We give an elementary proof of a theorem that characterizes quasisymmetric maps the unit circle in terms shear coordinates on Farey tesselation. The only uses normal family argument for and some hyperbolic geometry.

[1] The solar wind is filled with strong current sheets and sudden velocity shears; often the two are co-located. Sudden velocity shears at 1 AU are statistically analyzed using ACE measurements from 1998 to 2008. The occurrence rates of passage and the orientations of the shear planes are examined. For shear layers with vector velocity changes |Dv| > 50 km/s, an average of 12 pass the Earth pe...

We show that a rotation in three dimensions can be achieved by a composition of three shears, the rst and third along a speciied axis and the second along another given axis orthogonal to the rst; this process is invertible. The resulting rotation algorithm is practical for the processing of ne-grained digital images, and is well adapted to the access constraints of common storage media such as...

Abstract We use the shear construction to construct and classify a wide range of two-step solvable Lie groups admitting left-invariant SKT structure. reduce this specification data on Abelian algebras, which then is studied more deeply in different cases. obtain classifications structure results for $$\mathfrak {g}$$ g <...

PURPOSE Genitofemoral nerve injury is an underappreciated complication after laparoscopic varicocele ligation in teenage boys. We describe the incidence according to ligation instrument and the pattern of spontaneous symptom resolution. MATERIALS AND METHODS Patients who underwent laparoscopic varicocele ligation between 2004 and 2007 were retrospectively grouped by ligation modality (clippin...