general
Finding the ACF of AR(1) process
For an AR(1) process: $X_{t} = \phi X_{t-1} + w_{t}$ with $w_{t} \sim N(0,\sigma^{2})$ How do you derive the ACF of the process? Since $E[X_{t}] = 0$, wou...
Apr 22, 2026
Archive: General
general
A sequel for Elementary Analysis by Ross?
I've been learning real analysis from this book: Elementary Analysis, K.A. Ross I really liked the style of this book. It is quite old, and sometimes...
Apr 22, 2026
![How to determine if some line segments are collinear [duplicate]](https://news.conceivablytech.com/uploads/how-to-determine-if-some-line-segments-are-collinear-duplicate_720.jpg)
general
How to determine if some line segments are collinear [duplicate]
Let's say I have several Line Segments that are connected to each other and make a Polyline. How can I determine if they are on a single straight lin...
Apr 22, 2026
general
How can I rotate a coordinate around a circle?
I need to rotate an object in a circle around a central point. All I know is the rotation of the centre point in degrees, the centre point location (Which...
Apr 22, 2026
general
What is the meaning of $x*\sqrt{3} \mod 1$?
What is the meaning of $x*\sqrt{3} \mod 1$? I'm trying to understand this: $$5( x*\sqrt{3} \mod 1) $$ If we talk about: $x=19,22,48,98$ what will be ...
Apr 22, 2026
general
What is the carrier set functor?
In https://www.mimuw.edu.pl/~tarlecki/teaching/ct/slides/fnats.pdf , page 5, the carrier set functor is defined thus: Carrier set functors: |_| : $Alg(Σ) ...
Apr 22, 2026
general
Algorithm for generating integer partitions up to a certain maximum length
I'm looking for a fast algorithm for generating all the partitions of an integer up to a certain maximum length; ideally, I don't want to have t...
Apr 22, 2026
general
How to draw a contour map of $ f(x,y)=x^2+y^2+xy$
I have used a program to see that it is an ellipse but I want to know the process of thinking to actually draw the contour map myself. $x^2+y^2+xy=C$ for ...
Apr 22, 2026
general
Solving a non-homogeneous linear recurrence relation
So i have this non-homogeneous linear recurrence relation to solve: $$a_{n}=2a_{n-1}-a_{n-2}+2^n+2$$ $a_{1}=7$ and $a_{2}=19$ I know that the non-homogene...
Apr 22, 2026
general
Differentiating logsumexp
If I've got a function $$ \log p(\tau | \theta) = \log ( \frac{\exp(\theta^T \tau)}{\sum_\tau \exp(\theta^T\tau)} ) $$ how do I calculate its derivat...
Apr 22, 2026
