What does it mean when the point has an x-axis invariant? Given the transformation x = -u + v, y = 2u + v - w, z = 3u -v , describe the relationship between the differential volume dx \, dy \, dz and the differential volume du \, dv \, dw ...
If what you say [whatever you mean by it] is true, then the same thing can be said about Euclidean diagrams [as projections of a 4d-space?]. I had two diagrams (projections of worldlines with respect to different rest frames) which contained invariant elements. Inspecting the diagrams di...
What does cyclic mean in abstract algebra? Explain the importance of Fourier transformation. 11. Use the fundamental properties of the dot product to prove that ||x+y||^2+ ||x-y||^2=2(||x||^2+||y||^2). Interpret the result geometrically. ...
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 ...
By averaging the above dilation lemma, we can also establish a “structure theorem” that decomposes the indicator function of into components, each of which are invariant with respect to a certain shift in . We can establish this theorem in the case of measure-preserving actions on probability...
invariant measure of the\(N-1\)dimensional hyper-surface\(H({\pmb \Gamma }) = E\):\(\int _{\partial \Omega _S(N, V, E)} \textrm{d}\sigma /|\nabla H(\Gamma )|\). For regular enough Hamiltonians, this integral is a non-decreasing quantity ofE, which is one of the ...
math, geophysics, meteorology, data analysis & data visualization. We started discussing general UI & user workflow and ended at mathematicly proving our current approach (and probably not only ours) being incorrect (it appeared to be non-invariant to grid resolution). I realized that this projec...
I think there isn't much problem rely on invariant or variable substitution in my experience (at least ~ orange, not sure about red~ but probably not much still). And I feel most of the problems from ARC and old AGC can be solved by just proper reasoning and basic combinatoric skill ra...
Conservation is assumed to be born in the phase, just as momentum is for instance. In other words, all known phenomena in physics are deterministic, classical and real, in the sense that information does propagate locally and experiments conducted statistically do hide latent variables....
Due to the reversibility of such a process, entropy does not change, and its value must be the same in both reference frames. i.e., entropy is a Lorentz invariant1. Einstein also proposed that in the I′ frame the heat transfer dQ′ can be written as an exact differential as $$dQ^...