What is torsion in differential geometry? Is differential geometry Euclidean? What is computational algebraic geometry? Discuss some contemporary applications of geometry. What does edge of regression mean in differential geometry? What is the differential of a wedge product?
In the two-dimensional case one can arrange matters so that all the velocities are parallel. If we furthermore assume that the tile is connected, we can also show that the union of all the translates with a common velocity form a -invariant subset of the torus. Finally, we show that til...
What does a bracket mean in vector maths? What does squaring a vector mean? In \mathbb{R}^3 you are given the point P(2, -34, -5) and the vector v = (6, -29, -91). If the arrow \vec{PQ} represents v, then what is Q? What is mean by a zero vector? If vector u =...
Theorem 1 There does not exist any algorithm which, given a dimension , a periodic subset of , and a finite subset of , determines in finite time whether there is a translational tiling of by . The caveat is that we have to work with periodic subsets of , rather than all of ; we ...
There is a big difference between "conserved" (does not change over time) and "invariant" (is agreed on by different reference frames). The body which is at rest or in motion in the non-inertial frame experiences a change in momentum (changes over time) which is apparently not caused ...
Though plenty of the problems on Atcoder are ad-hoc / brain teaser / maths but they are very fun to solve and most of those can be done within 20 lines of code. → Reply Misuki 9 months ago, # ^ | ← Rev. 3 +35 I think there isn't much problem rely on invariant or ...
Latent profile analysis was performed to estimate and decide the number of profiles. This approach does not rely on random values (e.g. a standard deviation above the mean) but on the fit of models with a different number of profiles. To decide the number of profiles, we attended both the...
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So does this mean that you now accept that there is no problem in Cantor's Diagonal argument in the extant mathematical world where aleph-0 and 2^aleph-0 are clearly and demonstrably not the same, and that the constructions you claim must be true are not in fact constructions t...
This is consistent with the random matrix theory interpretation, since is also the spectral measure of , where is the orthogonal projection to the span of the first basis elements, so in particular has spectral measure . If is unitarily invariant then (by a fundamental result of Voiculescu) ...