# Paxinum

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bio website people.su.se/~peal0658 location Sweden age 27 member for 3 years, 11 months seen Jun 30 at 1:15 profile views 232

Languages: Java, C, C++, Mathematica, Php, HTML, CSS, LaTeX.

Interests in computer science: Fractals, genetic algorithms and AI programming.

# 183 Actions

 Jul2 awarded Curious Jun13 comment Solving systems of linear congruential equations See planetmath.org/florentinsmarandache perhaps. Jun7 comment On combining $n$ and $n^2$ into one number @BenjaminDickman: Why discriminate on age? Perhaps it might be suitable for math.stackexchange, but it is seemingly a non-trivial question. Jun7 comment Show, by the element method that, for all subsets P, Q, and R of U, (P − Q) ∩ (R − Q) = (P ∩ R) − Q. Draw a picture. Venn diagrams is your friend. Clarification: This type of problem, can easily be proved using Venn diagrams. Even an elementary picture, can be considered as a proof. In this case, draw 3 circles, as on the wikipedia page, and identify left hand side, and right hand side in the picture. Note that the regions for both "interpretations" are the same. Jun7 answered Is $i$ irrational? Jun7 comment Number of solutions to sudoku puzzle @Jeff: General Sudoku ($n^2 \times n^2$ board) is NP-complete. The and the 9x9-board can be reduced to a SAT-problem, so it depends on your efficiency of the SAT-solver. However, this is equivalent to trying to solve the puzzle, I would say. If there was a quick way for 9x9-then most likely, this generalizes to all sizes, and you would become famous/assassinated by CIA. Jun7 asked Number of solutions to sudoku puzzle Jun1 comment How to evaluate $\int_{0}^{\frac{\pi}{2}}\frac{1}{(1+x^2)(1+\tan x)}\,\mathrm dx$ I think this is a typo; tan should perhaps be arctan in the question. Then things makes sense. May29 comment compact and convex set How about using weak inequality in your definition, instead of strict? Is that what you mean? What are $X_1,X_2$ and $H$? Vectors? Mar22 comment Prove that a point is optimal in LP-problem Eh, nevermind, found a way to solve the equivalent problem in another way, but it is involved. Mar22 awarded Tumbleweed Mar15 asked Prove that a point is optimal in LP-problem Mar9 comment Invertibility of NxN nonnegative matrix with diagonally dominant elements As Benoit tells you; the intuition is as follows; for any such generic matrix, all elements are non-equal. Thus, we may fiddle each element a little bit and still satisfy all conditions you describe. Thus, there is an open ball around each generic matrix. If the generic matrix you started with was non-invertible, then some (most) elements in the small ball around this matrix must be invertible. Dec8 answered Circular Permutations With Repetitions (Mirrored Ignored) Nov30 comment Fields that require both CS and pure math Added now, see link. Nov30 revised Fields that require both CS and pure math added link Nov13 comment Proving constant function given the second derivative. Well, since we already assumed that $f' \leq 0$ everywhere, and it is also weakly increasing, so if the limit to the left is 0, then the entire f' is at least 0, but at the same time, it is at most 0. Thus, constant. Nov13 comment Proving constant function given the second derivative. Well, for some $X$, we have that $f'(x)\geq a/2$ if $x>X$, (follows from how limits work). Now, $f$ is just the area under $f'$, from say $X$, plus some constant. But, area under $f'$ from $X$ to infinity is at least the area of a rectangle with height $a/2$ and infinite width, so $f$ must have go to infinity as x does. Or, you can just argue that $f(x)$ must lie above the line $y=ax/2+c$ for some fixed $c$. Nov13 answered Proving constant function given the second derivative. Sep23 answered How to show that $\cos\frac{2\pi}{n} + \cos\frac{4\pi}{n} + \ldots+ \cos\frac{2\pi(n-1)}{n} = -1$ for all positive integers $n$?