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| bio | website | quantdec.com |
|---|---|---|
| location | ||
| age | ||
| visits | member for | 1 year, 4 months |
| seen | 14 mins ago | |
| stats | profile views | 900 |
Consultant (environmental stats a specialty) and teacher.
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14m |
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Finding integral points on a surface The equation is a cubic (parameterized by $n$), so it's possible a more efficient method to obtain all solutions can be found by computing generators of its group of integral points. But typically these groups are so small--I haven't found one larger than $12$ yet--as a practical matter it might not be worth the effort. |
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1h |
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Finding integral points on a surface You're welcome. You shouldn't be so quick to accept this answer, though: this community does a great job of improving answers over the course of a day or two. Much better answers might appear soon :-). |
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1d |
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CorrelationTest small bug? It seems to me they are testing the same hypotheses but are using different approximations to the sampling distribution of the test statistic. |
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1d |
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Composition: how to make a day and night world map? This question also has an answer (using MMA illustrations) on the GIS site. |
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1d |
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How can I detect an ellipse in a photo? +1 That's a real tour de force, beautifully described. Impressive. |
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2d |
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Behaviour of prediction bands Heteroscedasticity can be complicated: no longer does it suffice to stipulate that all residuals have the same variance, so now you need a model not only for the data values, but also an equally complicated one for the variances of their residuals. You're in the realm of highly specialized coding. If you know what you're doing, MMA is a great platform for writing that code; otherwise, look to specialized platforms like R and hope someone has contributed a model that might be appropriate for your situation. |
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2d |
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Speeding up a numerical constrained quadratic optimization @OleksandrR's suggestion to use a quadratic programming solution typically requires 0.02 seconds or less when applied to problems of the same size having random coefficients. |
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2d |
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How can I detect an ellipse in a photo? Substantial progress towards a solution can be found by reviewing these related posts. A Hough transform looks attractive. |
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May 20 |
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Problem with the Plot of Functions and PlotLegends What specifically is wrong with the output? |
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May 20 |
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Solar System Orbital Parameters Just in case you are interested in accuracy, it might be worth noting that the system of ODEs described in your previous question at mathematica.stackexchange.com/questions/25039/… is not what is usually meant by an "n-body simulation," because it does not account for interactions among the bodies: it's just a collection of independent central field solutions. It might be a fine approximation for times close to the initial time but will be observably incorrect. |
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May 20 |
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Find all the integer numbers $a$, $b$, $c$, $d$, $e$, $f$, $k$ to this equation have three integer different solutions? The question, which evidently is missing several words, now reads as if you are asking for all integral values of $a,\ldots,k$ in the interval $[-10,10]$ for which your equation has three distinct integral solutions. Is this a correct interpretation? |
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May 18 |
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Using single replacement rule to convert algebraic expression You might find Alternatives to be useful. |
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May 17 |
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Solving an ODE in power series +1 This is a good start. Power series solutions, though, are frequently used to obtain recursion equations for the coefficients (of any solution that might be analytic within a neighborhood of the point of expansion). It would be nice, then, to have a function that outputs these equations (given a differential operator as input), rather than just obtaining an approximate solution with a limited radius of accuracy. In order to analyze singular points, it would also be useful to consider slightly more general series of the form $z^\alpha(a_0+a_1z+a_2z^2+\cdots)$ for non-integral $\alpha$. |
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May 15 |
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Integration of a rational function Alternatively, use the Residue Theorem. Implicitly assuming $b\gt 0$ (WLG) and $c\gt 0$, we may (very quickly) obtain the solution as 2 \[Pi] I Sum[Residue[(a + x)/((b^2 + (a + x)^2) (1 + c (a - x)^2)), {x, z}], {z, {b I - a, I/Sqrt[c] + a}}] // Simplify, yielding $\frac{2 a \sqrt{c} \pi }{1+2 b \sqrt{c}+4 a^2 c+b^2 c}$. |
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May 15 |
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How to deal with zero in NDSolve in mathematica? That completely changes the question! |
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May 15 |
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How to deal with zero in NDSolve in mathematica? +1 This argument can be made rigorous by considering the approximate differential equation as a perturbation of the original. Applying DSolve with initial conditions is not very persuasive. It's more insightful to omit initial conditions: the solution will include a Bessel function of the second kind. This captures the singular behavior at the origin and approximates the singular behavior of the original equation there, too. Standard theory shows that's all the solutions you can have--just two dimensions of them--and then the rest of the analysis goes through as shown here. |
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May 14 |
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How to deal with zero in NDSolve in mathematica? The equations are inconsistent with the initial conditions. At $t=0$ you are requiring that $0 = t y'(t) = -x(t) - t \exp(x(t)) = -1$ which is impossible. |
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May 14 |
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draw a graph of a polynomial function with variables in the denominator When the syntax is corrected, the plot draws within seconds (MMA 8.0). Specifically, use f[u,z1,z2] and define its downvalue with SetDelayed, as in f[u_, z1_, z2_] := 0.0435 - u + etc. (Voting to close as too localized.) |
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May 10 |
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How do I draw a hemisphere? +1 -- but it's a little bit harder to use this technique to draw an arbitrary hemisphere. :-) |
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May 10 |
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How do I draw a hemisphere? One method (using RegionFunction) is shown here. |
