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Everything posted by ajb

  1. The best thing is to pick up a book on classical mechanics - or just read wikipedia for now. Look up Lagrangian, momentum and phase space.
  2. Degrees of freedom are the parameters - basic examples from mechanics include position, velocity or momentum.
  3. You can usually treat the collection of all possible values of the parameters that describe a rigid body or a collection of bodies or particles as coordinates on a smooth manifold.
  4. Probably not - this sort of thing is not my area of expertise. But then this is irrelevant as I have not claimed anything here other than I know that people have put a lot of effort into being sure that have measured something real. This really needs stressing again - the wave form measured fits the models very well including the 'ring down' towards the end of the merger.
  5. Why perhaps? I mean you have read the literature on this, right? You understand the kind of analysis involved? You do understand how well the signal matches the predictions? If you really have some evidence that a clear signal from a black hole merger was detected then write a paper.
  6. What do you want a picture of? Anyway, as you are interested in engineering, geometric mechanics with constraints and control theory has been applied to many things including space-craft, underwater craft etc. The methods are also being exploited in economic theory. You can google more for details.
  7. Pictures? Not really, but you can find textbooks and papers that use these notions.
  8. I am sure that they took their time in eliminating such things. They kept things quite for a while until the team was happy that they measured something interesting.
  9. For sure, the team did not shout about their results until they were very sure that they measured something real. This took several month. I have no idea if lightning was considered as a possible source, however given two separated detectors and that the signal matches predictions (the classical ring down was observed) I think it is not a plausible source and would be discounted straight away.
  10. Phase spaces in classical mechanics (assuming autonomous) are 6 dimensional - 3 positions and 3 momenta. So classical mechanics and control theory applied to engineering often uses spaces (usually smooth manifolds) of dimension greater than 3. In physics 4 dimensional manifolds are to be found in relativity theory. Infinite dimensional spaces are often found in functional analysis as applied to engineering and physics - you already stated Hilbert spaces and quantum mechanics. But other spaces such as Banach and Fréchet spaces also appear. There are also more general notions of 'spaces' that appear in physics, I am not such if they appear in engineering.
  11. basic yes, but the point is that we do have binary operations that are not associative. This is the definition of a monoid. Monoids are not uncommon, but for sure they are less well known that say a group. An example of a monoid are the real numbers with standard multiplication. Lie algebras are fundamental in mathematical physics and differential geometry. They are also of great interest from a pure algebra point of view. I would be very suprised if you have not encountered these in your studies - at least just the basics and some simple examples. Yes, you have defined a monoid. Typically a monoid is a 'group' for which not all the elements have an inverse. So, for the case of the real numbers and muliplication, 0 has no inverse.
  12. Standard multiplication and addition of real or complex numbers; Group multiplication; vector addition; matrix multiplication... all these are associative. Non-associative examples include multiplication of octonians and Lie brackets. Associativity means that you can make sense of a*b*c without having to put in the parenthesis -- that is a*(b*c) = (a*b)*c
  13. I am worried that if I eat a meal of antipasto and then pasta that I will vanish in a flash of croutons!

    1. Show previous comments  1 more
    2. MigL


      No worries AJB.

      PastO in this context means meal, so antipasto is 'before meal'. Not pastA with an opposite charge.

    3. zapatos


      Har! That was hilarious ajb! :)

    4. Elite Engineer
  14. As long as the domain and range are compatible one can make sense of associativity - so partial binary operations can be associative. For example, when dealing with groupoids where we have a partial multiplication.
  15. He or she has asked for the generic name of binary operations that satisfy f(f(a,b),c) = f(a, f(b,c)). Such binary operations are known as associative binary operations. They can now simply 'google' this for more examples.
  16. I think the word 'function' in the opening post is not correct - rather we have a binary operation. It is true that composition of functions is associative...
  17. I don't think we are dealing with implicit functions here - the example given in the opening post suggest that we are dealing with binary operations that are associative. An examples of something that does not satisfy the associative property are Lie algebras.
  18. This is the associative property for a binary operation on a set. For example, standard multiplication of real numbers satisfies this property.
  19. I agree - you can find some older papers with simple hand drawn diagrams (for example Feynman diagrams) and even old papers where the equations are written by hand! But today with LaTex and simple drawing applications there is little excuse for hand-drawn diagrams.
  20. Insulting the people you wish to engage with is never a good idea. Anyway, as a science forum - albeit this is the religion section - how could you support the position that we are all Satan and that we are in Hell? This philosophical/religious point of view seems quite at odds with what the Bible says about the Devil.
  21. You are trying to over think this problem... The function in question is just f(x) = x-x =0 which is defined on the real line. We then want to take the limit as x -> \infty, but as f(x) = constant this limit is just that constant, i.e. zero. What one has to be more careful with is lim(x) - lim(x) = ? as x -> \infty. This is my point and I think what has confused people.
  22. Yes, 3 is correct - in that n-n =0 and so this limit is 0 - and what others said very early on in this thread.
  23. I think that it can do for many men - why I have no idea. Anyway, the problem is being over confident in the first place methinks.
  24. All scientific and engineering societies sponsor meetings, schools and conferences. You need to think about what you are interested in and find the closest matching event. Typically no. Some journals may publish methods rather than the scientific conclusions that these methods lead to. People tend not to want to publish proposals anyway - proposals are for the funding people and not journals. That said, it maybe possible to publish some plans for possible future experiments and so on. I don't think what you are talking about really fits that bill. Typically meetings have fees, you pay for accommodation and travel - or in reality one's grant does that. For students and young researchers there maybe reduced rates and even direct help with some or all of the costs. You should ask the organisers about this. Assess what exactly? If the meeting has agreed to publish a proceedings, then usually these are peer-reviewed, but check this carefully for the individual meetings in question.
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