It is well-known that tensor decompositions show separations, is, constraints on local terms (such as positivity) may entail an arbitrarily high cost in their representation. Here we many of these separations disappear the approximate case. Specifically, for every approximation error $\varepsilon$ and norm, define rank minimum element $\varepsilon$-ball with respect to norm. For positive semide...

It is well known that the Poiseuille mass flow rate along microchannels shows a stationary point as fluid density decreases, referred to Knudsen minimum. Surprisingly, if characteristic length comparable molecular size, minimum disappears, reported for first time by Wu et al. ( J. Fluid Mech. , vol. 794, 2016, pp. 252–266). However, there still no fundamental understanding why monotonically inc...