All Questions
0
votes
0answers
7 views
Understanding the relation of weak and weak star toplogy
I'm working with Eberlein- Smulian Theorem fromm the book "Topics in Banach Space Theory". During the proof I have seen that there is used a lot the concept of weak topology and weak star topology. ...
0
votes
0answers
5 views
Copulas/Probability Theory
So I have a basic understanding of copulas but wanted to verify I'm applying things correctly to reach the correct outcomes..
Show that as $\theta\to\infty, C^{Fr}(u_1,u_2)\to\min(u_1,u_2)$, the ...
2
votes
3answers
30 views
$A \oplus B = A \oplus C$ imply $B = C$?
I don't quite yet understand how $\oplus$ (xor) works yet. I know fundamentally in terms of truth tables it means that only 1 value(p or q) can be true, but not both.
But when it comes to solving ...
0
votes
0answers
4 views
Question about Katz centrality
As you may know the Katz centrality is defined by $[I-\alpha G]^{-1}$ where $G$ is a weighted graph. As long as $\alpha$ is less than the $1/\lambda_{max}$ one can expand it to: $$[I-\alpha ...
0
votes
0answers
11 views
Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$
I'm reading a book functional analysis, and reading and have seen an example of somebody please help me if you can. The example that I've seen is the following:
If $A$ is a normed algebra and ...
0
votes
2answers
34 views
Find $\lim_{n\to\infty} \frac{n^2}{2^n}$
$$\lim_{n\to\infty}\frac{n^2}{2^n}$$
Do you have some tips so I could solve this problem, without the use of L'Hôpital's rule?
Indeed, we didn't see formally L'Hôpital's rule, nor Taylor series so ...
0
votes
0answers
13 views
Finding position vector of cross product
I have been stuck trying to find the solution doe this following question:
If a = (-1, 5, r ) b = (-5, 1, 1) and c = (-1, 1, -3) find the values of for which a x b is perpendicular to a x c. (state ...
2
votes
0answers
22 views
If $f$ is integrable then so is $1/f$
Let $f$ be an integrable function on $[a,b]$ with $|f| \geq p > 0 $ for $a \leq x \leq b$. Show that $\frac{1}{f}$ is also integrable on $[a,b]$.
I was told the Cauchy-Schwarz Inequality might be ...
0
votes
1answer
16 views
Using angle formula to solve $3\tan\theta = 2\cos\theta$
This may seem fairly straightforward, but I have been stuck on this for the past half-hour.
I need to use Double Angle Formulae such as the following:
$\sin2A ≡ 2\sin A \cos A$
$\cos2A ≡ \cos^2A - ...
0
votes
1answer
16 views
orthogonal projections and subspaces relations
Let $\mathcal{S}$ and $\mathcal{T}$ be two subspaces of $\mathbb{R}^n$, let $P$ be the orthogonal projection of $\mathbb{R}^n$ on $\mathcal{S}$ and let $Q$ be the orthogonal projection of ...
0
votes
0answers
22 views
Point coords after rotate
The first square is the workspace (Downloaded image size). Green point is 0.0 (x, y). Down / right value increases.
Image is rotated, and its overall size varies - the red square is the new size. ...
1
vote
0answers
12 views
Confusion related to interior point method
I was reading this wiki article related to interior point method.
I didn't get when they say that it applied Newton's method to get an update for $(x,\lambda)$. How the expression at the end ...
0
votes
2answers
14 views
Polynomial with complex coefficients
I can't solve the following questions:
Let $a,b$ be real numbers, $Z= a + ib$.
How much polynomials with complex coefficients $q(x) = x^3 + b_2 x^2 + b_1 x + b_0$ there are so that $Z$ is a root of ...
0
votes
2answers
22 views
A and B play a series of games which can not be drawn and p,q are their respective chances of winning a single game.
Problem :
A and B play a series of games which can not be drawn and p,q are their respective chances of winning a single game. What is the chance that A wins $m$ games before B wins $n$ games.
...
0
votes
0answers
7 views
Problem with finding a projective transformation
I want to practice finding projective transformations but I'm not sure if I do it right.
For example:
$[1:1:0] \rightarrow [1:0:0]$
$[1:0:1] \rightarrow [0:1:0]$
$[1:1:1] \rightarrow [0:1:0]$
...
