Effect of a change of basis on the matrix of a bilinear form Updated 2025-04-24 +Created 1970-01-01
If is the change of basis matrix, then the matrix representation of a bilinear form that looked like:then the matrix in the new basis is:Sylvester's law of inertia then tells us that the number of positive, negative and 0 eigenvalues of both of those matrices is the same.
Proof: the value of a given bilinear form cannot change due to a change of basis, since the bilinear form is just a function, and does not depend on the choice of basis. The only thing that change is the matrix representation of the form. Therefore, we must have:and in the new basis:and so since:
With X-ray crystallography by David Chilton Phillips. The second protein to be resolved fter after myoglobin, and the first enzyme.
Published at: Structure of Hen Egg-White Lysozyme: A Three-dimensional Fourier Synthesis at 2 Å Resolution (1965). The work was done while at the Davy Faraday Research Laboratory of the Royal Institution.
Phillips also published a lower resolution (6angstrom) of the enzyme-inhibitor complexes at about the same time: Structure of Some Crystalline Lysozyme-Inhibitor Complexes Determined by X-Ray Analysis At 6 Å Resolution (1965). The point of doing this is that it points out the active site of the enzyme.
Experimental Evidence for Quantized Flux in Superconducting Cylinders Updated 2025-04-24 +Created 1970-01-01
Paywalled at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.7.43
The paper that follows it in the journal is also of interest, "Theoretical Considerations Concerning Quantized Magnetic Flux In Superconducting Cylinders" by N. Byers and C. N. Yang, it starts:So there was some previous confusion about the flux quantum due to the presence of Cooper pairs or not.
In a recent experiment, the magnetic flux through a superconducting ring has been found to be quantized in units of ch/2e. Quantization in twice this unit has been briefly discussed by London' and by Onsager. ' Onsager' has also considered the possibility of quantization in units ch/2e due to pairs of electrons forming quasi-bosons.
Dumping the fitures at: archive.org/details/experimental-evidence-for-quantized-flux-in-superconducting-cylinders One day we can also dump the paper scans when it goes into the public domain in 2056! Public domain scientific paper by year.
(Upper) Trapped flux in cylinder No. 1 as a function of magnetic field in which the cylinder was cooled below the superconducting transition. temperature. The open circles are individual data points. The solid circles represent th, e average value of all data points at a particular value of applied field including all the points plotted and additional data which could not be plotted due to severe overlapping of points. Approximately two hundred data points are represented. The lines are drawn at multiples of hc/2e.(Lower) Net flux in cylinder No. 1 before turning off the applied field in which it was cooled as a function of the applied field. Open and solid circles have the same significance as above. The lower line is the diamagnetic calibration to which all runs have been normalized. The other lines are translated vertically by successive steps of hc/2e.
(Upper) Trapped flux in cylinder No. 2 as a function of magnetic field in which the cylinder was cooled below the superconducting transition temperature. The circles and triangles indicate points for oppositely directed applied fields. Lines are drawn at multiples of hc/2e.(Lower) Net flux in cylinder No. 2 before turning off the applied field as a function of the applied field. The circles and triangles are points for oppositely directed applied fields. The lower line is the diamagnetic calibration to which all runs have The other been normalized. lines are translated vertically by successive steps of hc/2e.
The term and idea was first introduced initialized by Hermann Weyl when he was working on combining electromagnetism and general relativity to formulate Maxwell's equations in curved spacetime in 1918 and published as Gravity and electricity by Hermann Weyl (1918). Based on perception that symmetry implies charge conservation. The same idea was later adapted for quantum electrodynamics, a context in which is has even more impact.
- microbit/micropython/uart.py: the Micro BIt comes with a UART simulator via the USB connection, it is very convenient: support.microbit.org/support/solutions/articles/19000022103-outputing-serial-data-from-the-micro-bit-to-a-computer To output data to the computer simply use Python
print. To receive you can e.g. use GNU screen:It appears to be very unreliable however, some times it shows up, sometimes it doesn't.screen /dev/ttyACM0 115200
If it only it were written in JavaScript instead of Haskell (!?), then Ciro might have used it as the basis for OurBigBook Markup.
To send voice and music, amplitude modulation had to be developed. And a key ingredient of this is the carrier wave.
The problem is, the carrier wave needs to have somewhat high frequencies, in the hundreds of kHz TODO why. But as you might imagine, that is hard to achieve by mechanical means such as a hand cranck like Hippolyte Pixiis alternator!
Interestingly, some of the first carrier wave generators were actually mechanical, e.g. the Alexanderson alternator.
But clearly such mechanical machines were not very scalable, and soon more electronic devices were introduced, notably the vacuum tube.
To use a prebuilt firmware, you can just use What that does is:
uflash, tested on Ubuntu 22.04:git clone https://github.com/bbcmicrobit/micropython
cd micropython
git checkout 7fc33d13b31a915cbe90dc5d515c6337b5fa1660
uflash examples/led_dance.py- convert the MicroPython code to bytecode
- join it up with a prebuilt firmware that ships with uflash which contains the MicroPython interpreter
- flashes that
To build your own firmware see:
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