How to build it: math.stackexchange.com/questions/3137319/how-in-general-does-one-construct-a-cycle-graph-for-a-group/3162746#3162746 good answer with ASCII art. You basically just pick each element, and repeatedly apply it, and remove any path that has a longer version.
Immediately gives the generating set of a group by looking at elements adjacent to the origin, and more generally the order of each element.
TODO uniqueness: can two different groups have the same cycle graph? It does not seem to tell us how every element interact with every other element, only with itself. This is in contrast with the Cayley graph, which more accurately describes group structure (but does not give the order of elements as directly), so feels like it won't be unique.
Stable isotope.
where:
- : matrix in the old basis
- : matrix in the new basis
- : change of basis matrix
Subtle is the Lord by Abraham Pais (1982) page 85:so it is quite cool to see that organic chemistry is one of the things that pushed atomic theory forward. Because when you start to observe that isomers has different characteristics, despite identical proportions of atoms, this is really hard to explain without talking about the relative positions of the atoms within molecules!
However, it became increasingly difficult in chemical circles to deny the reality of molecules after 1874, the year in which Jacobus Henricus van't Hoff and Joseph Achille Le Bel independently explained the isomerism of certain organic substances in terms of stereochemical properties of carbon compounds.
TODO: is there anything even more precise that points to atoms in stereoisomers besides just the "two isomers with different properties" thing?
Ciro's ASCII art circuit diagram notation by 
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01This notation is designed to be relatively easy to write. This is achieved by not drawing ultra complex ASCII art boxes of every component. It would be slightly more readable if we did that, but prioritizing the writer here.
Two wires are only joined if but the following are:
+ is given. E.g. the following two wires are not joined: |
--|--
| |
--+--
|Simple symmetric components:
-,+and|: wireAC: AC source. Parameters:e.g.:Hz: frequencyV: peak voltage
If only one side is given, the other is assumed to be at a groundAC_1Hz_2VG.C: capacitorG: ground. Often used together withDC, e.g.:means applying a voltage of 10 V across a 10 Ohm resistor, which would lead to a current of 1 ADC_10---R_10---GL: inductorMICROPHONE. As a multi-letter symmetric component, you can connect the two wires anywhere, e.g.or:---MICROPHONE---| MICROPHONE |SPEAKERR: resistorSQUID: SQUID deviceX: Josephson junction
Asymmetric components have multiple letters indicating different ports. The capital letter indicates the device, and lower case letters the ports. The wires then go into the ports:
D: diodeSample usage in a circuit:a: anode (where electrons can come in from)c: cathode
Can also be used vertically like aany other circuit:--aDc--We can also change the port order, the device is still the same due to capital| a D c |D:--cDa-- | Dac-- | Dca-- | --caDDCDC source. Ports:E.g. a 10 V source with a 10 Ohm resistor would be:p: positiven: negative
If only one side is given, the other is assumed to be at a the ground+---pDC_10_n---+ | | +----R_10------+G. We can also omitpandmin that case and assume thatpis the one used, e.g. the above would be equivalent to:If the voltage is not given, it is assumed to be a potentiometer.DC_10---R_10---GT: transistor. The ports aresgTd:Sample usage in a circuit:s: sourceg: gated: gate
All the following are also equivalent:---+ | --sgTd--| g --sTd-- | --Tsgd-- |I: electric current source. Ports:s: electron sourced: electron destination
V: Voltmeter. Ports:If we don't need to specify explicit positive and negative sides, we can just use:p: positiven: negative
without any ports. This is notably often the case for AC circuits.---V---Optionaly, we can also add the sides as in:
Numbers characterizing components are put just next to each component with an underscore. When there is only one parameter, standard units are assumed, e.g.:means:Micro is denoted as
+-----+
| |
C_1p R_2k
| |
+-----+- a capacitor with 1 pico Faraday
- a resistor with 2 k Ohms
u.Wires can just freely come in and out of specs of a component, they are then just connected to the component, e.g.:means applying a voltage of 10 V across a 10 Ohm resistor, which would lead to a current of 1 A
DC_10---R_10---G The best advertisements of all time by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01 Powder vs single crystal X-ray crystallography by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01After removing it:
- the black tape used pulled out the paint in parts of the wall, and even worse small bits of plaster on some corners
- the sticky from the blinds bits also pulled out a bit of plaster
Of course, we already knew that minimal plaster work would be needed from the start, since we have to hammer two small nails into the wall. But that level of damage might have been easily dealt with by a non-professional tenant himself. But the level I had was a bit more than I felt I should handle myself.
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