news
The projective model structure on chain complexes
Let $\mathcal{A}$ be an abelian category with enough projective objects and let $\mathcal{M}$ be the category of chain complexes in $\mathcal{A}$ concentr...
Apr 11, 2026
Archive: News
news
Show that $Q(x):=200x^3-200x^2+200x+100$ is an irreducible polynomial over the field $\mathbb{Q}$ of rational numbers.
Show that $Q(x):=200x^3-200x^2+200x+100$ is an irreducible polynomial over the field $\mathbb{Q}$ of rational numbers. I'm trying to use Eisenstein&#...
Apr 11, 2026
news
Derivative Riccati-Bessel function
I have found two derivatives of the so-called Riccati-Bessel functions in a textbook $$ (x j_n(x))'=xj_{n-1}(x)-nj_{n}(x)$$ and $$ (x h_n^{(1)}(x))&#...
Apr 11, 2026
news
Complex exponential squared does not equal sinusoid squared?
I just noticed this today and I'm a bit confused by it. If we represent cos(x) as the real part of exp(ix), then I always thought that we could then ...
Apr 11, 2026
news
MATLAB Code for triple integral
I want to evaluate the $\int\int\int dxdydz$ using 'integral3' function in MATLAB. But the only code my intuition has helped me it this: g = @(x...
Apr 11, 2026
news
What does "discrete" really mean, in plain English?
Can someone explain what a "discrete" function really means, in a philosophical sense, in plain English? As a guess, does discrete mean there ar...
Apr 11, 2026
news
Divergent Integral?
Why is $$\int_{-\infty}^{\infty} \frac{2x}{1+x^2}dx$$ divergent, when the function being described is clearly an odd function and $$\int_{-a}^{a} \frac{2x...
Apr 11, 2026
news
Is there something similar for division as this Japanese multiplication method?
In this youtube link, a really cool method to multiply two big numbers is given. Only works of integers. I was wondering if something unconventional and s...
Apr 11, 2026
news
Maximizing the Sharpe ratio by finding the optimal weights
In calculating the Sharpe Ratio: $S = (\frac{\bar r_p - r_f}{\sigma_p})$ Where: $\bar r_p$ = Portfolio return (See below) $r_f$ = Risk free rate = 0.03 (f...
Apr 11, 2026
news
Coefficients of characteristic polynomial of a matrix
For a given $n \times n$-matrix $A$, and $J\subseteq\{1,...,n\}$ let us denote by $A[J]$ its principal minor formed by the columns and rows with indices f...
Apr 11, 2026
