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Nov
21
answered how many lines can be drawn from a point in space with n degrees of freedom?
Nov
21
comment Distribute small number of points on a disc
As you are aware, there are many possible optimization criteria, and they may yield different optimal configurations. It's not possible to say which one is "the best"; different criteria will be useful for different purposes.
Nov
21
answered A connected path between shapes
Nov
21
accepted You can't solve Laplace's equation with boundary conditions on isolated points. But why?
Nov
20
comment Most ambiguous and inconsistent phrases and notations in maths
I feel like your answer needs a little more justification. Right now you've shown that uses of the term "trivial" are broad but not that they are ambiguous. To me they all fall under the umbrella of "nothing much to it": the "nothing much" in the colloquial usage being in terms of effort, while in the mathematical uses, it is "nothing much" in terms of structure or complexity.
Nov
20
revised Are there functions that satisfy $f(km)\bmod m=f(m)$ that are not of the form $m\mapsto n\bmod m$?
fixed range of f, renamed q to more obviously-natural-number m
Nov
20
revised You can't solve Laplace's equation with boundary conditions on isolated points. But why?
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Nov
19
comment How to find fitting parameters of the function?
You could do worse than to start by checking the Wikipedia page for nonlinear least squares, which is basically what you are doing. The Gauss-Newton and Levenberg-Marquardt algorithms are popular numerical methods for such problems.
Nov
18
awarded  Tumbleweed
Nov
17
comment Convex sets in $\mathbb R^n$: Do they have a particular form ? Does the gradient of a linear convex function $f$ exist on such a set?
Is $S$ necessarily some ball or a Cartesian product of intervals? Not at all, see the first illustration on Wikipedia.
Nov
17
revised Are there functions that satisfy $f(km)\bmod m=f(m)$ that are not of the form $m\mapsto n\bmod m$?
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Nov
17
revised A Characterization of the Tangent Function?
added 53 characters in body
Nov
17
asked Are there functions that satisfy $f(km)\bmod m=f(m)$ that are not of the form $m\mapsto n\bmod m$?
Nov
15
revised A Characterization of the Tangent Function?
added 251 characters in body
Nov
15
answered A Characterization of the Tangent Function?
Nov
14
comment Random Sampling of vectors on the Complex Unit Sphere
Ah, in that case, it's geometrically equivalent to the unit sphere in $\mathbb R^{2n}$ because $\mathbb C\cong\mathbb R^2$. So you just have to sample from a real unit sphere and interpret the result as a vector in $\mathbb C^n$. In fact, since it's a one-liner in Mathematica, here you go: ({1, I}.#) & /@ Partition[Normalize@RandomVariate[NormalDistribution[], 2 n], 2]
Nov
14
comment Random Sampling of vectors on the Complex Unit Sphere
Can you provide a definition of the complex unit sphere? I found a reference which said it is the subset of $\mathbb C^n$ such that $z_1^2+\cdots+z_n^2=1$, but such a set is unbounded and so I'm not sure it even makes sense to sample from it uniformly.
Nov
13
answered A Characterization of the Tangent Function?
Nov
13
comment Constraining mathematics to a subset of $\mathbb{R}$
See Why do we need the real numbers? Part IV discusses definable real numbers, which is what you are asking about.
Nov
13
comment A Characterization of the Tangent Function?
There are also two more trivial solutions $f=\pm\sqrt3$.