Neon isotope line split photograph by J. J. Thomson
. Source. J. J. Thomson took this picture in 1912:There can, therefore, I think, be little doubt that what has been called neon is not a simple gas but a mixture of two gases, one of which has an atomic weight about 20 and the other about 22. The parabola due to the heavier gas is always much fainter than that due to the lighter, so that probably the heavier gas forms only a small percentage of the mixture.
Sets both a Dirichlet boundary condition and a Neumann boundary condition for a single part of the boundary.
Can be used for hyperbolic partial differential equations.
We understand intuitively that this imposes stricter requirements on solutions, which makes it easier to guarantee uniqueness, but also harder to have existence. TODO intuitively why hyperbolic need this extra level of restriction.
Analogous to a linear form, a bilinear form is a Bilinear map where the image is the underlying field of the vector space, e.g. .
Some definitions require both of the input spaces to be the same, e.g. , but it doesn't make much different in general.
The most important example of a bilinear form is the dot product. It is only defined if both the input spaces are the same.
Since DNA is the centerpiece of life, Ciro Santilli is extremely excited about DNA-related technologies, see also: molecular biology technologies.
Metric space vs normed vector space vs inner product space by
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
TODO examples:
- metric space that is not a normed vector space
- norm vs metric: a norm gives size of one element. A metric is the distance between two elements. Given a norm in a space with subtraction, we can obtain a distance function: the metric induced by a norm.
Hierarchy of topological, metric, normed and inner product spaces
. Source. youtu.be/Ca7c5B7Js18?t=803 compares Lagrangian mechanics equation vs the direct x/y coordinate equation.
Name origin: likely because it "determines" if a matrix is invertible or not, as a matrix is invertible iff determinant is not zero.
Luckily, early teens Ciro Santilli was partly protected from this by Ciro Santilli's cheapness.
But Ciro distinctly remembers one day in his early teens that he couldn't sleep very well, and he got up, and the was decided that he would become the greatest Magic: The Gathering player who ever lived. Can you imagine the incredible loss that this would have been to humankind? And talk about the incredible lack of development opportunity present in poor countries, related:
Supervised and unsupervised learning by
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
Feud between Sabine Hossenfelder and Luboš Motl by
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
Unlisted articles are being shown, click here to show only listed articles.