Rahul
Reputation
84/100 score
 Mar3 comment Unique circle through two points perpendicular to a given line? Perform an inversion with respect to one of the points? Mar3 comment Singular value decomposition for matrices that are not square? Your matrix has 3 rows and 2 columns, so just to make the dimensions match you must have $U$ with 3 rows and $V^T$ with 2 columns. Is that what you mean by the "missing last component"? Mar3 comment How to calculate the critical density estimation for “continuum” percolation model in “3D space” when we have “spatial correlation”? This looks more like a percolation theory problem to me. Feb28 comment Insertion into an optimal route – is it still optimal? For a concrete example, consider points SABCDE lying clockwise on a circle, with distance SA < SE; then the optimal path is SABCDE. Now insert X between S and E so that SX = XE < SA; now the optimal path is SXEDCBA. Feb28 comment Insertion into an optimal route – is it still optimal? Unfortunately, the new optimal route cannot always be the old optimal route with the new point inserted, otherwise you could solve the travelling salesman problem in polynomial time by inserting one point at a time. Feb25 comment Intersection of 8 spheres: find the volume I'm pretty sure that by symmetry the intersection looks like a rounded octahedron. It's the union of 8 disjoint congruent pieces, one of which is the portion of the unit sphere centered at $(0,0,0)$ that lies in the region $x,y,z\ge1/2$. Feb23 comment How is it possible to change the pitch and the tempo of an audio track independently of each other? Relevant Wikipedia article: en.wikipedia.org/wiki/Audio_time-scale/pitch_modification. Possibly relevant StackExchange site: dsp.stackexchange.com. Feb23 awarded Enlightened Feb23 awarded Nice Answer Feb20 comment Irregular Implicit Plot in Mathematica What Mathematica is actually doing is trying to plot the regions where $y-x\tan(\cdots)$ changes sign. 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.