In the past Euler has shown considerable interest in specific cases of similarity in which one figure is constructed from another in some way (consider, e.g., E-129, Opera Omnia I.27 130-180 “Investigatio curvarum quae evolutae sui similes producant”, in which the objects of study are planar curves which are similar to their own evolutes). In the current work, he considers any two similar figur...

Snow avalanches are relatively dry and dense granular flows for which the Savage-Hutter (SH) equations have been demonstrated to be an adequate mathematical model. We review these equations and point out for which cases the equations have been tested against laboratory experiments. Since the equations are scale invariant and because agreement with experiments is good, laboratory experiments can...

Traditional classification algorithms can be limited in their performance when a specific user is targeted. User preferences, e.g. in recommendation systems, constitute a challenge for learning algorithms. Additionally, in recent years user’s interaction through crowdsourcing has drawn significant interest, although its use in learning settings is still underused. In this work we focus on an ac...

Let G = GSp(2) be the symplectic group with similitude of degree two, which is defined over Q. For a generic cusp form F on the adelized group GA which generates a large discrete series representation at infinity, we show that its spinor Lfunction is continued to an entire function and satisfies the functional equation. 0. Introduction. Let G = GSp(2) be the symplectic group with similitude of ...

Air-water flow measurements were conducted in two large-size stepped chute facilities (θ = 3.4 & 16o) to study experimental distortion caused by scale effects and result extrapolation to prototypes. The stepped geometries corresponded to moderate slopes typical of embankment dams and storm waterways. Experimental data included distributions of air concentration, air-water flow velocity, bubble ...