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 ...
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. ...
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...
Wang’s argument is not known to be reversible: the failure of the periodic tiling conjecture does not automatically imply the undecidability of the translational monotiling problem, as it does not rule out the existence of some other algorithm to determine tiling that does not rely on the exist...
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...
We perform a bordism computation to show that the $$E_{7(7)}({\mathbb {R}})$$ U-duality symmetry of 4d $${\mathcal {N}} = 8$$ supergravity could have an an
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....
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...
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^...
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 ...