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Einstein notation for partial derivatives by Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
The Einstein summation convention works will with partial derivatives and it is widely used in particle physics.
In particular, the divergence and the Laplacian can be succintly expressed in this notation:
In order to expresse partial derivatives, we must use what Ciro Santilli calls the "partial index partial derivative notation", which refers to variales with indices such as , , , , and instead of the usual letters , and .
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.
Of all the rich person foundations, this is the one that feels the most hardcore.
They put huge focus on autism. Do they have an autistic child? Yes: www.forbes.com/pictures/eilm45mll/james-simons-autism/?sh=7825234250ce his adughter.
Can represent a symmetric bilinear form as shown at matrix representation of a symmetric bilinear form, or a quadratic form.
Mahayana adds a bunch of stuff on top of the Pali Canon. Most of it appears to be random mysticism. Maybe there is something good in it... maybe.
Psalm 46:10 from the bible:
Be still, and know that I am God;
I will be exalted among the nations,
I will be exalted in the earth.
Theses places give out free food all the time.
The first time Ciro Santilli went to one was when an Indian friend of his took him to the one in the North of Paris when they were living there in the first half of the 2010's, the Gurdwara Singh Sabha France.
Much like Islam's Ramadan, Ciro Santilli appreciates this a lot due to due to Ciro Santilli's self perceived compassionate personality and Ciro Santilli's cheapness.
Instead of just talking, those people really go out, and put food on the plate for anyone who needs it (or even for those that don't really need it! Although who would be so souless to eat for free and not donate a few bucks if they can afford to???). There's a beauty to that.
Writing this also remembered Ciro of non-religious groups that would give out free food to the poor at
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