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  1. J

    Scaling Pareto between 1 and 0

    Hello, Thanks for the reply and sorry for the confusion. I think a pareto like distribution from 0 to 1 is what I'm going for. So would I just have it be bounded between 0 and 1? Thanks!
  2. J

    Scaling Pareto between 1 and 0

    Hello and thank you for taking the time to read this. I am making a number generator that generates a number based on a pareto distribution. The problem is, the distribution essentially goes from 0 to infinity. How would I go about scaling the values so I get a range between 0 and 1...
  3. J

    Galois Fields, Grobner Bases, N queens

    Hi all. Thank you for taking the time to read this. I am currently studying Grobner Bases and I've been given a problem that I'm struggling to find any resources for. I am interested in find if a certain n for the n queens problem have solutions. Now there are SAT solvers and such which can...
  4. J

    Complex Number, properties of moduli

    Well what confused me is the inequality. I understood the expression when it has the equal sign, but the problem that was given was |z+i| \leq 3 so I was trying to find a way to change it into simply an equals sign. Thanks, I see what you mean now. Do you have any advice on approaching a...
  5. J

    Complex Number, properties of moduli

    Yes that makes sense but how do I show that graphically? I tried changing it to \left.|z| + i = 3 is simply because I thought that would help make graphing it easier? Could I also say it is a circle with the radius of 3-i? So should I be transforming these z's into their components such that...
  6. J

    Complex Number, properties of moduli

    Thanks for the reply! I understand what you mean, but would that be the extent of "showing". I guess sometimes I'm just not sure how to properly write these proof type problems. On a somewhat related note, I'm suppose to graph \left.|z+i|\leq3 and \left.|z+i|\geq3 I know that normally, if...
  7. J

    Complex Number, properties of moduli

    Homework Statement Hello! I'm lost on how to start this, I've got formulas given to me from the text, but I have no idea on how to piece everything together. So I need to use established properties of moduli to show that when \left.\left|z_{3}\right|\neq\left|z_{4}\right|, then...
  8. J

    Fourier transform with mixed derivatives/ 2nd order ODE

    Hello! I've been working on this problem and was wondering if someone could check if I've done the rest of this problem correctly! So after finding the roots, I apply the initial conditions where: \left.\widehat{u}\left(\omega,0\right) = \widehat{f}\left(\omega\right) since t = 0, I...
  9. J

    Fourier transform with mixed derivatives/ 2nd order ODE

    Hi TinyTim, thanks for the reply! I just realized where I made my mistake! Thanks very much for the help!
  10. J

    Fourier transform with mixed derivatives/ 2nd order ODE

    Homework Statement Hi, So I'm suppose to solve the following problem: \left.\frac{d^{2}u}{dt^{2}}-4\frac{d^{3}u}{dt dx^{2}}+3\frac{d^{4}u}{dx^{4}}=0 \left.u(x,0) = f(x) \left.\frac{du}{dt}(x,0) = g(x) Homework Equations The Attempt at a Solution First I use fourier transform on...
  11. J

    Solving for non moving points of a 1-D wave

    regardless.... Thank you very much for being so patient. It makes sense how you approached this problem now. once again, Thanks!!!!!!!! :P
  12. J

    Solving for non moving points of a 1-D wave

    It definitely does not. So I did a bad job in choosing the appropriate time interval then? My graphs definitely made me think I'd be getting answers for nonmoving x values...
  13. J

    Solving for non moving points of a 1-D wave

    That's because we were to graph 10 plots at various t, I decidedly went t=1..10 and from the graphs the roots looked stationary Also I had the impression that the problem would've been simpler in terms of all the trig stuff...
  14. J

    Solving for non moving points of a 1-D wave

    yes but...so am I suppose to say that even though they seem to be stationary, that's not the case since they will be dependent on beta?
  15. J

    Solving for non moving points of a 1-D wave

    yes heh, considering I don't know how to get maple to do anything correctly, what are some alternatives to find the roots? Thanks
  16. J

    Solving for non moving points of a 1-D wave

    so to solve for the roots then, would just plain old factoring be the best way?
  17. J

    Solving for non moving points of a 1-D wave

    I would say 0, 7, and -2y if we knew what y is but-2y would mean there's some kind of dependency between the two variables?
  18. J

    Solving for non moving points of a 1-D wave

    by itself alpha is independent of beta
  19. J

    Solving for non moving points of a 1-D wave

    well no because all the terms have\left.-\frac{1}{2}\pi\alpha\beta in common....
  20. J

    Solving for non moving points of a 1-D wave

    But in this case we don't know what f(\alpha) is though? You're saying to find all the values of f(\alpha) that gives us zero right? is f(\alpha) u(x,0)? when solving for the equation we had learned to use u(x,0) = f(x) and the derivative of it to be the velocity so...other than that where does...
  21. J

    Solving for non moving points of a 1-D wave

    I understand the reasoning but I am having troubles translating the meaning into math. I mean I set the expression to zero but mathematically, how does "for all values of t" fit in. This is what I'm thinking currently: \left. 0 = 2087-16500\alpha^{2}+32928\alpha^{4}-18816\alpha^{6} This is...
  22. J

    Solving for non moving points of a 1-D wave

    Is there a thread where I can ask questions about maple because I've been searching the internet trying to find out how to factor the polynomial and was unable to find an answer. Apparently the Factors command is suppose to factor multivariate polynomials but when I type in the command to...
  23. J

    Solving for non moving points of a 1-D wave

    Ok so for the x terms I ended up double checking my previous expansion(fixed the mistakes) and then substituted for the x terms. I also used \cos^2\theta=1-\sin^2\theta and combined some like terms after multiplying stuff through and got the following: \left.-\pi sin(\pi...
  24. J

    Solving for non moving points of a 1-D wave

    Hm alright thanks, do you know why maple only applied multiple angle rule to the t variable and not the x? Is there a way to specify that in maple?
  25. J

    Solving for non moving points of a 1-D wave

    I've only started using maple until recently but I entered my original derivative, and I right clicked on it and told maple to expand it? I got the following: \left.-\pi sin(\pi x)sin(\pi t) - 6\pi sin(3\pi x)sin(\pi t)cos^{2}(\pi t) + \frac{3}{2}\pi sin(3\pi x)sin(\pi t) \left.- 1344\pi...
  26. J

    Solving for non moving points of a 1-D wave

    Thanks, so after expanding a bit I get this: \left. -\pi sin(\pi x)sin(\pi t) + \frac{3}{2}\pi (3cos^{2}(\pi x)sin(\pi x) - sin^{3}(\pi x))(3cos^{2}(\pi t)sin(\pi t) - sin^{3}(\pi t)) - 21\pi (3sin(\pi x)cos^{6}(\pi x) \left. - 21sin^{3}(\pi x)cos^{4}(\pi x) + 35sin^{5}(\pi x)cos(\pi...
  27. J

    Solving for non moving points of a 1-D wave

    so I'm kind of stuck on converting my function using multiple angle formula. This is the formula I found: \left.sin(nx) = \sum^{\frac{n-1}{2}}_{k = 0}(-1)^{k}\left(\stackrel{n}{2k+1}\right)sin^{2k+1}xcos^{n-2k-1}x so if my n is \left.7\pi, how does the summation work since...
  28. J

    Solving for non moving points of a 1-D wave

    So if I take the derivative of the function in respect to time, then \left.\frac{du}{du}(u,t) = -\pi sin(\pi x)sin(\pi t) - \frac{3}{2}\pi sin(3\pi x)sin(3\pi t) - 21\pi sin(7\pi x)sin(7\pi t) so now I set it equal to zero: \left. -\pi sin(\pi x)sin(\pi t) - \frac{3}{2}\pi sin(3\pi x)sin(3\pi...
  29. J

    Solving for non moving points of a 1-D wave

    zero right because u(x,t) at those times would just be some kind of constant?
  30. J

    Solving for non moving points of a 1-D wave

    Homework Statement Hi! I'm suppose to find the points x on the "string" 1-D wave which are not moving during the vibrations, i.e., 0<x<1 such that u(x,t) = 0 for all times t >0 Homework Equations \left.u(x,t) = sin( \pi x)cos(\pi t) + \frac{1}{2}sin(3\pi x)cos(3\pi t) + 3sin(7\pi x)...
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