# All Questions

1,274,200 questions
Filter by
Sorted by
Tagged with
89 views

813 views

### Find outline of $N$ points in a plane

If I have $N$ point coordinates $P_i = ( x_i, \, y_i )$ and I want to draw the outline connecting only the points on the "outside", what is the algorithm to do this? This is what I want to do: Not ...
59 views

### Calculating interest-like problem

I'll make this short as this is a silly question. I have a number say 500. And a number n, which represents how many times I apply to my first number a transformation(add 20% to current value). This ...
94 views

### enumeration of subsets

Good evening. Let $\lambda>\omega$ a cardinal. We know that there is a bijection $\pi$ between $\lambda^+$ and $\lambda\times\lambda^+$. I don't understand in Remark 1 of the paper Shelah's proof ...
149 views

### Rolle's theorem for showing that $(x-a)^k$ divides $p(x)$ . . .

Have the following I'm stuck on: Suppose $p(x)=p_0+p_1 x+p_2 x^2+\cdots+p_n x^n$ is a polynomial of degree $n \geq 1$. Show that if $(x-a)^k$ divides $p(x)$ for some $a\in\mathbb R$ and some ...
485 views

### Analytic versus Analytical Sets

Browsing MathOverflow I came across a question about analytical sets. Through the discussion following a comment made by our very own Asaf, I learned that bold face $\mathbf{\Sigma^1_1}$ and light ...
57 views

### Are tempered representations unitarizabile?

Let $G$ be a locally compact, unimodular group and $Z$ be its center Clearly, square integrable representations with central unitary character is unitarizabile, since their matrix coeffecient imbed ...
19k views

### Find equation of a plane that passes through point and contains the intersection line of 2 other planes

Find equation of a plane that passes through point P $(-1,4,2)$ that contains the intersection line of the planes \begin{align*} 4x-y+z-2&=0\\ 2x+y-2z-3&=0 \end{align*} Attempt: I found ...
669 views

### Evaluating $\int_{-\infty}^{\infty}x\exp\left(-b^{2}\left(x-c\right)^{2}\right)\mathrm{erf}^{2}\left(a\left(x-d\right)\right)\,\mathrm{d}x$

I have big difficulties solving the following integral: $$\int_{-\infty}^{\infty}x\exp\left(-b^{2}\left(x-c\right)^{2}\right)\mathrm{erf}^{2}\left(a\left(x-d\right)\right)\,\mathrm{d}x$$ I tried to ...
2k views

### Why are persistent states of a Markov chain on a finite state space non-null?

i would like to understand the following statement about Markov chains on a finite state space S: "If S is finite, then one state ist persistent and all persistent states are non-null." It is more ...
407 views

### closest point on a plane to another point in $\mathbb{R}^3$

Given $4$ points in $\mathbb{R}^3$: $A(0,2,4);B(-2,6,-2);C(2,-4,8);D(10,2,0)$, find the line equation $AK$ when $K$ is the projection of $D$ on the plane $ABC$. The first thing I did was find the ...
3k views

### Direction of arrows in a phase portrait.

If I have a system like: $\frac{dx}{dt} = x, \frac{dy}{dt} = -y+x^2$ and I am asked to draw a phase portrait, once I have found the type of portrait (saddle point, node, spiral, etc.) from the ...
2k views

365 views

### Sex distribution

Suppose there are N male and N female students. They are randomly distributed into k groups. Is it more probable for a male student to find himself in a group with more guys and for female student ...
88 views

968 views

### Ramanujan Summation

It seems that under the light of Ramanujan Summation the following is plausible: $$1 + {2^{2n - 1}} + {3^{2n - 1}} + \cdots = - \frac{{{B_{2n}}}}{{2n}}(\Re)$$ Alas, I can't really find any ...
2k views

### Two Disk/Washer Method Problems (given a diagram)

Given a diagram from Calculus of a Single Variable by Larson and Edward (9th edition): I am interested in finding the volume of various regions when rotated about various lines. Specifically, I am ...
I have encountered the following problem: Let $f$ be continuous on $[a,b]$. Define the length of $f$ on $[a,b]$ by $$l=\sup_P[\lambda_P(f)],$$ where \lambda_P(f)=\sum_{k=1}^N\sqrt{(x_k-x_{k-...