Distributive property by Ciro Santilli 37 Updated 2025-07-16
One of the defining properties of algebraic structure with two operations such as ring and field:
This property shows how the two operations interact.
Existence and uniqueness results are fundamental in mathematics because we often define objects by their properties, and then start calling them "the object", which is fantastically convenient.
But calling something "the object" only makes sense if there exists exactly one, and only one, object that satisfies the properties.
One particular context where these come up very explicitly is in solutions to differential equations, e.g. existence and uniqueness of solutions of partial differential equations.
CuriousMarc by Ciro Santilli 37 Updated 2025-07-16
Mostly on vintage electronics. Lots of focus on microwave, which he has worked a lot with.
Has been going wild with restoration and reverse engineering of the Apollo moon mission.
Video 1.
Inside the WILD Lab of CuriousMarc by Keysight Labs (2022)
Source.
TODO what is the point of them? Why not just sum over every index that appears twice, regardless of where it is, as mentioned at: www.maths.cam.ac.uk/postgrad/part-iii/files/misc/index-notation.pdf.
Vectors with the index on top such as are the "regular vectors", they are called covariant vectors.
Those in indices on bottom are called contravariant vectors.
It is possible to change between them by Raising and lowering indices.
The values are different only when the metric signature matrix is different from the identity matrix.
Semiconductor diode by Ciro Santilli 37 Updated 2025-07-16
Figure 1.
I-V curve of a diode
. Source. This image shows well how the diode is only an approximation of the ideal one way device. Notably, there is this non-ideal voltage drop across the device, which can be modelled as constant. It is however an exponential in fact.
Video 1.
Diodes Explained by The Engineering Mindset (2020)
Source. Good video:

Unlisted articles are being shown, click here to show only listed articles.