https://ir.cwi.nl/pub/10189/10189D.pdf Proof of 5 square packing in a square. In this papar, after define some nice length, slightly smaller-size square are prepared, and the 4 nice points are selected. And, it is shown that each of the sq…

en.wikipedia.org from wikipedia. As a continous extension of discrete graph, we can consider real tree, which is in the metric space. there are several conditions that real tree must satisfy. (such as Gromov product) The interesting thing …

youtu.be This video explains the algorithm of Delaunay triangulation nicely, even I could understand the concept. First draw big triangle that contains all vertex, and draw circumcircle of triangle. If some point (we call P) are inside of …

I like reading books on mathematics. I often go to the library and borrow several books. Now I bring two book on functional analysis. These days, I am thinking about the purpose of reading. Of course, you can gain lots of knowledge, and th…

using Optim n = [3 4 5 6 7 8 9 13 15 17] k = [1 2 5 7 11 15 21 47 65 85] lambda = 2.5 f(lam, x) = 1/size(k)[2] * sum((x[1] .+ x[2].*(n) .+ x[3].*(n).^2 .- (k)) .^ 2) - lam * sum(abs.(x)) #f(lam, x) = 1/size(k)[2] * sum((x[1] .+ x[2].*(n) .…

en.wikipedia.org Vertex cover is the subset of vertex sets such that for all edges, at least one endpoint belongs to that subset. It is related to maximal matching of graph. For bipartite graph, there is a nice theorem. en.wikipedia.orgKőn…

When we learn support vector machine, we often want to know the meaning of support. en.wikipedia.org In mathematics, support of function means some set that maps nonzero value by the function. (also, I found nice theorem related to support…

https://www.jstage.jst.go.jp/article/jsiaml/8/0/8_29/_pdf This study shows truncation error of particle method by using Taylor expansion, and mean value theorem, and triangular inequality. Also, open ball is used. And the change of variabl…

Hadwiger Nelson problem is the unsolved problem in mathematics, about minimum chromatic number of unit distance graph. en.wikipedia.org For planar graph, four color theorem is famous, but the unit distance graph allows intersection of edge…

scrapbox.io I found interesting problem related to separation of variables. We can see separation of variables not only in ODE problem, but PDE problem. www.sciencedirect.com For PDE, it is convenient because we can decompose into time dep…