 47-88 (1883).
This applied mathematics-related article is a stub. You can help Wikipedia by expanding it.
Tidy!!!!!!!!!!!!!
Yuwipi Woman
Whack-A-Mole Queen
Col_Buendia
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Haylz, yesterday.
i have not ever as far as i can remember shat on my own doorstep. if, due to temporary incontinence, such an event were to take place, i would obviously, without question and with the minimum possible fuss, clean it up myself. it is very obvious that no-one else would do it and if i did not do it i know that i would be likely to be treading shit into my own home, which would be more difficult to clean up in the long run,especially if any of it were to get on any of the carpets.haylz said:if you shit on your doorstep, be prepared to clean up your mess mate
i try to maintain a healthy attitude to human shit- it is excrement, but it can be composted, and in the long run used very productively as a soil improver.
it is a shame that so much of it is pumped into the sea, but even i would rather that than deposit it on my own doorstep.
occasionly in the past i have shat in the wrong place. whenever possible i would clean it up to the best of my ability. i have occasionally cleaned up other peoples shit and some dog shit, although i have never had a dog.
if it is not possible to clean it up i would cover it to the best of my ability.
these instances have occurred outside, rather than in the confinements of a building.
i have occasionally got some of my own poo on my clothes. this i have cleaned up in the most hygienic and practical way that i could see available to me at the time.
knowing the properties of excrement if ever i see any in the wrong place i will generally try to rectify the situation as best i can if appropriate, as i know my tolerance for performing such tasks is higher than most peoples. generally i would attribute this to the fact that i have raised 3 children in the western way of nappy using as generally practised in this country.
RubberBuccaneer
Hedd Wyn
When we going to get all together for a beer then ?
Sweaty Betty
Hemo rising!
RubberBuccaneer said:
very soon i think!!!!!!
lewislewis
Lumumba Cymru
kate44 said:
I think the amount of excrement distributed upon doorsteps in Wales, correlates exactly with the continuing hegemonic dominance of our country by the London imperialist powers.
I wonder if shite releases methane, if so we could possibly use it to generate power. A pretty renewable source too if supported with large scale importing of curries.
lewislewis
Lumumba Cymru
llantwit said:Or maybe we could somehow harness the hot air generated by the WAG, LL?
If only ! The energy remit is held by our rulers in London : p
What's all this got to do with the emo kids threat to Cardiff?
I quite like them - black clothes, make-up nicked out of their mother's hand-bags, what's wrong with that? At least they are making some kind of an effort. Most of them seem dead young to me but if you're a boy wearing eye-liner at 14 then that's pretty cool. Some emo graffiti has even sprung up near me under the Western Avenue bridge: "emo hardcore" and "emo CF14". Hey. All youth cults are interesting. It'd be good if they rioted or something. The Emo riots - bring it on.
I quite like them - black clothes, make-up nicked out of their mother's hand-bags, what's wrong with that? At least they are making some kind of an effort. Most of them seem dead young to me but if you're a boy wearing eye-liner at 14 then that's pretty cool. Some emo graffiti has even sprung up near me under the Western Avenue bridge: "emo hardcore" and "emo CF14". Hey. All youth cults are interesting. It'd be good if they rioted or something. The Emo riots - bring it on.
Sweaty Betty
Hemo rising!
If my daughter turns emo shes out picking spuds for her tea, it didnt hurt my ancestors, and im damned if i'll have an arsey emo in my home...ffs teenagers have enough varying emotions as it is without this emo shit too!!!
worried parent whose daughter plays the guitar.
worried parent whose daughter plays the guitar.
Sweaty Betty
Hemo rising!
Brockway said:
Just wait till she brings home her first Funeral for a Friend CD and starts self-harming. She got any black suede boots with straps down the side? I used to have a pair. Smart.
Buckles?????
She already listens to avril lavigne, should i implement precaution?
Sweaty Betty
Hemo rising!
*quickly hides copies of steve vai and pink floyd cd's*
Sweaty Betty
Hemo rising!
Brockway said:3 buckles per suede boot. Nice.
You should be on full scale emo alert. Lavigne is often the last phase before proper emo breaks out. Check her room for fingerless gloves.
*faints*
Sweaty Betty
Hemo rising!
kate44 said:
Sing it for us Kate?
Sweaty Betty
Hemo rising!
nwnm said:
2 Hardcore
mad old bat
haylz said:She already listens to avril lavigne, should i implement precaution?
No, don't worry - as a sprog, so did violentviolet - yet look what she's posted further up @ post32. All will be well
(by the way, have you seen Ms Lavigne lately? Not so emo these days....)
