Rahul
Reputation
22,743
79/100 score
 Feb20 comment Are there real solutions to $\exp(X)=-I$? Hint: $-I$ is also a rotation by $\pi$. Feb19 comment Why erf(a-b)+erf(a)+erf(a+b) is so close to 3erf(a)? This is true for "most" functions, not just $\operatorname{erf}$. Feb18 comment A mathematical abstraction of colours? I don't know what you mean by "one set can't have two distinct parent sets", but you can consider the set of colours generated by additive combinations of (a given set of) colours as a convex cone. Maybe also take a look at how colour models are formalized. Feb10 comment Why is a local min also a global min for convex functions? If $x$ is a local minimum, $f(x)\le f(y)$ for all $y$ in a neighbourhood of $x$. To prove that $x$ is a global minimum, you need to show that $f(x)\le f(z)$ for all possible $z$. Find a $y$ that is on the line segment between $x$ and $z$ and lies in the aforementioned local neighbourhood, then apply convexity. Feb10 awarded Reversal Feb9 comment intuitive meaning of sphericity Intuitively, by "flat space generated by $C$" they mean that if you have (say) a two-dimensional triangle floating in three-dimensional space, you should measure its sphericity by looking only at disks lying in the plane of the triangle, not full three-dimensional balls. (If you did the latter, the asphericity would always be $1$ because there is no 3D ball of positive radius lying entirely inside a triangle.) Further reading: affine hull. Feb9 comment Is $4 \times 6$ defined as $4 + 4 + 4 + 4 + 4 + 4$ or $6 + 6 + 6 + 6$? It doesn't matter. You define $4\times 6$ one way, I define it the other way, we prove multiplication is communicative so our definitions are equivalent, everything is dandy. Feb4 revised There is only one interesting measure space don't use MathJax for text formatting Feb2 comment Improvement over gamma correction for brightening images? You could try $y=x/(a(1-x)+x)$ with $a>0$, which is the one-parameter family of rational functions through $(0,0)$ and $(1,1)$. Related: math.stackexchange.com/q/297768/856 Feb2 comment Constraint optimization with Calculus of Variations. How to handle positive function constraint? I don't know. I've only read the textbook by Gelfand and Fomin. It wasn't too forbidding, as I recall. Jan31 comment Is it possible to construct a system of equations for which the set of solutions is a plane? Then mm-aops's second example works: $0x+0y+z=0$. There are $n$ equations in $3$ variables; here $n=1$. Jan31 comment In how many ways can we distribute 24 bullets among four burglars? Are the burglars being armed with these bullets or being shot by them? Jan31 comment Decorating eggs I imagine that a very good empirical solution is already well known, at least for a spherical egg. Jan30 comment Constraint optimization with Calculus of Variations. How to handle positive function constraint? I don't remember the theory, but here's the intuition: If you only enforced nonnegativity at a finite number of points $x_0, x_1, x_2, \ldots$, your Lagrangian would be $L[f] = F[f]-\lambda_0(f(x_0)-0)-\lambda_1(f(x_1)-0)-\lambda_2(f(x_2)-0)-\cdots$ with $\lambda_i\ge0$. But nonnegativity at all points is an infinite number of constraints. So you may consider $\lambda$ a function of $x$, and write the Lagrangian as $$L[f] = F[f]-\int\lambda(x)(f(x)-0)\,\mathrm dx,$$ with $\lambda(x)\ge0$ for all $x$. Jan26 comment Physical meaning of some identity in a weighted undirected graph How did you come across this equation? Some context might help for finding a meaningful interpretation. Jan25 comment The top 1% own 50% of the world's wealth - how do we turn this into a function? en.wikipedia.org/wiki/Pareto_principle Jan24 comment Generating Symmetric Matrix Any such matrix is of the form $A=Q\Lambda Q^T$ with orthogonal $Q$ and diagonal $\Lambda$, such that the minimum diagonal entry of $\Lambda$ has multiplicity at least $2$. Generate such a $Q$ and $\Lambda$ randomly and you're set. Jan23 comment Infinite connected graph such that every vertex has finite degree Sounds about right. Pick a vertex $v$ and consider the number of vertices that can be reached from $v$ in up to $n$ steps. (I assume a connected infinite graph is one in which any two vertices have a path of finite length between them.) Jan23 comment How to Distribute Points in a Poisson Distribution in a Circle Do you mean a Poisson-disk distribution? Jan23 comment Confusion about order of operations with point-in-tetrahedron formula Here's the easy way to test if a point is in a tetrahedron: steve.hollasch.net/cgindex/geometry/ptintet.html