Answering a question of Benjamini, we present an isometry-invariant random partition the Euclidean space Rd, d≥3, into infinite connected indistinguishable pieces, such that adjacency graph defined on pieces is 3-regular tree. Along way, it proved any finitely generated one-ended amenable Cayley can be represented in Rd as to bounded polyhedra, and also pieces. A new technique developed prove i...

In this article, we pursue our investigation of the connections between theory computation and hydrodynamics. We prove existence stationary solutions Euler equations in Euclidean space, Beltrami type, that can simulate a universal Turing machine. particular, these possess undecidable trajectories. Heretofore, known complete constructions steady flows dimension 3 or higher were not associated to...

In this study, the effect of fractional derivatives on curves, whose application area is increasing day by day, investigated. While investigating effect, conformable derivative, which best suits algebraic structure differential geometry, selected. As a result, many special curves and Frenet frame previously obtained using classical have been redefined with help derivatives.

In this paper, we examine the image of geodesic curves Riemann 2-manifolds under isometric immersions, in three dimensional Euclidean space. We show that curvature these is equal to normal manifold direction tangent vector field geodesics. Moreover, prove if parameter are line curvature, then torsion geodesics curve.