12,297 reputation
22180
bio website mathproblems123.wordpress.com
location Chambery, France
age 26
visits member for 3 years, 1 month
seen 13 hours ago

PHD - interests: PDE, Free boundaries, Shape Optimization


1d
comment Can a cube always be fitted into the projection of a cube?
Have you proved this for $n=3$? Does the projection of the unit cube on a plane contains a unit square? (I'm just asking. I don't know the answer)
2d
comment Write a non-recursive algorithm to compute n!
Just write a for loop. Recursion is not that bad for a factorial, since at each step you only use the last step. Recursion would be a bad idea for calculating Fibonacci's sequence, for example.
2d
revised Write a non-recursive algorithm to compute n!
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2d
comment Suppose $x_{\theta} = (\cos(\theta),\sin(\theta )) \in \mathbb R^2$. Prove $||x_{\theta + \theta^{'}} - x_{\theta}|| = ||x_{\theta^{'}} - x_{0}||$.
Smooth means of class $C^\infty$ which is differentiable by definition. In the case of the circle you have $x \to \sqrt{1-x^2}$ on an interval $(-1,1)$.
Apr
16
revised Suppose $x_{\theta} = (\cos(\theta),\sin(\theta )) \in \mathbb R^2$. Prove $||x_{\theta + \theta^{'}} - x_{\theta}|| = ||x_{\theta^{'}} - x_{0}||$.
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Apr
16
comment Suppose $x_{\theta} = (\cos(\theta),\sin(\theta )) \in \mathbb R^2$. Prove $||x_{\theta + \theta^{'}} - x_{\theta}|| = ||x_{\theta^{'}} - x_{0}||$.
I did not use the derivatives of sin and cos above.
Apr
14
comment Suppose $x_{\theta} = (\cos(\theta),\sin(\theta )) \in \mathbb R^2$. Prove $||x_{\theta + \theta^{'}} - x_{\theta}|| = ||x_{\theta^{'}} - x_{0}||$.
Yes, it is as rigorous as it gets. The circle is smooth, which means that it is locally the graph of a smooth function like $y=g(x)$, so locally you could write $x(t)=(t,g(t))$ in a certain coordinate system (possibly rotated), which is smooth. Reparametrizing to arclength preserves smoothness.
Apr
14
awarded  Revival
Apr
14
comment Odds of winning at minesweeper with perfect play
This is nice to know :)
Apr
13
comment Any two disjoint open sets are the interior and exterior of some set
Pick two disjoint open disks. How can you make one disk the interior of a set and the other the exterior of the same set? It is not possible. Do you mean to say that there is an open set $A$ such that the first of your sets is in the interior of $A$ and the second in the exterior of $A$? And try not to ask the question in the title.
Apr
13
comment Show a function is not continuous
$f^{-1}(\Bbb{R})=[0,1)$ which is not open.
Apr
13
answered Finding formula for a series and proving
Apr
13
revised A basic question on measurability of lim sup and lim inf of a function
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Apr
13
comment Suppose $x_{\theta} = (\cos(\theta),\sin(\theta )) \in \mathbb R^2$. Prove $||x_{\theta + \theta^{'}} - x_{\theta}|| = ||x_{\theta^{'}} - x_{0}||$.
The circle is a smooth surface (write any analitic representation) therefore its parametric representation is smooth.
Apr
13
comment if $a_n=\frac{a_{[\frac{n}{2}]}}{2}+\frac{a_{[\frac{n}{3}]}}{3}+\ldots+\frac{a_{[\frac{n}{n}]}}{n}$,then $a_{2n}<2a_{n}$
@china math: I was not eager to get the bounty, but why put a bounty on a question and when you receive the answer forget about it?
Apr
13
comment A basic question on measurability of lim sup and lim inf of a function
Yes, I get what you mean. I don't have the time now to write the proof that if $f$ is measurable then $g(x)=\liminf_{t \to x}f(t)$ is also measurable. You can prove it using the definition of $\liminf$. If someone else doesn't do it, I will write it tonight.
Apr
13
comment what is the dimension of this subspace for given problem
Yes, you are right.
Apr
13
comment A basic question on measurability of lim sup and lim inf of a function
$g$ is the liminf and $h$ is the limsup which you know are measurable. You say you need to prove that the set where $g=h$ is measurable. This is what I did above.
Apr
13
answered what is the dimension of this subspace for given problem
Apr
13
answered A basic question on measurability of lim sup and lim inf of a function