« first day (1503 days earlier)   

1:23 AM
1
Q: A topology different from discrete and anti-discrete, in which every open set is closed, and every closed set is open.

Nitro KansasTo give an example of a topology on a set of four points, different from discrete and anti-discrete, in which every open set is closed, and every closed set is open.I have 0 ideas at all, I thought that just the same, that only a discrete topology has such characteristics for sets.

2
Q: What is the number of lattice paths of length 16 from the point (0,0) to (8,8) that go through (4,4) but don't go through (1,1), (2,2), (3,3)

Yaniv Polischukwhat is the number of lattice paths of length 16 from $(0,0)$ to $(8,8)$ that go through $(4,4)$, don't go through $(1,1), (2,2), (3,3)$, and don't go over $y=x$? Here's what I tried: since we can't go through those 3 points above, we can first go to $(3,2)$ from $(1,0)$ (there is one forced move...

 
 
3 hours later…
3:57 AM
8
Q: Regarding a Coin Toss Experiment by Neil DeGrasse Tyson, and its validity

Mystic MickeyIn one of his interviews, Clip Link, Neil DeGrasse Tyson discusses a coin toss experiment. It goes something like this: Line up 1000 people, each given a coin, to be flipped simultaneously Ask each one to flip if heads the person can continue If the person gets tails they are out The game contin...

1
Q: Is Schwarz's Lemma true for squares?

CarlyleIn a recent complex analysis exam, we were asked which step(s) in the proof of the Riemann Mapping Theorem fail, when you replace every instance of $\mathbb{E}$ with the square $$\mathbb{S} = \{z\in\mathbb{C}:|Re(z)|, |Im(z)| < 1 \}$$ One error that arose is that the square root function is not a...

 
4:40 AM
2
Q: A ring whose all elements are zero divisors

ChaudharyI know that set of nilpotent elements in commutative ring forms an ideal, but set of zero divisors does not form a well known structure. I am wondering if there exists a ring $R$ such that all elements of $R$ are zero divisors. For example we can take $S=\lbrace 0,2,4,6 \rbrace$ as a subring of $...

 
 
1 hour later…
6:07 AM
1
Q: Kernel Regression & Weights Normalization

MistapopoLet be $X=[x_j(t_i)]_{i,j} \ M_{n,p}(\mathbb{R})$ a state matrix of $n$ $x(t_i) \in M_{1,p}(\mathbb{R})$ observations of $p$ sensors $X_j$ representing the normal conditions of a system for some timesteps $t_1, ..., t_n \in T_n \subset T$. The linear estimator of the Kernel Regression is : $$ \fo...

 
 
3 hours later…
8:58 AM
3
Q: Derived set of a closed subspace

EarnurSuppose $X$ is a compact Hausdorff topological space with a basis of clopen sets. Let $A$ be a closed subspace of $X$ and let $A^{(0)}=A$, $A^{(1)}=A^\prime$, etc. My question is: it is true that $A^{(n)}=A\cap X^{(n)}$ for all $n\in\mathbb{N}$? Since $A\subset X$, then $A^{(n)}\subset X^{(n)}$. ...

 
 
2 hours later…
11:26 AM
0
Q: Heat Equation : Can a singularity develop away from origin?

DesuraConsider a radial, nonlinear, 2D-heat equation \begin{align*} u_t &= u_{rr} + \frac{1}{r}u_r + F(t,r,u,u_r), \quad (t,r) \in [0,+\infty) \times [0,1] \\ u(0,r) &= f(r) \in C^{\infty}([0,1]), \quad f(0) = 0 \\ u_{|[0,+\infty) \times \{0,1\}} &= 0 \end{align*} where $F(t,r,p,q)$ is a smooth functio...

 
 
3 hours later…
1:57 PM
4
Q: Manipulating Algebraic Equations

LucasI'm sorry if this question (or possibly multiple depending on how long this I intend for this to be) is a little too elementary, but I've been seriously struggling with this for the past week. I never really questioned this until recently and it has me stumped and I can't move on with math witho...

 
 
3 hours later…
4:27 PM
2
Q: Is there is way to determine if the n-th roots of a polynomial is a polynomial?

pieI was this problem: $$\int\frac{dx}{\sqrt{x^4+2x^3+3x^2+2x+1}}$$ I solved this question because I just knew that $(1+x+x^2)^2=x^4+2x^3+3x^2+2x+1$ but this made me wonder is there is a way to know if the $n-$th root of a certain polynomial is a polynomial? Given a polynomial how to determine $n$ w...

 
 
5 hours later…
9:49 PM
3
Q: Calculating a Conditional expectation

MaximilianMy question is the following. Given that we have $n$ i.i.d. random variables $X_1,...,X_n$ with distribution $f(x)=\frac{2}{\lambda^2}x\mathbf{1}_{[0,\lambda]}(x)$, where $\lambda> 0$ is some parameter, how do I calculate the the conditional expectation $$E[X_i|X_{\max}],$$ with $X_{\max}=\max\{X...

 

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