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How to Find a Finite-Difference Matrix
I have read several websites trying to explain finite-differential equations, but I haven't been able to find one that explains how it's put int...
Apr 22, 2026
Archive: News
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Asymptotic growth of recurrence sequences
A sequence $(a_n)_{nā„0}$ in $R$ satisfies $6š_š = a_{n-2} + a_{n-1},$ where $ š_0 =-1$ $ š_1 = -1$ Determine the asymptotic growth of $(a_n)_{nā„0}$. My qu...
Apr 22, 2026
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Reflection inside spherical mirror
Suppose you are inside a perfectly spherical mirror. You shoot one beam of light and it reflects on the walls of the mirror. Considering the intensity is ...
Apr 22, 2026
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What is $\max $ and $ \min $ in set theory?
I keep seeing $\max ( \cdot ) $ and $ \min ( \cdot ) $ everywhere. EDIT : It appears like this, $\max(4,9]$ or $\min[a,b)$ or sometimes with curly bracket...
Apr 22, 2026
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Range of Controllability is A-Invariant
Consider the controllability matrix $C= [B, AB, A^2B,...,A^{n-1}B]$ such that $A \in \mathbb{R}^{n\times n}$ and $B \in \mathbb{R}^{n\times m}$. Now consi...
Apr 22, 2026
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Jar of candies: Minimum subset size to satisfy a condition
Here is a problem my son was trying to solve: A bowl contains 100 pieces of candy: 48 green, 30 red, 12 yellow and 10 blue. They are all wrapped in a foil...
Apr 22, 2026
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Determine if a graph exists knowing the degree of its vertices
Problem: There is a graph on ten vertices whose degrees are $9,8,8,8,6,5,4,4,2,2$ Answer: False. My attempt: Since we know that $2 | E | = \sum _ { v \in ...
Apr 22, 2026
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Conjugate of unit quaternion
In the context of using unit quaternions to represent 3D rotations, I'm aware that the inverse is the conjugate. So if I have a unit quaternion Q = {...
Apr 22, 2026
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Green's function of an ODE (first order)
What is the Green's Function of the following ODE (in general form)? $$ \frac{dy}{dt} = f(t) y(t) + g(t) $$
Apr 22, 2026
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What does the 3-sphere look like?
The 3-sphere is a surface of a 4D sphere, and is thus 3 dimensional. Then we should be able to look at it in our 3 dimensions. So what does it look like? ...
Apr 22, 2026
