All Questions
0
votes
0answers
11 views
Can every real number be represented by a (possibly infinite) decimal?
Does every real number have a representation within our decimal system? The reason I ask is because, from beginning a mathematics undergraduate degree a lot of 'mathematical facts' I had previously ...
0
votes
0answers
13 views
What is meant by the matrix of $f$ relative to a given basis of $V$?
Let $f$ be a linear operator on a finite dimensional vector space $V$ over a field $K$.
What is meant by the matrix of $f$ relative to a given basis of $V$?
(ask for definition)
2
votes
0answers
15 views
Algorithm to find rectangle inside a triangle
I am trying to write a program that generate procedural cities.
However, I am stuck on a problem : I don't know how to subdivide a triangle into a rectangle and other triangles. I know how to ...
0
votes
0answers
16 views
Why does Black-Scholes equation hold on continuation region of American Option?
Explanation for Put Option:
$ \frac{\partial V}{\partial t}+ \mathcal{L}_{BS} (V) = 0 $, where
$\mathcal{L}_{BS} (V) = \frac{1}{2} \sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + (r-\sigma) S ...
0
votes
0answers
6 views
Algorithms for covering a rectilinear polygon using the same multiple rectangles
All angles of the polygon are right. It may be convex or concave. Use the same rectangle to cover the polygon. The edge of the polygon and rectangle are parallel with the coordinate axis. Overlapping ...
1
vote
1answer
26 views
Polynomials $p$ of degree $ \le 2$
Find all polynomials $p$ of degree $ \le 2$ which satisfy the given condition:
a) $p(0)=p(1)=p(2)=1$
b) $p(0)=p(1)$
IN each case, find all polynomials $p$ of degree $ \le 2$ which satisfy the given ...
0
votes
0answers
14 views
solving laplace in 3d using finite differences
I have created a function laplace3d() which accepts a 3D array describing the boundary conditions and -Inf at the places of unknown. It then calculates these ...
0
votes
0answers
4 views
Matlab code for fixed point iteration
I want to write in Matlab a function that appreciates the fixed point iteration for a system of equations. The idea is:
$\begin{bmatrix}
x{_{1}}^{m+1}\\
x{_{2}}^{m+1}
\end{bmatrix}= ...
0
votes
1answer
29 views
How to show an matrix is an inner product ? Let $B$ be the bilinear form
Let $V=\mathbb{R}^2$
Let $B$ be the bilinear form with matrix \begin{pmatrix}
6&-5 \\
-5 & 6 \\
\end{pmatrix}
Is $B$ an inner product?
Thanks so much!!!
0
votes
1answer
19 views
Definite integral doubt
I'm starting to study Calculus now, I've got the following problem:
What's the minimum value of $\displaystyle F(a) = \int_{0}^{2} |x^2 - a^2|\, \mathrm{d}x$
When $0 < a < 2$, I managed to ...
0
votes
1answer
16 views
algorithm to determine complexity of algorithms?
Given a decision problem X, can there exist an algorithm A which, given any algorithm B which solves X in finitely many steps, determines whether B runs in polynomial time? If such an A exists, when ...
0
votes
0answers
13 views
Primes: Constant scaling factor for $p$ and $m_j$? A fractal dimmension?
Taking into account the theorem from my previous post "Combination of positive integers in terms of primes" let me state the following theorem (notation and conditions follow that post and its answer ...
2
votes
1answer
13 views
Looking for bounds of a recursively defined sequence
I'm looking for the tightest upper and lower bounds on the sequence defined recursively by $a_{0}=1$
and $a_{n}={\displaystyle \sum_{k=0}^{n-1}\frac{4}{n^{2}}a_{k}+c\cdot n}$
for $c>0$. It is ...
5
votes
3answers
31 views
Is the cartesian product of groups the product of a normal subgroup and its quotient group?
I'm studying elementary group theory, and just seeing the ways in which groups break apart into simpler groups, specifically, a group can be broken up as the sort of product of any of its normal ...
2
votes
1answer
39 views
About continuity of functions and limits of sequences
I know that there's a theorem which says that if $f$ is a continuous function, then:
$$\lim f(x_n) = f(\lim x_n)$$
This is used to solve, for example:
$$\lim(\sin(\frac{2n\pi}{1 + 8n})) = \sin(\lim ...
